https://twitter.com/pnin1957/status/641284556818096128
Let’s test that. Since we don’t have the original data, we can’t use that. We can however use open datasets. I like to use Wicherts’ dataset. So let’s analyze!
library(pacman) p_load(kirkegaard, psych, stringr) #load wicherts data w = read.csv("wicherts_data.csv", sep = ";") w = subset(w, select = c("ravenscore", "lre_cor", "nse_cor", "voc_cor", "van_cor", "hfi_cor", "ari_cor", "Zgpa")) #remove missing w = na.omit(w) #standardize w = std_df(w) #subset the subtests w_subtests = subset(w, select = c("ravenscore", "lre_cor", "nse_cor", "voc_cor", "van_cor", "hfi_cor", "ari_cor")) #factor analyze fa = fa(w_subtests) #plot plot_loadings(fa) + scale_x_continuous(breaks = seq(0, 1, .05)) #save scores w_subtests$g = as.numeric(fa$scores) #residualize w_res = residualize_DF(w_subtests, "g") #include GPA w_res$GPA = w$Zgpa #cors write_clipboard(wtd.cors(w_res)) #predict GPA fits = lm_beta_matrix(dependent = "GPA", predictors = colnames(w_res)[-9], data = w_res, return_models = "n") write_clipboard(fits) #why does the last model have NA for one variable? model = str_c("GPA ~ ", str_c(colnames(w_res)[-9], collapse = " + ")) fit = lm(model, w_res) summary(fit)
Results
Correlations
ravenscore | lre_cor | nse_cor | voc_cor | van_cor | hfi_cor | ari_cor | g | GPA | |
ravenscore | 1 | -0.125 | -0.201 | -0.115 | 0.057 | 0.022 | -0.294 | 0 | -0.028 |
lre_cor | -0.125 | 1 | -0.316 | -0.143 | -0.195 | -0.23 | -0.288 | 0 | -0.074 |
nse_cor | -0.201 | -0.316 | 1 | -0.206 | -0.381 | -0.103 | 0.099 | 0 | -0.116 |
voc_cor | -0.115 | -0.143 | -0.206 | 1 | 0.198 | -0.141 | -0.207 | 0 | 0.08 |
van_cor | 0.057 | -0.195 | -0.381 | 0.198 | 1 | -0.081 | -0.406 | 0 | 0.137 |
hfi_cor | 0.022 | -0.23 | -0.103 | -0.141 | -0.081 | 1 | -0.233 | 0 | 0.037 |
ari_cor | -0.294 | -0.288 | 0.099 | -0.207 | -0.406 | -0.233 | 1 | 0 | 0.007 |
g | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0.334 |
GPA | -0.028 | -0.074 | -0.116 | 0.08 | 0.137 | 0.037 | 0.007 | 0.334 | 1 |
Model fits
Model # | ravenscore | lre_cor | nse_cor | voc_cor | van_cor | hfi_cor | ari_cor | g | r2.adj. |
1 | -0.028 | -0.003 | |||||||
2 | -0.074 | 0.002 | |||||||
3 | -0.116 | 0.01 | |||||||
4 | 0.08 | 0.003 | |||||||
5 | 0.137 | 0.015 | |||||||
6 | 0.037 | -0.002 | |||||||
7 | 0.007 | -0.003 | |||||||
8 | 0.334 | 0.108 | |||||||
9 | -0.038 | -0.079 | 0 | ||||||
10 | -0.054 | -0.127 | 0.009 | ||||||
11 | -0.019 | 0.078 | 0 | ||||||
12 | -0.036 | 0.139 | 0.013 | ||||||
13 | -0.029 | 0.038 | -0.005 | ||||||
14 | -0.029 | -0.001 | -0.006 | ||||||
15 | -0.028 | 0.334 | 0.106 | ||||||
16 | -0.123 | -0.155 | 0.02 | ||||||
17 | -0.064 | 0.071 | 0.004 | ||||||
18 | -0.049 | 0.127 | 0.014 | ||||||
19 | -0.069 | 0.021 | -0.001 | ||||||
20 | -0.078 | -0.015 | -0.001 | ||||||
21 | -0.074 | 0.334 | 0.111 | ||||||
22 | -0.104 | 0.059 | 0.01 | ||||||
23 | -0.075 | 0.108 | 0.017 | ||||||
24 | -0.114 | 0.026 | 0.007 | ||||||
25 | -0.118 | 0.019 | 0.007 | ||||||
26 | -0.116 | 0.334 | 0.119 | ||||||
27 | 0.055 | 0.126 | 0.015 | ||||||
28 | 0.087 | 0.05 | 0.002 | ||||||
29 | 0.086 | 0.025 | 0 | ||||||
30 | 0.08 | 0.334 | 0.112 | ||||||
31 | 0.141 | 0.049 | 0.014 | ||||||
32 | 0.168 | 0.075 | 0.017 | ||||||
33 | 0.137 | 0.334 | 0.124 | ||||||
34 | 0.041 | 0.017 | -0.005 | ||||||
35 | 0.037 | 0.334 | 0.107 | ||||||
36 | 0.007 | 0.334 | 0.105 | ||||||
37 | -0.082 | -0.14 | -0.177 | 0.023 | |||||
38 | -0.029 | -0.068 | 0.067 | 0.001 | |||||
39 | -0.043 | -0.054 | 0.129 | 0.013 | |||||
40 | -0.038 | -0.074 | 0.021 | -0.003 | |||||
41 | -0.049 | -0.09 | -0.033 | -0.003 | |||||
42 | -0.038 | -0.079 | 0.334 | 0.109 | |||||
43 | -0.046 | -0.115 | 0.052 | 0.008 | |||||
44 | -0.052 | -0.086 | 0.107 | 0.016 | |||||
45 | -0.054 | -0.125 | 0.026 | 0.007 | |||||
46 | -0.053 | -0.127 | 0.004 | 0.006 | |||||
47 | -0.054 | -0.127 | 0.334 | 0.119 | |||||
48 | -0.03 | 0.052 | 0.128 | 0.012 | |||||
49 | -0.02 | 0.085 | 0.05 | -0.001 | |||||
50 | -0.013 | 0.083 | 0.021 | -0.003 | |||||
51 | -0.019 | 0.078 | 0.334 | 0.109 | |||||
52 | -0.038 | 0.143 | 0.05 | 0.012 | |||||
53 | -0.017 | 0.166 | 0.07 | 0.014 | |||||
54 | -0.036 | 0.139 | 0.334 | 0.122 | |||||
55 | -0.027 | 0.04 | 0.009 | -0.008 | |||||
56 | -0.029 | 0.038 | 0.334 | 0.104 | |||||
57 | -0.029 | -0.001 | 0.334 | 0.103 | |||||
58 | -0.115 | -0.146 | 0.034 | 0.018 | |||||
59 | -0.097 | -0.119 | 0.072 | 0.021 | |||||
60 | -0.125 | -0.157 | -0.008 | 0.017 | |||||
61 | -0.127 | -0.155 | -0.014 | 0.017 | |||||
62 | -0.123 | -0.155 | 0.334 | 0.129 | |||||
63 | -0.043 | 0.051 | 0.118 | 0.013 | |||||
64 | -0.055 | 0.078 | 0.036 | 0.001 | |||||
65 | -0.062 | 0.072 | 0.004 | 0 | |||||
66 | -0.064 | 0.071 | 0.334 | 0.113 | |||||
67 | -0.039 | 0.133 | 0.039 | 0.012 | |||||
68 | -0.024 | 0.158 | 0.065 | 0.014 | |||||
69 | -0.049 | 0.127 | 0.334 | 0.123 | |||||
70 | -0.072 | 0.018 | -0.009 | -0.005 | |||||
71 | -0.069 | 0.021 | 0.334 | 0.108 | |||||
72 | -0.078 | -0.015 | 0.334 | 0.108 | |||||
73 | -0.068 | 0.046 | 0.102 | 0.015 | |||||
74 | -0.099 | 0.065 | 0.036 | 0.008 | |||||
75 | -0.106 | 0.065 | 0.031 | 0.007 | |||||
76 | -0.104 | 0.059 | 0.334 | 0.119 | |||||
77 | -0.069 | 0.114 | 0.039 | 0.015 | |||||
78 | -0.07 | 0.139 | 0.071 | 0.017 | |||||
79 | -0.075 | 0.108 | 0.334 | 0.126 | |||||
80 | -0.116 | 0.031 | 0.026 | 0.004 | |||||
81 | -0.114 | 0.026 | 0.334 | 0.116 | |||||
82 | -0.118 | 0.019 | 0.334 | 0.116 | |||||
83 | 0.063 | 0.129 | 0.057 | 0.015 | |||||
84 | 0.067 | 0.158 | 0.085 | 0.017 | |||||
85 | 0.055 | 0.126 | 0.334 | 0.124 | |||||
86 | 0.098 | 0.061 | 0.042 | 0 | |||||
87 | 0.087 | 0.05 | 0.334 | 0.111 | |||||
88 | 0.086 | 0.025 | 0.334 | 0.109 | |||||
89 | 0.183 | 0.075 | 0.099 | 0.018 | |||||
90 | 0.141 | 0.049 | 0.334 | 0.123 | |||||
91 | 0.168 | 0.075 | 0.334 | 0.126 | |||||
92 | 0.041 | 0.017 | 0.334 | 0.104 | |||||
93 | -0.078 | -0.135 | -0.171 | 0.017 | 0.02 | ||||
94 | -0.076 | -0.116 | -0.144 | 0.064 | 0.023 | ||||
95 | -0.082 | -0.144 | -0.179 | -0.012 | 0.02 | ||||
96 | -0.099 | -0.158 | -0.181 | -0.05 | 0.022 | ||||
97 | -0.082 | -0.14 | -0.177 | 0.334 | 0.133 | ||||
98 | -0.036 | -0.048 | 0.045 | 0.121 | 0.011 | ||||
99 | -0.028 | -0.059 | 0.074 | 0.035 | -0.002 | ||||
100 | -0.033 | -0.072 | 0.064 | -0.01 | -0.003 | ||||
101 | -0.029 | -0.068 | 0.067 | 0.334 | 0.11 | ||||
102 | -0.042 | -0.044 | 0.134 | 0.039 | 0.011 | ||||
103 | -0.026 | -0.032 | 0.154 | 0.053 | 0.011 | ||||
104 | -0.043 | -0.054 | 0.129 | 0.334 | 0.122 | ||||
105 | -0.048 | -0.085 | 0.012 | -0.029 | -0.006 | ||||
106 | -0.038 | -0.074 | 0.021 | 0.334 | 0.106 | ||||
107 | -0.049 | -0.09 | -0.033 | 0.334 | 0.107 | ||||
108 | -0.046 | -0.079 | 0.039 | 0.102 | 0.014 | ||||
109 | -0.045 | -0.11 | 0.058 | 0.035 | 0.006 | ||||
110 | -0.04 | -0.115 | 0.056 | 0.018 | 0.005 | ||||
111 | -0.046 | -0.115 | 0.052 | 0.334 | 0.118 | ||||
112 | -0.052 | -0.08 | 0.113 | 0.039 | 0.014 | ||||
113 | -0.034 | -0.078 | 0.133 | 0.059 | 0.015 | ||||
114 | -0.052 | -0.086 | 0.107 | 0.334 | 0.125 | ||||
115 | -0.051 | -0.125 | 0.028 | 0.011 | 0.003 | ||||
116 | -0.054 | -0.125 | 0.026 | 0.334 | 0.116 | ||||
117 | -0.053 | -0.127 | 0.004 | 0.334 | 0.115 | ||||
118 | -0.03 | 0.059 | 0.132 | 0.057 | 0.012 | ||||
119 | -0.005 | 0.066 | 0.158 | 0.084 | 0.014 | ||||
120 | -0.03 | 0.052 | 0.128 | 0.334 | 0.122 | ||||
121 | -0.007 | 0.096 | 0.06 | 0.039 | -0.003 | ||||
122 | -0.02 | 0.085 | 0.05 | 0.334 | 0.108 | ||||
123 | -0.013 | 0.083 | 0.021 | 0.334 | 0.106 | ||||
124 | -0.013 | 0.182 | 0.074 | 0.095 | 0.015 | ||||
125 | -0.038 | 0.143 | 0.05 | 0.334 | 0.122 | ||||
126 | -0.017 | 0.166 | 0.07 | 0.334 | 0.123 | ||||
127 | -0.027 | 0.04 | 0.009 | 0.334 | 0.101 | ||||
128 | -0.091 | -0.112 | 0.03 | 0.071 | 0.018 | ||||
129 | -0.115 | -0.145 | 0.034 | 0.001 | 0.014 | ||||
130 | -0.117 | -0.146 | 0.033 | -0.005 | 0.014 | ||||
131 | -0.115 | -0.146 | 0.034 | 0.334 | 0.127 | ||||
132 | -0.094 | -0.116 | 0.075 | 0.01 | 0.017 | ||||
133 | -0.081 | -0.11 | 0.092 | 0.032 | 0.018 | ||||
134 | -0.097 | -0.119 | 0.072 | 0.334 | 0.13 | ||||
135 | -0.132 | -0.158 | -0.014 | -0.019 | 0.014 | ||||
136 | -0.125 | -0.157 | -0.008 | 0.334 | 0.126 | ||||
137 | -0.127 | -0.155 | -0.014 | 0.334 | 0.127 | ||||
138 | -0.03 | 0.059 | 0.123 | 0.049 | 0.012 | ||||
139 | -0.011 | 0.065 | 0.155 | 0.08 | 0.014 | ||||
140 | -0.043 | 0.051 | 0.118 | 0.334 | 0.123 | ||||
141 | -0.045 | 0.085 | 0.044 | 0.022 | -0.002 | ||||
142 | -0.055 | 0.078 | 0.036 | 0.334 | 0.111 | ||||
143 | -0.062 | 0.072 | 0.004 | 0.334 | 0.11 | ||||
144 | 0.012 | 0.189 | 0.08 | 0.106 | 0.015 | ||||
145 | -0.039 | 0.133 | 0.039 | 0.334 | 0.122 | ||||
146 | -0.024 | 0.158 | 0.065 | 0.334 | 0.123 | ||||
147 | -0.072 | 0.018 | -0.009 | 0.334 | 0.105 | ||||
148 | -0.059 | 0.054 | 0.108 | 0.047 | 0.014 | ||||
149 | -0.061 | 0.058 | 0.135 | 0.08 | 0.017 | ||||
150 | -0.068 | 0.046 | 0.102 | 0.334 | 0.125 | ||||
151 | -0.1 | 0.076 | 0.048 | 0.044 | 0.006 | ||||
152 | -0.099 | 0.065 | 0.036 | 0.334 | 0.117 | ||||
153 | -0.106 | 0.065 | 0.031 | 0.334 | 0.117 | ||||
154 | -0.059 | 0.157 | 0.065 | 0.092 | 0.018 | ||||
155 | -0.069 | 0.114 | 0.039 | 0.334 | 0.124 | ||||
156 | -0.07 | 0.139 | 0.071 | 0.334 | 0.127 | ||||
157 | -0.116 | 0.031 | 0.026 | 0.334 | 0.114 | ||||
158 | 0.083 | 0.175 | 0.09 | 0.117 | 0.021 | ||||
159 | 0.063 | 0.129 | 0.057 | 0.334 | 0.124 | ||||
160 | 0.067 | 0.158 | 0.085 | 0.334 | 0.127 | ||||
161 | 0.098 | 0.061 | 0.042 | 0.334 | 0.109 | ||||
162 | 0.183 | 0.075 | 0.099 | 0.334 | 0.128 | ||||
163 | -0.072 | -0.112 | -0.139 | 0.015 | 0.063 | 0.019 | |||
164 | -0.079 | -0.138 | -0.174 | 0.015 | -0.009 | 0.016 | |||
165 | -0.1 | -0.158 | -0.182 | -0.002 | -0.05 | 0.018 | |||
166 | -0.078 | -0.135 | -0.171 | 0.017 | 0.334 | 0.13 | |||
167 | -0.075 | -0.115 | -0.143 | 0.065 | 0.003 | 0.019 | |||
168 | -0.083 | -0.127 | -0.152 | 0.052 | -0.018 | 0.019 | |||
169 | -0.076 | -0.116 | -0.144 | 0.064 | 0.334 | 0.133 | |||
170 | -0.106 | -0.173 | -0.19 | -0.034 | -0.063 | 0.019 | |||
171 | -0.082 | -0.144 | -0.179 | -0.012 | 0.334 | 0.13 | |||
172 | -0.099 | -0.158 | -0.181 | -0.05 | 0.334 | 0.132 | |||
173 | -0.035 | -0.035 | 0.053 | 0.125 | 0.048 | 0.01 | |||
174 | -0.01 | -0.015 | 0.063 | 0.153 | 0.075 | 0.011 | |||
175 | -0.036 | -0.048 | 0.045 | 0.121 | 0.334 | 0.121 | |||
176 | -0.024 | -0.054 | 0.077 | 0.038 | 0.009 | -0.005 | |||
177 | -0.028 | -0.059 | 0.074 | 0.035 | 0.334 | 0.108 | |||
178 | -0.033 | -0.072 | 0.064 | -0.01 | 0.334 | 0.107 | |||
179 | -0.01 | 0.008 | 0.186 | 0.078 | 0.1 | 0.012 | |||
180 | -0.042 | -0.044 | 0.134 | 0.039 | 0.334 | 0.12 | |||
181 | -0.026 | -0.032 | 0.154 | 0.053 | 0.334 | 0.121 | |||
182 | -0.048 | -0.085 | 0.012 | -0.029 | 0.334 | 0.104 | |||
183 | -0.044 | -0.07 | 0.046 | 0.107 | 0.046 | 0.012 | |||
184 | -0.022 | -0.067 | 0.053 | 0.131 | 0.072 | 0.014 | |||
185 | -0.046 | -0.079 | 0.039 | 0.102 | 0.334 | 0.124 | |||
186 | -0.034 | -0.108 | 0.067 | 0.044 | 0.032 | 0.003 | |||
187 | -0.045 | -0.11 | 0.058 | 0.035 | 0.334 | 0.116 | |||
188 | -0.04 | -0.115 | 0.056 | 0.018 | 0.334 | 0.115 | |||
189 | -0.028 | -0.066 | 0.152 | 0.062 | 0.082 | 0.015 | |||
190 | -0.052 | -0.08 | 0.113 | 0.039 | 0.334 | 0.124 | |||
191 | -0.034 | -0.078 | 0.133 | 0.059 | 0.334 | 0.125 | |||
192 | -0.051 | -0.125 | 0.028 | 0.011 | 0.334 | 0.113 | |||
193 | 0.004 | 0.083 | 0.176 | 0.091 | 0.118 | 0.018 | |||
194 | -0.03 | 0.059 | 0.132 | 0.057 | 0.334 | 0.122 | |||
195 | -0.005 | 0.066 | 0.158 | 0.084 | 0.334 | 0.124 | |||
196 | -0.007 | 0.096 | 0.06 | 0.039 | 0.334 | 0.106 | |||
197 | -0.013 | 0.182 | 0.074 | 0.095 | 0.334 | 0.125 | |||
198 | -0.083 | -0.105 | 0.035 | 0.076 | 0.018 | 0.015 | |||
199 | -0.065 | -0.095 | 0.042 | 0.098 | 0.046 | 0.016 | |||
200 | -0.091 | -0.112 | 0.03 | 0.071 | 0.334 | 0.128 | |||
201 | -0.118 | -0.146 | 0.032 | -0.002 | -0.006 | 0.011 | |||
202 | -0.115 | -0.145 | 0.034 | 0.001 | 0.334 | 0.124 | |||
203 | -0.117 | -0.146 | 0.033 | -0.005 | 0.334 | 0.124 | |||
204 | -0.053 | -0.089 | 0.12 | 0.039 | 0.059 | 0.015 | |||
205 | -0.094 | -0.116 | 0.075 | 0.01 | 0.334 | 0.127 | |||
206 | -0.081 | -0.11 | 0.092 | 0.032 | 0.334 | 0.128 | |||
207 | -0.132 | -0.158 | -0.014 | -0.019 | 0.334 | 0.124 | |||
208 | 0.044 | 0.094 | 0.195 | 0.11 | 0.144 | 0.019 | |||
209 | -0.03 | 0.059 | 0.123 | 0.049 | 0.334 | 0.122 | |||
210 | -0.011 | 0.065 | 0.155 | 0.08 | 0.334 | 0.124 | |||
211 | -0.045 | 0.085 | 0.044 | 0.022 | 0.334 | 0.108 | |||
212 | 0.012 | 0.189 | 0.08 | 0.106 | 0.334 | 0.125 | |||
213 | -0.044 | 0.075 | 0.157 | 0.082 | 0.11 | 0.019 | |||
214 | -0.059 | 0.054 | 0.108 | 0.047 | 0.334 | 0.124 | |||
215 | -0.061 | 0.058 | 0.135 | 0.08 | 0.334 | 0.127 | |||
216 | -0.1 | 0.076 | 0.048 | 0.044 | 0.334 | 0.116 | |||
217 | -0.059 | 0.157 | 0.065 | 0.092 | 0.334 | 0.128 | |||
218 | 0.083 | 0.175 | 0.09 | 0.117 | 0.334 | 0.131 | |||
219 | -0.071 | -0.109 | -0.136 | 0.017 | 0.065 | 0.007 | 0.016 | ||
220 | -0.078 | -0.12 | -0.145 | 0.011 | 0.056 | -0.011 | 0.016 | ||
221 | -0.072 | -0.112 | -0.139 | 0.015 | 0.063 | 0.334 | 0.13 | ||
222 | -0.117 | -0.188 | -0.201 | -0.024 | -0.045 | -0.077 | 0.016 | ||
223 | -0.079 | -0.138 | -0.174 | 0.015 | -0.009 | 0.334 | 0.127 | ||
224 | -0.1 | -0.158 | -0.182 | -0.002 | -0.05 | 0.334 | 0.128 | ||
225 | -0.09 | -0.142 | -0.163 | 0.038 | -0.014 | -0.032 | 0.016 | ||
226 | -0.075 | -0.115 | -0.143 | 0.065 | 0.003 | 0.334 | 0.13 | ||
227 | -0.083 | -0.127 | -0.152 | 0.052 | -0.018 | 0.334 | 0.13 | ||
228 | -0.106 | -0.173 | -0.19 | -0.034 | -0.063 | 0.334 | 0.129 | ||
229 | 0.023 | 0.056 | 0.101 | 0.201 | 0.118 | 0.16 | 0.016 | ||
230 | -0.035 | -0.035 | 0.053 | 0.125 | 0.048 | 0.334 | 0.12 | ||
231 | -0.01 | -0.015 | 0.063 | 0.153 | 0.075 | 0.334 | 0.121 | ||
232 | -0.024 | -0.054 | 0.077 | 0.038 | 0.009 | 0.334 | 0.105 | ||
233 | -0.01 | 0.008 | 0.186 | 0.078 | 0.1 | 0.334 | 0.122 | ||
234 | -0.009 | -0.046 | 0.072 | 0.155 | 0.08 | 0.106 | 0.016 | ||
235 | -0.044 | -0.07 | 0.046 | 0.107 | 0.046 | 0.334 | 0.123 | ||
236 | -0.022 | -0.067 | 0.053 | 0.131 | 0.072 | 0.334 | 0.124 | ||
237 | -0.034 | -0.108 | 0.067 | 0.044 | 0.032 | 0.334 | 0.114 | ||
238 | -0.028 | -0.066 | 0.152 | 0.062 | 0.082 | 0.334 | 0.125 | ||
239 | 0.004 | 0.083 | 0.176 | 0.091 | 0.118 | 0.334 | 0.128 | ||
240 | 0.015 | -0.034 | 0.08 | 0.168 | 0.09 | 0.121 | 0.016 | ||
241 | -0.083 | -0.105 | 0.035 | 0.076 | 0.018 | 0.334 | 0.125 | ||
242 | -0.065 | -0.095 | 0.042 | 0.098 | 0.046 | 0.334 | 0.126 | ||
243 | -0.118 | -0.146 | 0.032 | -0.002 | -0.006 | 0.334 | 0.121 | ||
244 | -0.053 | -0.089 | 0.12 | 0.039 | 0.059 | 0.334 | 0.126 | ||
245 | 0.044 | 0.094 | 0.195 | 0.11 | 0.144 | 0.334 | 0.129 | ||
246 | -0.044 | 0.075 | 0.157 | 0.082 | 0.11 | 0.334 | 0.13 | ||
247 | -0.071 | -0.109 | -0.136 | 0.017 | 0.065 | 0.007 | 0.016 | ||
248 | -0.071 | -0.109 | -0.136 | 0.017 | 0.065 | 0.007 | 0.334 | 0.127 | |
249 | -0.078 | -0.12 | -0.145 | 0.011 | 0.056 | -0.011 | 0.334 | 0.127 | |
250 | -0.117 | -0.188 | -0.201 | -0.024 | -0.045 | -0.077 | 0.334 | 0.127 | |
251 | -0.09 | -0.142 | -0.163 | 0.038 | -0.014 | -0.032 | 0.334 | 0.127 | |
252 | 0.023 | 0.056 | 0.101 | 0.201 | 0.118 | 0.16 | 0.334 | 0.127 | |
253 | -0.009 | -0.046 | 0.072 | 0.155 | 0.08 | 0.106 | 0.334 | 0.127 | |
254 | 0.015 | -0.034 | 0.08 | 0.168 | 0.09 | 0.121 | 0.334 | 0.127 | |
255 | -0.071 | -0.109 | -0.136 | 0.017 | 0.065 | 0.007 | 0.334 | 0.127 |
[Bonus points to whoever can explain why the last ari_cor has a missing value in the last model. I checked. It is not a problem with my function. I don’t know.]
So Timofey Pnin is right. The beta does stay exactly the same across models, at least two 3 digits.
We may also note that adding the other predictors did not have much effect: g alone (model #8) R2 adj. = .108, best model according to R2 adj. = 0.132 (#97). Notice how this model has negative betas for the other items. In other words, one is better off with lower scores. Surely that can’t be right. It is probably just a fluke due to overfitting…
Testing overfitting
We can test overfitting using lasso regression (read this book, seriously, it’s a great book!). Because lasso regression is indeterministic, we repeat it a large number of times and examine the overall results.
#lasso regression fits_2 = MOD_repeat_cv_glmnet(df = w_res, dependent = "GPA", predictors = colnames(w_res)[-9], runs = 500) write_clipboard(MOD_summarize_models(fits_2))
Lasso results
ravenscore | lre_cor | nse_cor | voc_cor | van_cor | hfi_cor | ari_cor | g | |
mean | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.096 |
median | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.104 |
sd | 0 | 0 | 0 | 0 | 0.001 | 0 | 0 | 0.033 |
fraction_zeroNA | 1 | 1 | 1 | 1 | 0.996 | 1 | 1 | 0.01 |
The lasso confirms our suspicions. The non-g variables were fairly useless, their apparent usefulness due to overfitting. g retained its usefulness in 99% of the runs. The most promising of the other candidates was only useful in .04% of runs.
This is probably worth writing into a short paper. Contact me if you are willing to do this. I will help you, but I don’t have time to write it all myself.