Categories
Differential psychology/psychometrics Genetics / behavioral genetics Sociology

Thinking about intergenerational stability of socioeconomic status

I read the following interesting paper:

  • Braun, S. T., & Stuhler, J. (2016). The Transmission of Inequality Across Multiple Generations: Testing Recent Theories with Evidence from Germany. The Economic Journal, n/a-n/a. https://doi.org/10.1111/ecoj.12453

This paper shows that across multiple generations, the persistence of occupational and educational attainment in Germany is larger than estimates from two generations suggest. We consider two recent interpretations. First, we assess Gregory Clark’s hypotheses that the true rate of intergenerational persistence is higher than the observed rate, as high as 0.75, and time-invariant. Our evidence supports the first but not the other two hypotheses. Second, we test for independent effects of grandparents. We show that the coefficient on grandparent status is positive in a wide class of Markovian models, and present evidence against its causal interpretation.

For some reason, they don’t report their numeric results in the abstract, but they find that the ‘persistence’ is about .60. They call it the heritability, but that’s an error because they can’t actually differentiate between genetics and environmental causation. I take it that the authors are not familiar with behavioral genetics. It’s weird that economists who try to work this stuff out don’t read the behavioral genetics literature, but instead try to reinvent methods. But I digress.

The good thing about this paper is that they come close to modeling the situation as I would i.e. with latent variables. They write:

Two distinct theories have gained particular attention. Clark (2014) and Clark and Cummins (2014) argue that wealth, education or occupational status is transmitted via an underlying and unobserved latent factor. They suggest that the persistence of this underlying factor is not only very high–much higher than the persistence in observed outcomes between parents and children–but also steady across social systems and time. Mare (2011) points to a very different interpretation of multigenerational correlations. He argues that the previous literature suffers from a fundamental conceptual limitation in that it considers only the transmission between parents and children. Following his call to overcome this “two-generation paradigm”, a fast-growing literature examines the existence of independent causal effects from other family members, in particular grandparents.

As usual, economists are fond of presenting their ideas in hard to understand jargon. They present the model as:

To capture this idea in a simple way, suppose that the intergenerational transmission of observable outcome yi,t and unobservable endowment ei,t in a one-parent one-offspring family is governed by

yi,t = ρei,t + ui,t (2)

ei,t = λei,t-1 + vi,t (3)

where ui,t and vi,t are noise terms that are uncorrelated with other variables and past values. For simplicity, we normalise the variances of yi,t and ei,t to one, so that slope coefficients can be interpreted as correlations. In this “latent factor model”, the offspring inherits her unobserved endowment from the parent (according to the “heritability” coefficient λ), and the endowment then translates into the observed outcome (according to the “transferability” coefficient ρ). The observed correlation in outcome y between generation t and generation t – m equals then

b-m = Cov(yi,t,yi,t-m)

= ρ2Cov(ei,t,ei,t-m)

= ρ2λm (4)

The persistence of socio-economic status over generations thus decreases with both the persistence of the unobserved endowment, as captured by

λ = Cov(ei,t, ei,t-m),

and the transferability of the unobserved endowment into the observed outcome, as captured by ρ. Across multiple generations, however, persistence is predominantly governed by λ rather than ρ. This is because the latent factor ei,t is inherited m times across generations but only twice transformed into outcome yi,t.

Hard to make sense of? Actually, it’s simpler to understand if one draws a SEM and changes it to use 2 latent variables instead of 1:

genetic human capital model

Each colored box is one generation, so the figure has 3 generations: blue, green and red. Each box is some aspect of socioeconomic inequality whether it be education, income or whatever. They are the indicators in factor analytic terms. The 2 circles are the latent variables. The first is genetic human capital, GHC, which is some mix of cognitive ability, work ethic, interests, preferences, personality but probably mostly the first. This is the part that parents actually transmit to their children. As people grow up and find their spot in society, they attain some socioeconomic outcomes which are correlated, and if we factor analyze them, we get the S factor I’ve been talking so much about. S is a formative factor, meaning that it doesn’t cause stuff; it’s basically an optimally weighted index of one’s relative social status. It has exactly the same indicators and loadings as the actual cause, GHC, and so the relative standing is exactly the same on these constructs if one can measure them without error.

Now we are able to easily explain traditional studies of intergenerational stability. They pick a single box, an indicator of S, and then correlate it between parents and children (average of parents and children if possible). This underestimates the actual stability because these single measures of S do not have factor loadings of 1.00. The actual realized stability is given by causal paths between each generation’s S scores. Grandparents only transmit genes to their grandchildren thru their own children, so there is no causal path from generation blue GHC to generation red GHC, but one can of course correlate them, shown by the dotted line between generation blue’s S and generation red’s S.

In their terms, they call the arrows between GHC for the heritability (that’s also technically correct in my model) and they call the factor loadings for the transferability.

To estimate the GHC path(s), one then has to gather a diverse set of socioeconomic indicators for each person, factor analyze them, and correlate the S scores across generations. Usually, it is hard to get this kind of data, so researchers only rely on single variables instead. One can do this, but then one has to correct for the measurement error i.e. the degree to which factor loadings are smaller than 1. What are the S factor loadings typically? Here’s some Argentine results:

S_method

There are two values because we used two different methods, neither of which is perfect. Pearson is based on the Pearson correlations between indicators, which are adjusted for survey year and sex. Latent does not adjust for anything but it is based on the latent correlations between indicators instead of the Pearson correlations. One cannot do both, or at least I don’t know how to calculate latent correlations with controls. Maybe one can do a logistic correlation and then convert the beta to a correlation-type metric in some way.

Whatever the case, we see that the S factor loadings are not quite close to 1. Family income is about .6 and education is about .5 (note that the first is based on 2 persons’ data, the second only on 1 person’s data). So that’s quite a bit of measurement error. To estimate S paths, one has to work backwards. If we observe intergenerational stability of education of r = .20 (1 parent to 1 child), and the loadings are .50, then the GHC must be .20 * 2 * 2 = .80, i.e. a heritability of 80%.

The model makes a lot of assumptions. One is that there are no environmental effects from parents to their children. Is this tenable? There is a meta-analysis of MZT-DZT twin studies for educational attainment. They find H ≈ 40%, C = 35%. C includes any parental effects and it is quite substantial (35% -> r = .59). However, MZT-DZT twin studies overestimate C when assortative mating is present, and assortative mating is very strong for S. Another two studies found small C for neighborhood deprivation and high H (65% in Sweden, 71% in Scotland). The Swedish study also had a twin sample which produced H = 41% and C = 26%. I can think of two interpretations. First, the twin study result is just a fluke. The confidence interval for C is in fact 5% to 47%. This does not fit with the meta-analysis results however. Second, the difference between twin and sibling models is due to the strong assortative mating which inflates C for the twin model, but does not for the sibling model (I think). In discussing with Amir (first author of Swedish study), he noted that the twins were also younger (24-25) than the siblings (31-35) which may affect results. Parents sometimes provide housing for persons in their 20s, but rarely in their 30s.

I don’t know any study that actually modeled assortative mating for S as a latent variable, but one can do a crude job at it with the PING data which only has 2 variables for each parent (also has household income which is based on 2 persons and which I ignored). I imputed the missing values which inflated the correlations somewhat (because persons with 1 datapoint get that value for all their variables thus moving correlations towards 1). However, not imputing the values biases the estimate downwards because lower S people are more likely to avoid reporting their income, education etc., so excluding these cases results in reduction of variance and hence observed correlations. If we use the imputed values, the parental S correlation looks like this:

S_assortative_mating

We can see that the measure of S is problematic because there is a ceiling effect at S ≈ 1.25. These are the cases where both parents had the maximum educational and occupation level.

Another assumption is that there is no outcome heritability for the indicators i.e. no heritable group factors for S indicators. In other words, after we can S into account, there will not be any correlations between e.g. educational levels between generations. This is problematic not entirely true, but maybe mostly true. One can modify the model to include paths from the indicators across generations.

In reality land the correlations between GHC and S will not be 1.00 because chance events probably have some effect on the attained S (according to Woody Allen at least). For instance, which education and hence career paths people choose often depend on uncertain/semi-random choices made while young. This would generally bias the observed S~~S relationships downwards. If one relies on aggregate data (e.g. surnames), as Clark does, then it will not be a problem. Clark’s approach will be unbiased if the assumption about no heritable group factors holds.

Related to the above is historically when women did not work outside the home or get educated means that for old data, female S is mostly just a function of their spouse’s S, and thus does not represent their own GHC so strongly as it could.

Grandparent effects, correlations between children’s and grandparents’ S (correlation between blue and red S) will be seen to the extent that there is measurement error in S. Thus, if we are able to form a number of different S’s that can be ranked in quality, the prediction is that the better S estimates will slow smaller grandparent effects than the worse estimates. It’s another instance of controlling for confounding variables is harder than you think.

Clark’s claim about the invariance of the heritability is simply the claim that all the GHC paths will be equal. This can be formally tested in SEM. An implication of this model together with Clark’s assumption of constant heritability is that cross-national or cross-temporal variation seen in correlations between single indicators simply reflect differential S factor loadings for these datasets. This can result from change in the distribution of education which influences the Pearson correlations/OLS estimates.

An interesting prediction can be made from the model: there will be stronger intergenerational relationships for the indicators that have stronger S loadings. I also conjecture that the assortative mating correlations will mirror the S loadings.

Another prediction is that if one has data for 3 generations, and one can identify chance events in generation 2 (green), then these will explain differences between generation 1 and 3 (blue and red). This is because children do not inherit the chance events from their parents and their S will be closer to their GHC. For instance, if there are high S grandparents/blues and low S parents/greens due to some chance event, the children’s/reds’ S will be higher than their parents’ and closer to their grandparents’. Such a chance event could be an infectious disease or a car accident that left the parents crippled and reduced their S.

See also:

  • https://westhunt.wordpress.com/2014/03/23/the-son-also-rises/
  • https://westhunt.wordpress.com/2014/03/24/simple-mobility-models/
  • https://westhunt.wordpress.com/2014/03/29/simple-mobility-models-ii/
  • https://jaymans.wordpress.com/2014/03/31/the-son-becomes-the-father/
Categories
Differential psychology/psychometrics Sociology

Data sharing and Add Health

I am doing an S factor study of US counties in the usual way. For that reason, I need some kind of county-level cognitive ability estimate. I know that this is possible to create using the Add Health database, but that the data are not sharable. However, it may be possible to do some tricks, so I wrote to their support to get things clarified.

Emil:

Dear Add Health,
I could not find an answer to this question anywhere. Suppose I or someone else has calculated an aggregate value (usually a mean) for each county in the US. Would it be against the Add Health data rules to release this non-personal data to other researchers?

Add Health:

Emil,

Thank you for contacting Add Health about this issue.  The following guidelines listed in the contract must be followed when publishing information about Add Health.

To avoid inadvertent disclosure of persons, families, or households by using the following guidelines in the release of statistics derived from the Data     Files.

  1. In no table should all cases in any row or column be found in a single cell.
  2. In no case should the total for a row or column of a cross-tabulation be fewer than three (3).
  3. In no case should a cell frequency of a cross-tabulation be fewer than three (3) cases.
  4. In no case should a quantity figure be based on fewer than three (3) cases.
  5. Data released should never permit disclosure when used in combination with other known data.

Since the mean for a county is likely to be unique you would not be able to satisfy the above conditions.  Also, the data may allow users to identify the county by comparing it with the source data.  Therefore, you would not be able to release the aggregate information.

I hope this is helpful.

Best,

Joyce Tabor

Add Health Data Manager

Emil:

Hi Joyce,
How about adding a random number to the county means and excluding the counties with few cases? In this way, one cannot derive the scores of the individuals in the counties. Alternatively, how about binning the data by rounding the mean score to the nearest e.g. 5 (on a scale with a mean of 100 and SD of 15). This would make the means non-unique.

Add Health:

Emil,

Please provide more details about what you would like to do to help me better understand your project.  For example, who do you want to make these data available to?  What measures do you want to create at the county level?  Would your data be linkable to Add Health data?  If so, how would they link?

Best,

Joyce

Emil:

Joyce,

Thank you for your reply. Let me clarify matters. I did not do a study using Add Health data. However, some other researchers published a few studies using Add Health data. The studies in question are:

  1. http://www.sciencedirect.com/science/article/pii/S0160289610001340
  2. http://www.sciencedirect.com/science/article/pii/S0160289612001201
  3. http://www.sciencedirect.com/science/article/pii/S019188691300189X

They used the Add Health data to calculate an average IQ score for each county with data and then correlated this with other variables. I am unable to gain access to the Add Health data myself, but I work in the same field and would like the IQ scores for my own analyses. I asked the authors to send me the numbers, but they refused on account on the Add Health data sharing rules. However, it is my thinking that the privacy rules of Add Health are there to protect individuals from being deanonymized and so it should be possible to release aggregate-level county data without risking deanonymization. Hence, I wrote to you to investigate whether it would be possible to release the aggregate-level data so that other researchers can use it (open data).

As far as I understand, you had some concerns about this because this world produce unique values by county. I’m not sure I understand why that is a problem, but my proposals to remedy this problem were to either to 1) add a little random noise to the variable, thus obscuring the true values, or 2) bin the datapoints into nearest e.g. 2 or 5 point score (so e.g. 113.1434 gets turned into 115). Both of these obscure the original data but do not cause serious statistical degradation of the data. The methods can also be combined.

I am not interested in the individual-level data for this analysis, so I’m not sure what you mean by making the data linkable to the Add Health data. To make it perfectly clear, I would like for it to be possible to release the mean IQ scores by county with the county names, so that they can be merged with other datasets (e.g. Measure of America’s) for analytic purposes. If it is not possible to release the real means, then it is my hope that we can release the means with some added noise or binning as described above.

Add Health:

Emil,

The researchers are correct that they cannot provide you with data that they constructed using Add Health.  Only Add Health can release and share data based on Add Health.  Add Health never releases geographic identifiers smaller than Census region, therefore, county level data are not available.  The researchers you cite only have access to pseudo county level codes.  They do not have the data you want and Add Health will not release any data by location.

Best,

Joyce

So, the Add Health data sharing rules are extremely strict making the dataset much less useful. Some other way to estimate county-level IQ must be found.

Categories
Sociology

The performance of immigrants from Yugoslavia in Denmark and Norway

This is actually an older post, but by accident I posted it on the Danish language sister blog.

I don’t know what study that is, however, I do have numbers for the performance of Yugoslavians in Denmark and Norway. There are both numbers for persons from Yugoslavia when that was one legal entity (actually multiple different with the same name) as well as for some of the constituent countries.

First a brief review. Many studies have looked at immigrant performance by macro-origin and recently country of origin. The country of origin studies are more useful because immigrants from e.g. “Asia” (which may or may not include the Muslim countries such as Afghanistan) are not very homogeneous. Cambodians and Chinese are different, but both are East Asians. Afghans are very different, but are sometimes included in the category. Mixing these together in a hodgepodge makes for uninterpretable results, especially when who is included changes over time and from study to study. For instance, whether a country is considered Western may depend on EU membership, which means that lots of non-Western became Western recently.

Because I was unsatisfied with the existing macro-origin studies for Denmark (most only found in Danish, but I guess I should do an English-language review some day) I began carrying out a series of such immigrants by country of origin studies with the underlying goal being to test the spatial transferability hypothesis (Fuerst’s name), which is that 1) when people move, they generally retain their mean levels of psychological traits, 2) and as a consequence, the effects of these traits follow them as well. Selective immigration and emigration makes this more difficult to test.

The two best such studies cover Denmark and Norway. They are the best because they include a large number of countries of origin and have data for many socioeconomic outcome variables. In brief, the S factors were extracted from available information regarding. income, educational attainment, crime, employment and use of social benefits. See the original papers for details (e.g. with regards to imputation).

The correlation between the S scores from DK and NO is .78 [CI .64 to .86], N=55. N’s by country are 70 and 67, DK and NO respectively. The table below shows all the data.

Abbrev. Country S in DK S in NO
AFG Afghanistan -1.38 -1.09
ARG Argentina 0.75
AUS Australia 1.131 1.03
AUT Austria 0.947 1.02
BDI Burundi -0.54
BEL Belgium 1.089 1.16
BGR Bulgaria 0.811 0.17
BIH Bosnia and Herzegovina -0.913 0.49
BRA Brazil 0.457 -0.34
CAN Canada 1.145 1.03
CHE Switzerland 1.119 1.13
CHL Chile 0.279 0.25
CHN China 0.627 0.61
COG Congo Rep. -1.07
COL Colombia 0.26
CZE Czech Republic 0.249 0.43
DEU Germany 0.846 1.04
DNK Denmark 1
DZA Algeria -0.775 -1.52
EGY Egypt Arab Rep. -0.241
ERI Eritrea -0.43
ESP Spain 0.788 0.52
EST Estonia 0.717 0.19
ETH Ethiopia -0.586 -0.16
FIN Finland 0.891 0.78
FRA France 1.098 0.97
GBR United Kingdom 0.848 1.14
GHA Ghana 0.162 0.03
GMB Gambia The -0.84
GRC Greece 0.613 0.61
HRV Croatia -0.12 0.54
HUN Hungary 0.837 0.45
IDN Indonesia 0.126 0.33
IND India 0.528 0.63
IRL Ireland 0.876
IRN Iran Islamic Rep. -0.688 -0.35
IRQ Iraq -1.654 -2.26
ISL Iceland 0.555 0.76
ISR Israel -0.061
ITA Italy 0.775 0.86
JOR Jordan -1.191
JPN Japan 1.018
KEN Kenya 0.088 -0.24
KSV Kosovo -0.43
KWT Kuwait -2.619
LBN Lebanon -2.027 -1.03
LKA Sri Lanka -0.749 -0.14
LTU Lithuania 0.897 -0.08
LVA Latvia 0.685 0.06
MAR Morocco -1.031 -0.63
MKD Macedonia FYR -0.439 -0.19
MMR Myanmar -1.812 -0.27
NGA Nigeria 0.336 -0.53
NLD Netherlands 1.118 1.11
NOR Norway 0.842
NPL Nepal 0.75
PAK Pakistan -0.679 -0.87
PER Peru 0.1
PHL Philippines 0.362 0.58
POL Poland 0.463 -0.02
PRT Portugal 0.631 0.54
PSE West Bank and Gaza -3.8
ROU Romania 0.703 0.31
RUS Russian Federation 0.447 -0.44
SDN Sudan -1.52
SOM Somalia -2.054 -3.06
SRB Serbia -1.931 0.46
SUN USSR 0.166
SVK Slovak Republic 0.42
SWE Sweden 0.766 1.03
SYR Syrian Arab Republic -1.997 -1.62
THA Thailand -0.233 -0.03
TUN Tunisia -0.825
TUR Turkey -1.42 -0.52
TZA Tanzania -0.254
UGA Uganda -0.341
UKR Ukraine 0.686 0.34
USA United States 1.259 0.97
VNM Vietnam -0.582 -0.11
YU2 Former Yugoslavia2 (Found in some Danish sources) -1.611
YUG Former Yugoslavia -1.247
ZAF South Africa 0.731

 

I have marked the Yugoslavian countries in italics above. The table below shows the Yugoslavian subset table:

Abbrev. Country S in DK S in NO
BIH Bosnia and Herzegovina -0.913 0.49
YUG Former Yugoslavia -1.247
YU2 Former Yugoslavia2 (Found in some Danish sources) -1.611
KSV Kosovo -0.43
MKD Macedonia FYR -0.439 -0.19
SRB Serbia -1.931 0.46

 

In both countries, the immigrants don’t perform well Well here means around native levels which is around +1. The natives are not found in the tables above because they are not immigrants. They perform worse in Denmark, in some cases by no small amount, which is somewhat puzzling. An S difference of 2.4 is case of Serbia is much larger than would be expected by sampling error (1.4 for BIH). Maybe differential selection. Looks like Denmark received more refugees than Norway despite similar population size, consistent with lower selection threshold for DK.

Studies

Crime, income, educational attainment and employment among immigrant groups in Norway and Finland

Educational attainment, income, use of social benefits, crime rate and the general socioeconomic factor among 71 immigrant groups in Denmark.

Categories
Differential psychology/psychometrics Sociology

Comments on Noah Carl’s new study: IQ and socio-economic development across local authorities of the UK

Paper is on Scihub.

There are a few researchers engaged in the cognitive sociology adventure. Aside from myself and John Fuerst, Noah Carl has also taken up the task. There is of course also Richard Lynn, the grand old man of these studies (publishing his first in 1979). Mostly the job of doing these analyses involves searching around to find a suitable dataset. Usually, one has to combine multiple resources. Noah has done exactly that.

Being British it is not surprising that Noah’s new study is also on the UK, like his previous study. The abstract reads:

Cross-regional correlations between average IQ and socio-economic development have been reported for many different countries. This paper analyses data on average IQ and a range of socio-economic variables at the local authority level in the UK. Local authorities are administrative bodies in local government; there are over 400 in the UK, and they contain anywhere from tens of thousands to more than a million people. The paper finds that local authority IQ is positively related to indicators of health, socio-economic status and tertiary industrial activity; and is negatively related to indicators of disability, unemployment and single parenthood. A general socioeconomic factor is correlated with local authority IQ at r = .56. This correlation increases to r = .65 when correcting for measurement error in the estimates of IQ.

In general, results are in line with the by now many previous studies: sizable correlations between group-level cognitive ability and group-level S indicators, and the existence of a clear S factor (16 of 16 loadings were in the expected direction; 15 correlated with cognitive ability in the expected direction). At a personal level, I am happy to be cited in the journal because it sends some attention towards the work published in the OpenPsych journals, including the new sociology & polit. sci. journal. Noah cites the London boroughs study, of which he was a reviewer.

Some things I am happy about:

  • He compiled a dataset of 16 S indicators.
  • He reported on the S factor.
  • He did some light multi-level analysis (reporting the variance associated with the regions and countries, which was small).
  • He used weighted analyses (square root of population, as we have also done before, but other weights could be used too).
  • He had access to 6 cognitive measures and used factor analysis to get a general factor.

Some critical comments:

  • The S factor loadings were not reported. Neither were the g loadings.
  • The scatterplot could have been better. For instance, one could have color boded the points by their region (helpful to spot regional effects) and mapped sample size to point size (like we did in the Admixture paper coming out in MQ sometimes soonish). Naming the outlier points could have been useful. I’m sure many readers wonder about the unit with an IQ of 110 and an S score of -1, or the unit with 90 IQ and an S score of 0. And what is that unit in the top right with 112 IQ and S of 2.5?
  • He did not use Jensen’s method to see if IQ is more strongly related to the indicators with stronger loadings, as one would expect. Because he does not report the loadings at all, no one else can do this. One could also use it on the cognitive measures, even if there are only 6 indicators. It is worth doing, like in the study of Indian states. It could be fed into a meta-analysis at some future point.
  • Related to the above, I did not see a mention of where one can find the data or analysis code. Is it public or hidden? I will ask. Not necessary:
    • “Next, average IQ was calculated for each of the 404 local authorities represented in the dataset. It is important to note that information on local authorities was obtained from the UK Data Service via a Special Licence. Therefore making these data available to other researchers is not possible. Information on local authorities are not included in the main Understanding Society dataset due to the fact that some local authorities contain relatively few respondents, which could permit identification of specific individuals.”
    • However, summary level information should be sufficient and the S data should still publishable. Noah is looking into it.
  • I’d like to see more multi-level analyses, e.g. like those done in my analysis of the religious general factor among Muslims. If one analyses the authorities in each region, are the S factor loadings the same as when analyzed at the national level? They need not be and differences could be revealing.
  • No demographic analyses. For some indicators, one would expect age to be a confound. One should at least try regressing it out if one can find mean age. Noah tells me it wasn’t (he did not report that in the paper I think).
    Noah didn’t do any correlations with SIRE (self-identified race/ethnicity). Perhaps he couldn’t find any data. Perhaps he did not want to be labelled a racist, only a classist. Perhaps one could find country of origin data for the units to try a compositional analysis like in this paper.

All in all, this study confirmed what has been found elsewhere. The findings in this field are very reproducible. There is still the odd case of Japan to wonder about, where results only are in line after ad hoc adjustment for population density, but that’s the only strange result I’ve come across. Well, that as Chile (the analysis of which will also be reported in more detail in the upcoming issue of Mankind Quarterly.)

Categories
Differential psychology/psychometrics Sociology

General model for immigrant group traits and outcomes

(Broad-strokes modeling of how to think about immigrant performance. Some references are gone because they were written using the Zotero plugin, which I later uninstalled. I have re-added those I could recall.)

Consider the model below:

General model for immigrant group traits and outcomes

Something much like this has been my intuitive working model for thinking about immigrant groups’ traits and socioeconomic outcomes. I will explain the model in this post and refer back to it or use the material in some upcoming paper (nothing planned).

The model shows the home country/a country of origin and two destination countries. The model is not limited to just two destination countries, but I did not draw more to avoid making the model larger. It can be worth using more in some cases which will be explained below.

Familial traits (or intergenerational) are those traits that run in families. This term includes both genetic and shared environmental effects. Because most children grow up with their parents (I assume), it does not matter whether the parents traits→children traits route is genetic or environmental. This means that both psychological traits (mostly genetic) and culturally traits (mostly shared environmental) such as specific religion are included.

When persons leave (emigrate) their home country, there is some selection: people who decide to leave are not random. Sometimes, it is not easy to leave because the government actively tries to restrict its citizens from leaving. This is shown in the model as the Emigration selection→Emigrant group familial traits link. Emigration selection seems to be mostly positive in the real world: the better off and smarter emigrate more than the poorer and less bright.

When the immigrants then move to other countries, there is Immigration selection because the destination countries usually don’t just allow whoever to move in if they want to. Immigration selection can have both positive and negative effects. Countries that receive refugees but try not to receive others have negative selection, while those that try to only pick the best potential immigrants have positive selection. Often countries have elements of both. Immigration selection and Emigrant group familial traits jointly lead to Immigrant group familial traits in a particular destination country.

Note that immigrant selection is unique for each destination country, but can be similar for some countries. This would show up at correlated immigration selection scores. There is also immigration selection that doesn’t happen in the destination country, namely selection that happens due to geographical distance. For this reason I placed the Immigration selection node half in the destination country boxes. With a more complex model, one could split these if desired.

Worse, it is possible that immigration selection in a given country depends on the origin country, i.e. a country-country interaction selection. This wasn’t included in the above model. Examples of this are easy to find. For instance, within the EU (well, it’s complicated), there is relatively free movement of EU citizens, but not so for persons coming in from outside the EU.

Socioeconomic outcomes: Human capital model + luck

The S factor score of the home country (the general factor of socioeconomic outcomes, which one can think of as roughly equal to the Human Development Index just broader is modeled as being the outcome of the Population familial traits and Environmental and historical luck. I think it is mostly the former. Perhaps the most obvious example of environmental luck is having valuable natural resources in your borders, today especially oil. But note that even this is somewhat complicated because borders can change by use of ‘bigger army diplomacy’ or by simply purchasing more land, so one could strategically buy or otherwise acquire land that has valuable resources on it, making it not a strict environmental effect.

Other things could be having access to water, sunlight, wind, earthquakes, mountains, large bodies of inland water & rivers, active underground, arable land, living close to peaceful (or not so much) neighbors and so on. These things can promote or retard economic development. Having suitable rivers means that one can get cheap and safe (well, mostly) energy from those. Countries without such resources have to look elsewhere which may cost more. They are not always strictly environmental, but some amount of their variance is more or less randomly distributed to countries. Some are more lucky than others.

There are some who argue that countries that were colonized are better off now because of it, so that would count as historical luck. However, being colonized is not just an environmental effect because it means that foreign powers were able to defeat your forces overwhelmingly for decades. If they were able to, you probably had a poor military which is linked to general technological development. There is some environmental component to whether you have a history of communism, but it seems to still have negative effects on economic growth decades after.

For immigrant groups inside a host country, however, the environmental effects with country-wide effects cannot account for differences. These are thus due to familial effects only (by a good approximation). To be sure, the other people living in the destination/host country, Other group familial traits, probably have some effect on the Immigrant familial traits as well, such as religion and language. These familial traits and the Other group S then jointly cause the Immigrant group S. This is the effect that Open Borders advocates often talk about one aspect of:

Wage differences are a revealing metric of border discrimination. When a worker from a poorer country moves to a richer one, her wages might double, triple, or rise even tenfold. These extreme wage differences reflect restrictions as stifling as the laws that separated white and black South Africans at the height of Apartheid. Geographical differences in wages also signal opportunity—for financially empowering the migrants, of course, but also for increasing total world output. On the other side of discrimination lies untapped potential. Economists have estimated that a world of open borders would double world GDP.

Paths estimated in studies

A path model is always complete which means that all causal routes are explicitly specified. All the remaining links are non-causal, but nodes can be substantially correlated. For instance, there is no link between the home country Country S and immigrant group S but these are strongly correlated in practice. I previously reported correlations between home Country S and Immigrant group S of .54 and .72 for Denmark and Norway.

There is no link between home country Population familial traits and Immigrant group familial traits, but there is only one link in between (Emigrant group familial traits), so seems reasonable to try to correlate these two nodes. A few studies have looked at these type of correlations. For instance, John Fuerst have looked at GRE/GMAT scores and the like for immigrant groups in the US. This is taken as a proxy for cognitive ability, probably the most important component of the psychological traits part of familial traits. In that paper, Fuerst found correlations of .78 and .81 between these and country cognitive ability using Lynn and Vanhanen’s dataset.

Rindermann and Thompson have reported correlations between cognitive ability (component of Immigrant group familial traits) and native population cognitive ability (component of Other group familial traits).

Most of my studies have looked at the nodes Population familial traits (sub-components Islam belief and cognitive ability) and Immigrant group S (or sub-components like crime if S was not available). Often this results in large correlations: .54 and .59 for Denmark and Norway (depending on how to deal with missing data, use of weighted correlations etc.). Note that in the model the first does cause the second, but there are a few intermediate steps and other variables, especially Emigrant selection (differs by country of origin which reduces the correlation) and Immigrant selection (which has no effect on the correlation).

There is much to be done. If one could obtain estimates of multiple nodes in a causal chain, one could use mediation analysis to see if mediation is plausible. E.g. right we we have Immigrant group S for two countries, cognitive ability for 100s of countries of origin, so if we could obtain immigrant group cognitive ability, one could test the mediation role of the last. With the current data, one can also check whether country of origin cognitive ability mediates the relationship between immigrant group S and country of origin S, which it should partly, according to the model. I say partly because the mediation is only to the extend that familial cognitive ability is a cause.

Categories
Science Sociology

Researcher degrees of freedom as sensitivity analysis

https://en.wikipedia.org/wiki/Sensitivity_analysis

Researcher degrees of freedom refer to the choices researchers make when conducting a study. There are many choices to be made, where to collect data, which variables to include, etc. However, a large subset of the choices concern only the question of how to analyze the data. Still I have now done 100s of analyses rigorous enough to publish, I know exactly what this means. I will give some examples from a work in progress.

1. Which variables to use?

The dataset I began with contains 75 columns. Some of these are names and the like, but many of them are socioeconomic variables in a broad sense. Which should be used? I picked some by judgment call with prior S studies, but I left out e.g. population density, mean age, pct. of population <16/working/old age. Should these have been included? Maybe.

2. What to do with City of London?

In the study, I examine the S factor among London boroughs. There are 32 boroughs and the City of London. The CoL is fairly small which can be rise to sampling error and effects related to being a very peculiar administrative division.

Furthermore, many variables in the dataset lack data for CoL. So I was faced with the question of what to do with it. Some options: 1) Exclude it. 2) Use only the variables for which there is data for CoL, 3) use more variables than has data for CoL and impute the rest. I chose (1), but one might have gone with either of the three.

3. The extra crime data

I found another dataset with crime counts. I calculated per capita versions of these. There are two level of types of crime: broad and detailed. Which should be used? One could also have factor analyzed the data and used the general factor scores. Or calculated a unit-weighted score (standardized all variables, then score cases by average of each variable). I used detailed variables.

4. The extra GCSE data

I found another dataset with GCSE measures. These exist for both genders together and for each gender alone. There are 9 different variables to choose from. Which should be used? Same options as before too: factor scores or unit-weighted average. I selected one for theoretical reasons (similarity to other scholastic variables e.g. PISA) and because Jensen’s method supported this choice.

5. How to deal with missing data

Before factor analyzing the data, one has the question of how to deal with missing data. Aside from CoL, a few other cases had some missing data. Some options: 1) exclude them, 2) impute them with means, 2) impute with best guess (various ways!). Which should be done? I used imputation with multiple regression method, one could have used e.g. k nearest means imputation instead.

6. How to deal with highly correlated variables

Sometimes including variables that correlate very strongly or even perfectly can seriously throw off the factor analysis results because they color the general factor. If extracted multiple factors, they will form their own factor. What should be done with these? 1) Nothing, 2) exclude based on a threshold value of max allowed intercorrelation. If (2), which value should be used? I used |.9|, but |.8| is about equally plausible.

7. How to deal with highly mixed cases

Sometimes some cases just don’t fit the factor structure of the data very well. They are structural outliers or mixed. What should be done with them? 1) Nothing, 2) Use rank-order data, 3) Use robust regression (many methods), 4) Change outlier values (e.g. any value >|3| sd gets reduced to 3 sd., 5) exclude them. If (5), which thresholds should we use for exclusion cutoff? [no answers forthcoming]. I chose to do (1), (2) and (5) and only excluded the most mixed case (Westminster).

Researcher choices as parameters

I made many more decisions than the ones mentioned above, but they are the most important ones (i think, so maybe!). Normally, research papers don’t mention these kind of choices. Sometimes they mention them, but doesn’t report results by different choices. I suspect a lot of this is due to the hassle of actually doing all the combinations.

However, the hassle is potentially much smaller if one had a general framework for doing it with programming tools. So I propose that as general, one should consider these kind of choices as parameters and calculate results for all of them. In the above, this means e.g. results with and without CoL, different variable exclusion thresholds, different choices with regards to mixed cases.

Theoretically, one could think of it as a hyperspace where every dimension is a choice for one of these options. Then one could examine the distribution of results over all parameter values to examine the robustness of the results re. analytic choices.

I have already been doing this for the choice of dealing with mixed cases, but perhaps I should ramp it up and do it more thoroly for other choices too. In this case, the threshold for exclusion of variables and which set of crime variables to use are important choices.

Categories
Sociology

How to do an S factor analysis

John Fuerst suggested that I write a meta-analysis, review and methodology paper on the S factor. That seems like a decent idea once I get some more studies done (data are known to exist on France (another level), Japan (analysis done, writing pending), Denmark, Sweden and Turkey (reanalysis of Lynn’s data done, but there is much more data).

However, before doing that it seems okay to post my check list here in case someone else is planning on doing a study.

A methodology paper is perhaps not too bad an idea. Here’s a quick check list of what I usually do:
  1. Find some country for which there exist administrative divisions that number preferably at least 10 and as many as possible.
  2. Find cognitive data for these divisions. Usually this is only available for fairly large divisions, like states but may sometimes be available for smaller divisions. One can sometimes find real IQ test data, but usually one will have to rely on scholastic ability tests such as PISA. Often one will have to use a regional or national variant of this.
  3. Find socioeconomic outcome data for these divisions. This can usually be found at some kind of official statistics bureau’s website. These websites often have English language editions for non-English speaker countries. Sometimes they don’t and one has to rely on clever use of guessing and Google Translate. If the country has a diverse ethnoracial demographic, obtain data for this as well. If possible, try to obtain data for multiple levels of administrative divisions and time periods so one can see changes over levels or time. Sometimes data will be available for a variety of years, so one can do a longitudinal study. Other times one will have to average all the years for each variable.
  4. If there are lots of variables to choose from, then choose a diverse mix of variables. Avoid variables that are overly dependent on local natural environment, such as the presence of a large body of water.
  5. Use the redundancy algorithm to remove the most redundant variables. I usually use a threshold of |.90|, such that if a pair of variables in the dataset correlate >= that level, then remove one of them. One can also average them if they are e.g. gendered versions, such as life expectancy or mean income by gender.
  6. Use the mixedness algorithms to detect if any cases are structural outliers, i.e. that they don’t fit the factor structure of the remaining cases. Create parallel datasets without the problematic cases.
  7. Factor analyze the dataset with outliers with ordinary factor analysis (FA), rank order and robust FA. Use ordinary FA on the dataset without the structural outliers. Plot all the FA loading sets using the loadings plotter function. Make note of variables that change their loadings between analyses, and variables that load in unexpected ways.
  8. Extract the S factors and examine their relationship to the ethnoracial variables and cognitive scores.
  9. If the country has seen substantial immigration over the recent decades, it may be a good idea to regress out the effect of this demographic and examine the loadings.
  10. Write up the results. Use lots of loading plots and scatter plots with names.
  11. After you have written a draft, contact natives to get their opinion. Maybe you missed something important about the country. People who speak the local language are also useful when gathering data, but generally, you will have to do things yourself.

 

If I missed something, let me know.
Categories
Differential psychology/psychometrics intelligence / IQ / cognitive ability Sociology

The performance of African immigrants in Europe: Some Danish and Norwegian data

Due to lengthy discussion over at Unz concerning the good performance of some African groups in the UK, it seems worth it to review the Danish and Norwegian results. Basically, some African groups perform better on some measures than native British. The author is basically arguing that this disproves global hereditarianism. I think not.

The over-performance relative to home country IQ of some African countries is not restricted to the UK. In my studies of immigrants in Denmark and Norway, I found the same thing. It is very clear that there are strong selection effects for some countries, but not others, and that this is a large part of the reason why the home country IQ x performance in host country are not higher. If the selection effect was constant across countries, it would not affect the correlations. But because it differs between countries, it essentially creates noise in the correlations.

Two plots:

NO_S_IQ DK_S_IQ

The codes are ISO-3 codes. SO e.g. NGA is Nigeria, GHA is Ghana, KEN = Kenya and so on. They perform fairly well compared to their home country IQ, both in Norway and Denmark. But Somalia does not and the performance of several MENAP immigrants is abysmal.

The scores on the Y axis are S factor scores for their performance in these countries. They are general factors extracted from measures of income, educational attainment, use of social benefits, crime and the like. The S scores correlate .77 between the countries. For details, see the papers concerning the data:

  • Kirkegaard, E. O. W. (2014). Crime, income, educational attainment and employment among immigrant groups in Norway and Finland. Open Differential Psychology. Retrieved from http://openpsych.net/ODP/2014/10/crime-income-educational-attainment-and-employment-among-immigrant-groups-in-norway-and-finland/
  • Kirkegaard, E. O. W., & Fuerst, J. (2014). Educational attainment, income, use of social benefits, crime rate and the general socioeconomic factor among 70 immigrant groups in Denmark. Open Differential Psychology. Retrieved from http://openpsych.net/ODP/2014/05/educational-attainment-income-use-of-social-benefits-crime-rate-and-the-general-socioeconomic-factor-among-71-immmigrant-groups-in-denmark/

I did not use the scores from the papers, I redid the analysis. The code is posted below for those curious. The kirkegaard package is my personal package. It is on github. The megadataset file is on OSF.


 

library(pacman)
p_load(kirkegaard, ggplot2)

M = read_mega("Megadataset_v2.0e.csv")

DK = M[111:135] #fetch danish data
DK = DK[miss_case(DK) <= 4, ] #keep cases with 4 or fewer missing
DK = irmi(DK, noise = F) #impute the missing
DK.S = fa(DK) #factor analyze
DK_S_scores = data.frame(DK.S = as.vector(DK.S$scores) * -1) #save scores, reversed
rownames(DK_S_scores) = rownames(DK) #add rownames

M = merge_datasets(M, DK_S_scores, 1) #merge to mega

#plot
ggplot(M, aes(LV2012estimatedIQ, DK.S)) + 
  geom_point() +
  geom_text(aes(label = rownames(M)), vjust = 1, alpha = .7) +
  geom_smooth(method = "lm", se = F)
ggsave("DK_S_IQ.png")


# Norway ------------------------------------------------------------------

NO_work = cbind(M["Norway.OutOfWork.2010Q2.men"], #for work data
                M["Norway.OutOfWork.2011Q2.men"],
                M["Norway.OutOfWork.2012Q2.men"],
                M["Norway.OutOfWork.2013Q2.men"],
                M["Norway.OutOfWork.2014Q2.men"],
                M["Norway.OutOfWork.2010Q2.women"],
                M["Norway.OutOfWork.2011Q2.women"],
                M["Norway.OutOfWork.2012Q2.women"],
                M["Norway.OutOfWork.2013Q2.women"],
                M["Norway.OutOfWork.2014Q2.women"])

NO_income = cbind(M["Norway.Income.index.2009"], #for income data
                  M["Norway.Income.index.2010"],
                  M["Norway.Income.index.2011"],
                  M["Norway.Income.index.2012"])

#make DF
NO = cbind(M["NorwayViolentCrimeAdjustedOddsRatioSkardhamar2014"],
           M["NorwayLarcenyAdjustedOddsRatioSkardhamar2014"],
           M["Norway.tertiary.edu.att.bigsamples.2013"])


#get 5 year means
NO["OutOfWork.2010to2014.men"] = apply(NO_work[1:5],1,mean,na.rm=T) #get means, ignore missing
NO["OutOfWork.2010to2014.women"] = apply(NO_work[6:10],1,mean,na.rm=T) #get means, ignore missing

#get means for income and add to DF
NO["Income.index.2009to2012"] = apply(NO_income,1,mean,na.rm=T) #get means, ignore missing

plot_miss(NO) #view is data missing?

NO = NO[miss_case(NO) <= 3, ] #keep those with 3 datapoints or fewer missing
NO = irmi(NO, noise = F) #impute the missing

NO_S = fa(NO) #factor analyze
NO_S_scores = data.frame(NO_S = as.vector(NO_S$scores) * -1) #save scores, reverse
rownames(NO_S_scores) = rownames(NO) #add rownames

M = merge_datasets(M, NO_S_scores, 1) #merge with mega

#plot
ggplot(M, aes(LV2012estimatedIQ, NO_S)) +
  geom_point() +
  geom_text(aes(label = rownames(M)), vjust = 1, alpha = .7) +
  geom_smooth(method = "lm", se = F)
ggsave("NO_S_IQ.png")

sum(!is.na(M$NO_S))
sum(!is.na(M$DK.S))

cor(M$NO_S, M$DK.S, use = "pair")

 

Categories
Differential psychology/psychometrics intelligence / IQ / cognitive ability Sociology

IQ and socioeconomic development across Regions of the UK: a reanalysis

Abstract

A reanalysis of (Carl, 2015) revealed that the inclusion of London had a strong effect on the S loading of crime and poverty variables. S factor scores from a dataset without London and redundant variables was strongly related to IQ scores, r = .87. The Jensen coefficient for this relationship was .86.

 

Introduction

Carl (2015) analyzed socioeconomic inequality across 12 regions of the UK. In my reading of his paper, I thought of several analyses that Carl had not done. I therefore asked him for the data and he shared it with me. For a fuller description of the data sources, refer back to his article.

Redundant variables and London

Including (nearly) perfectly correlated variables can skew an extracted factor. For this reason, I created an alternative dataset where variables that correlated above |.90| were removed. The following pairs of strongly correlated variables were found:

  1. median.weekly.earnings and log.weekly.earnings r=0.999
  2. GVA.per.capita and log.GVA.per.capita r=0.997
  3. R.D.workers.per.capita and log.weekly.earnings r=0.955
  4. log.GVA.per.capita and log.weekly.earnings r=0.925
  5. economic.inactivity and children.workless.households r=0.914

In each case, the first of the pair was removed from the dataset. However, this resulted in a dataset with 11 cases and 11 variables, which is impossible to factor analyze. For this reason, I left in the last pair.

Furthermore, because capitals are known to sometimes strongly affect results (Kirkegaard, 2015a, 2015b, 2015d), I also created two further datasets without London: one with the redundant variables, one without. Thus, there were 4 datasets:

  1. A dataset with London and redundant variables.
  2. A dataset with redundant variables but without London.
  3. A dataset with London but without redundant variables.
  4. A dataset without London and redundant variables.

Factor analysis

Each of the four datasets was factor analyzed. Figure 1 shows the loadings.

loadings

Figure 1: S factor loadings in four analyses.

Removing London strongly affected the loading of the crime variable, which changed from moderately positive to moderately negative. The poverty variable also saw a large change, from slightly negative to strongly negative. Both changes are in the direction towards a purer S factor (desirable outcomes with positive loadings, undesirable outcomes with negative loadings). Removing the redundant variables did not have much effect.

As a check, I investigated whether these results were stable across 30 different factor analytic methods.1 They were, all loadings and scores correlated near 1.00. For my analysis, I used those extracted with the combination of minimum residuals and regression.

Mixedness

Due to London’s strong effect on the loadings, one should check that the two methods developed for finding such cases can identify it (Kirkegaard, 2015c). Figure 2 shows the results from these two methods (mean absolute residual and change in factor size):

mixedness
Figure 2: Mixedness metrics for the complete dataset.

As can be seen, London was identified as a far outlier using both methods.

S scores and IQ

Carl’s dataset also contains IQ scores for the regions. These correlate .87 with the S factor scores from the dataset without London and redundant variables. Figure 3 shows the scatter plot.

IQ_S
Figure 3: Scatter plot of S and IQ scores for regions of the UK.

However, it is possible that IQ is not really related to the latent S factor, just the other variance of the extracted S scores. For this reason I used Jensen’s method (method of correlated vectors) (Jensen, 1998). Figure 4 shows the results.

Jensen_method
Figure 4: Jensen’s method for the S factor’s relationship to IQ scores.

Jensen’s method thus supported the claim that IQ scores and the latent S factor are related.

Discussion and conclusion

My reanalysis revealed some interesting results regarding the effect of London on the loadings. This was made possible by data sharing demonstrating the importance of this practice (Wicherts & Bakker, 2012).

Supplementary material

R source code and datasets are available at the OSF.

References

Carl, N. (2015). IQ and socioeconomic development across Regions of the UK. Journal of Biosocial Science, 1–12. http://doi.org/10.1017/S002193201500019X

Jensen, A. R. (1998). The g factor: the science of mental ability. Westport, Conn.: Praeger.

Kirkegaard, E. O. W. (2015a). Examining the S factor in Mexican states. The Winnower. Retrieved from https://thewinnower.com/papers/examining-the-s-factor-in-mexican-states

Kirkegaard, E. O. W. (2015b). Examining the S factor in US states. The Winnower. Retrieved from https://thewinnower.com/papers/examining-the-s-factor-in-us-states

Kirkegaard, E. O. W. (2015c). Finding mixed cases in exploratory factor analysis. The Winnower. Retrieved from https://thewinnower.com/papers/finding-mixed-cases-in-exploratory-factor-analysis

Kirkegaard, E. O. W. (2015d). The S factor in Brazilian states. The Winnower. Retrieved from https://thewinnower.com/papers/the-s-factor-in-brazilian-states

Revelle, W. (2015). psych: Procedures for Psychological, Psychometric, and Personality Research (Version 1.5.4). Retrieved from http://cran.r-project.org/web/packages/psych/index.html

Wicherts, J. M., & Bakker, M. (2012). Publish (your data) or (let the data) perish! Why not publish your data too? Intelligence, 40(2), 73–76. http://doi.org/10.1016/j.intell.2012.01.004

1There are 6 different extraction and 5 scoring methods supported by the fa() function from the psych package (Revelle, 2015). Thus, there are 6*5 combinations.

Categories
Uncategorized

A replication of the S factor among US states using a new and larger dataset

Abstract

A dataset of 127 variables concerning socioeconomic outcomes for US states was analyzed. Of these, 81 were used in a factor analysis. The analysis revealed a general socioeconomic factor. This factor correlated .961 with one from a previous analysis of socioeconomic data for US states.

 

Introduction

It has repeatedly been found that desirable outcomes tend to be associated with other desirable outcomes and likewise for undesirable outcomes. When this is the case, one can extract a general factor — the general socioeconomic factor (S factor) — such that the desirable outcomes load positively and the undesirable outcomes negatively. This pattern has been found at the country level (1), within country divisions of many countries (2–10), at the city district level (11), at the level of first names (12) and at the level of country of origin groups in two countries (13,14).

A previous study have found that the pattern holds for US states too (7). However, a new and larger dataset has been found, so it is worth examining whether the pattern holds in it, and if so, how strongly correlated the extracted factor scores are between the datasets. This would function as a kind of test-retest reliability.

Data sources

The previous study (7) of the S factor among US states used a dataset of 25 variables compiled from various official statistics found at The 2012 Statistical Abstract website. The current study relies upon a dataset compiled by Measure of America, a website that visualizes social inequality. It is possible to download the datasets their maps rely upon here.

As done with earlier studies, I excluded the capital district. I also excluded the data for US as a whole since it was not a state like the other cases.

The dataset contains a total of 127 variables. However, not all of these are useful for examining the S factor:

  • 4 variables are the composite indexes calculated by Measure of America. These are fairly similar to the Human Development Index scores, except that they are scaled differently.
  • 6 variables concern the population sizes in percent of 6 sociological race categories: Non-Hispanic White, Latino, African American, Asian, Amerindian (Native American) and other.
  • 1 variable contains the total population size for each state.
  • A number of variables were not given in a form adjusted for population size e.g. per capita, percent or rate per 100k persons. These variables were excluded: Rape (total number), Homeless Population (total number), Medicare Recipients (thousands), Medicaid Recipients (thousands), Army Recruits (total), Total Military Casualties in Operations Enduring Freedom and Iraqi Freedom to April 2010, Prisoners State or Federal Jurisdiction (total number), Women in Congressional Delegation (total), Men in Congressional Delegation (total), Carcinogen Releases (pounds), Lead Releases (pounds), Dioxin Releases (grams), Superfund Sites (total), Protected Forest (acres), and Protected Farm and Ranch Land (acres).
  • 1 variable was excluded due to being heavily reliant on local natural environment (presence of water and forests): Farming fishing and forestry occupations (%).
  • 1 variable was excluded because most of its data was missing: State Earned Income Tax Credit (% of federal Earned Income Tax Credit).

The variables that were not given in per population format almost always had a sibling variable that was given in a suitable format and which was included in the analysis. After these exclusions, 101 variables remained for analysis.

Missing data

An analysis of missing data showed that some variables still had missing data. Because the dataset had more variables than cases, it was not possible to impute the missing data using multiple regression as commonly done in these analyses. For this reason, these variables were excluded. After this, 93 variables remained for analysis.

Duplicated, reverse-coded and highly redundant variables

An analysis of correlations among variables showed that 2 of them had duplicates (r = 1): Diabetes (% age 18 and older) and Low-Birth-Weight Infants (% of all infants). I’m not sure why this is the case.

Furthermore, 4 variables had a reverse-coded sibling (r = -1):

  1. Less Than High School (%) + At Least High School Diploma (%)
  2. 4th Graders Reading Below Proficiency (%) + 4th Grade National Assessment of Educational Progress in Reading (% at or above proficient)
  3. Urban Population (%) + Rural Population (%)
  4. Public High School Graduation Rate (%) + High School Freshmen Not Graduating After 4 Years (%).

Finally, some variables were so strongly related to other variables that keeping both would perhaps result in factor analytic errors or headily influence the resulting factor. I decided to use a threshold of |.9| as the limit. If any pair of variables correlated at this level or above, one of them was excluded. There were 6 pairs of variables like this and the first of the pair was excluded:

  1. Poverty Rate (% below federal poverty threshold) + Child Poverty (% living in families below the poverty line), r = .985.
  2. Poverty Rate (% below federal poverty threshold) + Children Under 6 Living in Poverty (%), r = .968.
  3. Management professional and related occupations (%) + At Least Bachelor’s Degree (%), r = .925.
  4. Preschool Enrollment (% enrolled ages 3 and 4) + 3- and 4-year-olds Not Enrolled in Preschool (%), r = -.925.
  5. Army Recruits (per 1000 youth) + Army Recruits (per 1000 youth), r = .914.
  6. Graduate Degree (%) + At Least Bachelor’s Degree (%), r= .910.

The army recruit variable seems to be a duplicate, but the numbers are not identical for all cases. The two preschool enrollment variables seem to be meant to be a reverse-coding of each other, but they don’t correlate perfectly negatively.

After exclusion of these variables, there were 81 remaining.

Factor analysis

Next I extracted a general factor from the data. Since one previous study had found instability across extraction methods when extracting factors from datasets with more variables than cases (2), I examined the stability across all possible extraction and scoring methods, 30 in total (6 extraction methods, 5 scoring methods). 11 of these 30 methods did not result in an error tho they gave warnings. There was no loading instability or scoring instability across methods: all correlations >.996.1 I saved the results from the minres+regression combination.

Inspection of the loadings revealed no important variables with the ‘wrong loading’ i.e., either a desirable outcome but with a negative loading or an undesirable outcome with a positive loading. Some variables are debatable. E.g. binge drinking in adults has a loading of .566, but this could be seen as a good thing (sufficient free time and money to spend it drinking large quantities of alcohol), or a bad thing (binge drinking is bad for one’s health). Figure 1 shows the loadings plot.

AHDI_S
Figure 1: Loadings on the S factor. Some variable names were too long and were cut at the 40th character. Consult the main data file to see the full name.

Factor scores

The extracted factor scores were compared with previously obtained similar measures:

  • HDI2010 scores calculated from HDI2002 scores found in (16).
  • Measure of America’s own American Human Development Index found in the dataset.
  • The S factor scores from the previous study of US states (7).

The correlation matrix is shown in Table 1.

 

HDI2010

S_previous

S_current

AHDI

HDI2010

0.868

0.843

0.750

S_previous

0.852

0.961

0.922

S_current

0.826

0.961

0.941

AHDI

0.724

0.913

0.945

 

Table 1: Correlation matrix of S and HDI scores. Weighted correlations below the diagonal (sqrt of population).

The correlation between the previously obtained S factor and the new one was very strong at .961. The two different HDI measures had the lowest correlation. This is the expected result if they are the worst approximations of the S factor. Note however that the HDI2010 is rescaled from 2002 data, whereas the AHDI and current S factor are based on 2010 data. The previous S factor is based on data from approximately the last 10 years that were averaged.

Mixedness

Finally, factorial mixedness was examined using two methods detailed in a previous paper (17). In short, mixedness is when cases are incongruent with the overall factor structure found for the data. The methods showed convergent results (r = .65). Figure 2 shows the results.

mixedness
Figure 2: Factorial mixedness in cases.

If one was doing a more detailed study, one could examine the residuals at the case level and see if one can find the reasons for why an outlier state is an outlier. In the case of Alaska, the residuals for each variable are shown in Table 2.

 

Variable

Residual

Population.over.65….

-3.34

Renters.with.Severe.Housing.Cost.Burden..gross.rent…50..of.household.income.

-2.64

School.Enrollment….

-2.44

High.School.Graduates.Enrolling.in.College….

-2.08

Infant.Mortality.Rate..per.1000.live.births.

-2.07

Low.Birth.Weight.Infants….of.all.infants.

-1.99

Change.in.Turnout.from.2004

-1.89

Adults.65.and.Older.Living.in.Poverty….

-1.83

Gini.Coefficient

-1.74

Bankruptcies..filings.per.1000.

-1.67

Less.Than.High.School….

-1.34

Children.Under.6.Living.in.Poverty….

-1.32

Diabetes….age.18.and.older.

-1.29

Individuals.with.Home.Internet.Access….ages.3.and.older.

-1.14

Child.Immunization.Rate….

-1.12

Economically.Disadvantaged.Students….public.K.12.

-1.01

Renters.Spending.30..or.More.on.Housing….

-0.85

Housing.Units.Occupied.by.Owner….

-0.80

Production.transportation.and.material.moving.occupations….

-0.80

Children.on.Medicaid….age.0..18.

-0.75

Commute.60.Minutes.or.More….of.workers.16.and.over.

-0.73

Prisoners.State.or.Federal.Jurisdiction..total.number.

-0.68

Change.in.Army.Recruits.from.2007.to.2008….

-0.53

Food.Stamps.Use….

-0.52

Service.occupations….

-0.50

Foreclosures..per.10000.homes.

-0.47

Urban.Population….

-0.44

Owners.Spending.30..or.More.on.Housing….

-0.39

Annual.Costs.of.Public.4.Year.College..average…

-0.38

Property.Crime..per.100000.

-0.28

Unemployment.Rate….ages.16.and.over.

-0.28

Obesity….age.20.and.older.

-0.25

Homicide..per.100000.

-0.23

Practicing.Physicians..per.10000.population.

-0.22

Water.Consumption..gallons.per.day.per.capita.

-0.22

Seats.in.State.Legislatures.Held.by.Women….

-0.21

Sales.and.office.occupations….

-0.06

Turnout….of.eligible.voters.who.voted.

-0.04

Life.Expectancy.at.Birth..years.

-0.02

State.Spending.on.Academic.Research.and.Development…..per.capita.

0.03

Farming.fishing.and.forestry.occupations….

0.17

Mercury.Releases..pounds.per.1000.population.

0.18

Births.to.Teenage.Girls..per.1000.age.15.19.

0.20

Medicaid.Eligibility.Cutoff..income.as…of.poverty.line.

0.21

8th.Grade.National.Assessment.of.Educational.Progress.in.Math….at.or.above.proficient.

0.25

At.Least.Bachelor.s.Degree….

0.30

Smoking….age.18.and.older.

0.31

High.School.Freshmen.Not.Graduating.After.4.Years….

0.33

Child.Mortality..age.1.4.per.100000.population.

0.46

Food.Insecure.Households….

0.47

Uninsured….of.individuals.lacking.coverage.

0.66

Labor.Force.Participation.Rate….ages.16.to.64.

0.74

Army.Recruits..per.1000.youth.

0.87

Binge.Drinking….adults.in.past.30.days.

0.96

Annual.Costs.of.Public.2.Year.College..average…

0.97

Homeless….of.population.

0.98

State.Expenditure.on.Corrections….per.prisoner.

1.02

4th.Graders.Reading.Below.Proficiency….

1.05

Marginally.Attached.Workers..per.10000.working.age.Adults.

1.16

Median.Earnings..2010.dollars.

1.25

Population.under.18….

1.25

Teenagers.Not.in.School.and.Not.Working….ages.16.19.

1.36

Trauma.Related.Death.Rate..per.100000.population.

1.45

3..and.4.year.olds.Not.Enrolled.in.Preschool….

1.50

Ineligible.to.Vote.Due.to.Felony.Convictions..per.100000.voting.age.population.

1.53

Construction.extraction.maintenance.and.repair.occupations….

1.57

State.Medicaid.Spending..per.recipient.

1.70

State.Spending.on.Higher.Education….per.capita.

1.77

Violent.Crime…per.100000.

1.82

Union.Membership….

2.02

Commute.by.Carpool….of.workers.

2.02

Per.Pupil.Spending.Public.K.12….

2.06

Housing.Units.with.1.01.or.More.Occupants.per.Room….

2.10

Carbon.Dioxide.Emissions..metric.tons.per.capita.

2.16

Federal.Revenue.to.Each.State….per.capita.

2.22

Suicide..per.100000.age.adjusted.

2.35

State.Police.Expenditure….per.resident.

2.39

State.Per.Capita.GDP….

2.67

Rape..per.100000.

4.06

Energy.Consumption..BTUs.per.capita.

4.41

State.Expenditure.on.Transportation….per.person.

6.41

 

Table 2: Residuals per variable for Alaska.

The meaning of the numbers is this: It is the number of standard deviations that Alaska is above or below on each variable given its score on the S factor (-.24); How much it deviates from the expected level. We see that the Alaskan state spends a much more on transportation per person than expected (more than 6 standard deviations). This is presumably due to it being located very far north compared to the other states and has the lowest population density. It also spends more energy per citizen, again presumably related to the climate. I’m not sure why rape is so common, however.

One could examine the other outlier states in a similar fashion, but this is left as an exercise to the reader.

Discussion and conclusion

The present analysis used a much larger dataset of 81 very diverse variables than the previous study of the S factor in US states which used 25, yet the findings were almost identical (r = .961). This should probably be interpreted as being because the S factor can be very reliably measured when an appropriate number of and diversity of socioeconomic variables are used. It should be noted however that many of the variables between the datasets overlapped in content, e.g. expected life span at birth.

Supplementary material

Data files and source code is available on OSF.

References

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Footnotes

1 The factor analysis was done with the fa() function from the psych package (15). The cross-method check was done with a home-made function, see the supplementary material.