Nerve conduction velocity and cognitive ability: a large sample study
Emil O. W. Kirkegaard, Michael A. Woodley & Helmuth S. Nyborg
About
This is the R notebook for the study:
- Kirkegaard, E. O. W., Woodley, M. A., & Nyborg, H. (2017?). Nerve conduction velocity and cognitive ability: a large sample study. Journal of to be decided.
Purpose A few old studies attempted to find the biological bases of cognitive ability. One plausible candidate – nerve conduction velocity – was examined in two small studies, with ‘conflicting’ results. Conflicting in the sense that one study found p < alpha and the other did not, which is not a real sign of incongruency of results. In the present study, we attempt to resolve the question about whether nerve conduction velocity is related to cognitive ability. The present study is about 100 times larger than the previous two studies.
Setup
First load the data and decide on settings.
library(pacman)
p_load(kirkegaard, readr, dplyr, haven, lavaan, rms)
options(digits = 2)
#load data
d = read_rds("data/VES_dataset.rds")
#rename variables
d %<>% rename(
#NCV
MED_MOTOR_NCV = NC01012,
MED_SENSORY_DL_NCV = NC01018,
MED_SENSORY_PL_NCV = NC01019,
ULN_SENSORY_NCV = NC01023,
PER_MOTOR_NCV = NC01028,
SUR_SENSORY_NCV = NC01032,
#temperature
TEMP_ULIMB_SIDE_TEST = NC01033,
TEMP_ULIMB_PALM = NC01034,
TEMP_ULIMB_FOREARM = NC01035,
TEMP_LLIMB_SIDE_TEST = NC01036,
TEMP_LLIMB_FOOT = NC01037,
TEMP_LLIMB_UPPER_CALF = NC01038,
#fix WAIS-Inf name
WAIS_Inf = WAIS_GI
)
#variable collections
g_tests = c("WRAT", "CVLT", "WCST", "WAIS_BD", "WAIS_Inf", "copy_direct", "copy_immediate", "copy_delayed", "PASAT", "GPT_left", "GPT_right", "WLGT", "ACB_verbal_early", "ACB_verbal_later", "ACB_arithmetic_early", "ACB_arithmetic_later", "PA", "GIT", "AFQT")
g_tests_noGPT = c("WRAT", "CVLT", "WCST", "WAIS_BD", "WAIS_Inf", "copy_direct", "copy_immediate", "copy_delayed", "PASAT", "WLGT", "ACB_verbal_early", "ACB_verbal_later", "ACB_arithmetic_early", "ACB_arithmetic_later", "PA", "GIT", "AFQT")
g_tests_early = c("ACB_verbal_early", "ACB_arithmetic_early", "AFQT", "GIT", "PA")
g_tests_later = setdiff(g_tests, g_tests_early)
ncv_tests = names(d) %>% str_filter("_NCV$")
temp_vars = names(d) %>% str_subset("TEMP_")
exploratory_vars = c("education", "income", "unemployment_3yrs", "height", "weight", "BMI")
#collect control variables
control_vars = c(temp_vars, "race", "AGE", "test_time")
control_vars_noSIRE = c(temp_vars, "AGE", "test_time")
#assert variables present
setdiff(c(g_tests, ncv_tests, exploratory_vars, control_vars), names(d))## character(0)#subset data
d_orig = d
d = d[c(g_tests,
ncv_tests,
exploratory_vars,
control_vars
)]Missing data
There may be some missing data. If so, this has to be dealt with.
#amount
miss_amount(d)## cases with missing data vars with missing data cells with missing data
## 0.1000 0.6800 0.0044miss_plot(d, reverse = F)
miss_plot(d, reverse = T)
#impute
d = silence(miss_impute(d)) %>% as_tibble()
#assert
assertthat::noNA(d)## [1] TRUEDescriptive
Description of the data.
#SIRE
table2(d$race) %>% write_clipboard()## Group Count Percent
## 1 White 3654.00 81.89
## 2 Black 525.00 11.77
## 3 Hispanic 200.00 4.48
## 4 Native 49.00 1.10
## 5 Asian 34.00 0.76
## 6 0.00 0.00#age
GG_denhist(d, "AGE")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
describe(d$AGE)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 4462 38 2.5 38 38 3 31 49 18 0.14 -0.01 0.04Adjust variables for test context variables
Relationships between variables of interest may be obscured by confounders. Here we adjust for some possible confounders.
#function to adjust with
do_adjust = function(df, vars=NULL, control_vars=NULL, keep_mean = F, std_resid = T) {
df
#if no vars or no control vars, return df as is
if (is.null(vars) | is.null(control_vars)) return(df)
#variables not in data frame
for (v in c(vars, control_vars)) {
if (!v %in% names(df)) {
stop(sprintf("Variable not found: `v`"))
}
}
#overlap in variables
if (length(intersect(vars, control_vars)) != 0) {
stop("Cannot control a variable for itself")
}
#loop over vars
for (v in vars) {
#subset data
df_sub = df[c(v, control_vars)]
#regress
fit = lm(sprintf("%s ~ .", v), data = df_sub, na.action = na.exclude)
#save resid
if (std_resid) {
df[[v]] = resid(fit) %>% standardize
} else {
#keep mean
if (keep_mean) {
df[[v]] = resid(fit) + wtd_mean(df[[v]] %>% as.vector)
} else {
df[[v]] = resid(fit)
}
}
}
df
}
#before adjusting, we examine the zero-order correlations between variables of interest
wtd.cors(d[c(g_tests, ncv_tests, control_vars)])## Warning in wtd.cors(d[c(g_tests, ncv_tests, control_vars)]): NAs introduced
## by coercion
## Warning in wtd.cors(d[c(g_tests, ncv_tests, control_vars)]): NAs introduced
## by coercion## WRAT CVLT WCST WAIS_BD WAIS_Inf copy_direct
## WRAT 1.0000 0.3101 0.2925 0.3830 0.6520 0.2700
## CVLT 0.3101 1.0000 0.1921 0.2685 0.3293 0.2052
## WCST 0.2925 0.1921 1.0000 0.3564 0.3302 0.2906
## WAIS_BD 0.3830 0.2685 0.3564 1.0000 0.4526 0.3980
## WAIS_Inf 0.6520 0.3293 0.3302 0.4526 1.0000 0.2783
## copy_direct 0.2700 0.2052 0.2906 0.3980 0.2783 1.0000
## copy_immediate 0.2695 0.3178 0.2678 0.4902 0.3431 0.4746
## copy_delayed 0.2715 0.3271 0.2679 0.4916 0.3446 0.4829
## PASAT 0.4195 0.2902 0.2867 0.3892 0.3671 0.2501
## GPT_left 0.2048 0.1153 0.1960 0.3082 0.1853 0.2252
## GPT_right 0.1971 0.1182 0.1865 0.3027 0.1733 0.2230
## WLGT 0.5041 0.2776 0.2091 0.2805 0.4136 0.1757
## ACB_verbal_early 0.7476 0.3133 0.3288 0.4360 0.7266 0.2914
## ACB_verbal_later 0.7659 0.3334 0.3613 0.4527 0.7193 0.3260
## ACB_arithmetic_early 0.5906 0.3285 0.3618 0.5025 0.6372 0.3344
## ACB_arithmetic_later 0.5852 0.3556 0.3956 0.5318 0.6216 0.3847
## PA 0.4134 0.2614 0.3334 0.6367 0.4832 0.3812
## GIT 0.5191 0.2475 0.2844 0.4197 0.5845 0.2563
## AFQT 0.5751 0.3159 0.3691 0.6291 0.6275 0.3713
## MED_MOTOR_NCV -0.0043 0.0032 0.0018 -0.0198 -0.0090 -0.0100
## MED_SENSORY_DL_NCV 0.0848 0.0299 0.0463 0.0492 0.1042 0.0533
## MED_SENSORY_PL_NCV 0.0221 0.0343 0.0390 0.0379 0.0410 0.0274
## ULN_SENSORY_NCV 0.1130 0.0474 0.0911 0.1116 0.1268 0.0728
## PER_MOTOR_NCV 0.0152 0.0040 0.0339 0.0021 0.0025 0.0121
## SUR_SENSORY_NCV 0.0267 -0.0077 0.0076 0.0190 0.0287 0.0247
## TEMP_ULIMB_SIDE_TEST -0.0134 -0.0041 -0.0223 -0.0209 -0.0171 -0.0165
## TEMP_ULIMB_PALM 0.0260 0.0132 -0.0082 0.0104 0.0176 0.0164
## TEMP_ULIMB_FOREARM 0.0264 0.0187 -0.0038 0.0040 0.0134 0.0087
## TEMP_LLIMB_SIDE_TEST -0.0042 -0.0141 -0.0385 -0.0220 -0.0033 -0.0179
## TEMP_LLIMB_FOOT 0.0183 0.0157 -0.0243 -0.0115 -0.0044 0.0291
## TEMP_LLIMB_UPPER_CALF 0.0191 0.0029 -0.0098 0.0023 0.0041 0.0131
## race NaN NaN NaN NaN NaN NaN
## AGE 0.0395 -0.0509 -0.0081 0.0228 0.1490 -0.0256
## test_time 0.0055 0.0212 0.0029 -0.0087 -0.0016 -0.0273
## copy_immediate copy_delayed PASAT GPT_left
## WRAT 0.2695 0.27147 0.41951 0.2048
## CVLT 0.3178 0.32709 0.29025 0.1153
## WCST 0.2678 0.26794 0.28665 0.1960
## WAIS_BD 0.4902 0.49161 0.38922 0.3082
## WAIS_Inf 0.3431 0.34460 0.36715 0.1853
## copy_direct 0.4746 0.48289 0.25008 0.2252
## copy_immediate 1.0000 0.91544 0.28403 0.2280
## copy_delayed 0.9154 1.00000 0.28293 0.2276
## PASAT 0.2840 0.28293 1.00000 0.2187
## GPT_left 0.2280 0.22762 0.21873 1.0000
## GPT_right 0.1941 0.19976 0.22836 0.6367
## WLGT 0.2134 0.21640 0.35772 0.1565
## ACB_verbal_early 0.3043 0.30254 0.41005 0.2046
## ACB_verbal_later 0.3158 0.31520 0.44174 0.2260
## ACB_arithmetic_early 0.3365 0.33975 0.52330 0.2087
## ACB_arithmetic_later 0.3866 0.38524 0.56373 0.2370
## PA 0.4592 0.45586 0.37183 0.2617
## GIT 0.3130 0.31094 0.36827 0.1897
## AFQT 0.4507 0.44996 0.43338 0.2674
## MED_MOTOR_NCV -0.0026 -0.00628 -0.01003 0.0043
## MED_SENSORY_DL_NCV 0.0073 0.00250 0.06461 0.0550
## MED_SENSORY_PL_NCV 0.0222 0.01971 0.06115 0.0743
## ULN_SENSORY_NCV 0.0698 0.06356 0.10203 0.0927
## PER_MOTOR_NCV -0.0055 -0.00954 0.02193 0.0541
## SUR_SENSORY_NCV 0.0244 0.01926 0.02110 0.0320
## TEMP_ULIMB_SIDE_TEST -0.0150 -0.02165 -0.00059 0.0449
## TEMP_ULIMB_PALM 0.0015 -0.00498 0.00901 -0.0021
## TEMP_ULIMB_FOREARM -0.0042 -0.00720 0.00989 0.0065
## TEMP_LLIMB_SIDE_TEST -0.0232 -0.02644 -0.00858 0.0345
## TEMP_LLIMB_FOOT 0.0015 0.00163 -0.00936 -0.0038
## TEMP_LLIMB_UPPER_CALF 0.0082 0.00653 0.00283 0.0157
## race NaN NaN NaN NaN
## AGE -0.0367 -0.03912 0.01614 -0.0524
## test_time 0.0010 0.00035 -0.01545 0.0080
## GPT_right WLGT ACB_verbal_early ACB_verbal_later
## WRAT 0.1971 0.50407 0.7476 0.7659
## CVLT 0.1182 0.27761 0.3133 0.3334
## WCST 0.1865 0.20913 0.3288 0.3613
## WAIS_BD 0.3027 0.28054 0.4360 0.4527
## WAIS_Inf 0.1733 0.41360 0.7266 0.7193
## copy_direct 0.2230 0.17573 0.2914 0.3260
## copy_immediate 0.1941 0.21338 0.3043 0.3158
## copy_delayed 0.1998 0.21640 0.3025 0.3152
## PASAT 0.2284 0.35772 0.4101 0.4417
## GPT_left 0.6367 0.15654 0.2046 0.2260
## GPT_right 1.0000 0.17061 0.1991 0.2220
## WLGT 0.1706 1.00000 0.4415 0.4631
## ACB_verbal_early 0.1991 0.44148 1.0000 0.8256
## ACB_verbal_later 0.2220 0.46309 0.8256 1.0000
## ACB_arithmetic_early 0.1957 0.36769 0.7014 0.6591
## ACB_arithmetic_later 0.2408 0.36536 0.6427 0.6907
## PA 0.2596 0.28846 0.5172 0.4855
## GIT 0.1725 0.30889 0.6619 0.6224
## AFQT 0.2521 0.35960 0.7165 0.6710
## MED_MOTOR_NCV -0.0037 -0.00597 -0.0034 -0.0174
## MED_SENSORY_DL_NCV 0.0647 0.06384 0.1072 0.1012
## MED_SENSORY_PL_NCV 0.0655 0.01060 0.0363 0.0400
## ULN_SENSORY_NCV 0.0656 0.07556 0.1302 0.1359
## PER_MOTOR_NCV 0.0554 -0.00026 0.0156 0.0232
## SUR_SENSORY_NCV 0.0374 0.01349 0.0286 0.0197
## TEMP_ULIMB_SIDE_TEST -0.0540 -0.01001 0.0110 -0.0080
## TEMP_ULIMB_PALM -0.0059 0.01665 0.0176 0.0254
## TEMP_ULIMB_FOREARM 0.0086 0.02004 0.0147 0.0160
## TEMP_LLIMB_SIDE_TEST -0.0393 0.00236 0.0240 0.0167
## TEMP_LLIMB_FOOT -0.0176 0.02024 -0.0148 0.0091
## TEMP_LLIMB_UPPER_CALF 0.0074 0.03731 -0.0066 0.0047
## race NaN NaN NaN NaN
## AGE -0.0585 0.01884 0.1245 0.0552
## test_time -0.0136 -0.00385 -0.0049 0.0008
## ACB_arithmetic_early ACB_arithmetic_later PA
## WRAT 0.5906 0.5852 0.41337
## CVLT 0.3285 0.3556 0.26142
## WCST 0.3618 0.3956 0.33342
## WAIS_BD 0.5025 0.5318 0.63672
## WAIS_Inf 0.6372 0.6216 0.48317
## copy_direct 0.3344 0.3847 0.38117
## copy_immediate 0.3365 0.3866 0.45921
## copy_delayed 0.3398 0.3852 0.45586
## PASAT 0.5233 0.5637 0.37183
## GPT_left 0.2087 0.2370 0.26165
## GPT_right 0.1957 0.2408 0.25958
## WLGT 0.3677 0.3654 0.28846
## ACB_verbal_early 0.7014 0.6427 0.51723
## ACB_verbal_later 0.6591 0.6907 0.48547
## ACB_arithmetic_early 1.0000 0.7867 0.57833
## ACB_arithmetic_later 0.7867 1.0000 0.54644
## PA 0.5783 0.5464 1.00000
## GIT 0.5925 0.5508 0.47000
## AFQT 0.7400 0.6892 0.73184
## MED_MOTOR_NCV -0.0050 -0.0063 -0.01163
## MED_SENSORY_DL_NCV 0.0953 0.1029 0.04759
## MED_SENSORY_PL_NCV 0.0464 0.0554 0.04737
## ULN_SENSORY_NCV 0.1106 0.1317 0.08268
## PER_MOTOR_NCV 0.0082 0.0180 0.01299
## SUR_SENSORY_NCV 0.0292 0.0213 0.01567
## TEMP_ULIMB_SIDE_TEST -0.0129 -0.0168 -0.01261
## TEMP_ULIMB_PALM 0.0166 0.0302 0.01565
## TEMP_ULIMB_FOREARM 0.0136 0.0243 0.01320
## TEMP_LLIMB_SIDE_TEST 0.0104 0.0038 -0.00020
## TEMP_LLIMB_FOOT -0.0152 -0.0028 -0.00834
## TEMP_LLIMB_UPPER_CALF -0.0071 0.0037 0.00016
## race NaN NaN NaN
## AGE 0.1258 0.0596 0.05648
## test_time 0.0019 0.0061 0.00095
## GIT AFQT MED_MOTOR_NCV MED_SENSORY_DL_NCV
## WRAT 0.5191 0.5751 -0.0043 0.0848
## CVLT 0.2475 0.3159 0.0032 0.0299
## WCST 0.2844 0.3691 0.0018 0.0463
## WAIS_BD 0.4197 0.6291 -0.0198 0.0492
## WAIS_Inf 0.5845 0.6275 -0.0090 0.1042
## copy_direct 0.2563 0.3713 -0.0100 0.0533
## copy_immediate 0.3130 0.4507 -0.0026 0.0073
## copy_delayed 0.3109 0.4500 -0.0063 0.0025
## PASAT 0.3683 0.4334 -0.0100 0.0646
## GPT_left 0.1897 0.2674 0.0043 0.0550
## GPT_right 0.1725 0.2521 -0.0037 0.0647
## WLGT 0.3089 0.3596 -0.0060 0.0638
## ACB_verbal_early 0.6619 0.7165 -0.0034 0.1072
## ACB_verbal_later 0.6224 0.6710 -0.0174 0.1012
## ACB_arithmetic_early 0.5925 0.7400 -0.0050 0.0953
## ACB_arithmetic_later 0.5508 0.6892 -0.0063 0.1029
## PA 0.4700 0.7318 -0.0116 0.0476
## GIT 1.0000 0.6487 -0.0241 0.0517
## AFQT 0.6487 1.0000 -0.0017 0.0508
## MED_MOTOR_NCV -0.0241 -0.0017 1.0000 0.0507
## MED_SENSORY_DL_NCV 0.0517 0.0508 0.0507 1.0000
## MED_SENSORY_PL_NCV 0.0206 0.0443 0.0402 -0.0020
## ULN_SENSORY_NCV 0.0994 0.0991 0.0417 0.3507
## PER_MOTOR_NCV -0.0028 0.0124 0.0014 0.0625
## SUR_SENSORY_NCV 0.0115 0.0197 0.0131 0.1622
## TEMP_ULIMB_SIDE_TEST 0.0229 -0.0078 0.0025 0.0835
## TEMP_ULIMB_PALM 0.0047 0.0107 0.0072 0.1387
## TEMP_ULIMB_FOREARM 0.0045 0.0126 0.0105 0.1350
## TEMP_LLIMB_SIDE_TEST 0.0347 0.0082 -0.0095 0.0305
## TEMP_LLIMB_FOOT -0.0183 -0.0120 0.0214 0.1021
## TEMP_LLIMB_UPPER_CALF -0.0142 -0.0012 -0.0037 0.0872
## race NaN NaN NaN NaN
## AGE 0.1369 0.1162 0.0072 -0.0169
## test_time -0.0139 -0.0035 0.0400 0.0705
## MED_SENSORY_PL_NCV ULN_SENSORY_NCV PER_MOTOR_NCV
## WRAT 0.022 0.1130 0.01521
## CVLT 0.034 0.0474 0.00404
## WCST 0.039 0.0911 0.03385
## WAIS_BD 0.038 0.1116 0.00213
## WAIS_Inf 0.041 0.1268 0.00248
## copy_direct 0.027 0.0728 0.01214
## copy_immediate 0.022 0.0698 -0.00547
## copy_delayed 0.020 0.0636 -0.00954
## PASAT 0.061 0.1020 0.02193
## GPT_left 0.074 0.0927 0.05407
## GPT_right 0.066 0.0656 0.05535
## WLGT 0.011 0.0756 -0.00026
## ACB_verbal_early 0.036 0.1302 0.01555
## ACB_verbal_later 0.040 0.1359 0.02318
## ACB_arithmetic_early 0.046 0.1106 0.00818
## ACB_arithmetic_later 0.055 0.1317 0.01800
## PA 0.047 0.0827 0.01299
## GIT 0.021 0.0994 -0.00282
## AFQT 0.044 0.0991 0.01237
## MED_MOTOR_NCV 0.040 0.0417 0.00142
## MED_SENSORY_DL_NCV -0.002 0.3507 0.06251
## MED_SENSORY_PL_NCV 1.000 0.2134 0.07123
## ULN_SENSORY_NCV 0.213 1.0000 0.12007
## PER_MOTOR_NCV 0.071 0.1201 1.00000
## SUR_SENSORY_NCV 0.153 0.2325 0.12516
## TEMP_ULIMB_SIDE_TEST 0.022 0.0213 -0.02479
## TEMP_ULIMB_PALM 0.038 0.1765 0.00915
## TEMP_ULIMB_FOREARM 0.031 0.1687 0.00634
## TEMP_LLIMB_SIDE_TEST 0.021 0.0027 -0.02761
## TEMP_LLIMB_FOOT 0.030 0.1199 0.02898
## TEMP_LLIMB_UPPER_CALF 0.017 0.0851 0.02353
## race NaN NaN NaN
## AGE -0.065 -0.0211 -0.03743
## test_time 0.039 0.0897 0.01766
## SUR_SENSORY_NCV TEMP_ULIMB_SIDE_TEST TEMP_ULIMB_PALM
## WRAT 0.0267 -0.01337 0.02595
## CVLT -0.0077 -0.00408 0.01317
## WCST 0.0076 -0.02226 -0.00818
## WAIS_BD 0.0190 -0.02095 0.01043
## WAIS_Inf 0.0287 -0.01705 0.01761
## copy_direct 0.0247 -0.01650 0.01638
## copy_immediate 0.0244 -0.01502 0.00155
## copy_delayed 0.0193 -0.02165 -0.00498
## PASAT 0.0211 -0.00059 0.00901
## GPT_left 0.0320 0.04487 -0.00208
## GPT_right 0.0374 -0.05398 -0.00588
## WLGT 0.0135 -0.01001 0.01665
## ACB_verbal_early 0.0286 0.01099 0.01760
## ACB_verbal_later 0.0197 -0.00803 0.02542
## ACB_arithmetic_early 0.0292 -0.01286 0.01664
## ACB_arithmetic_later 0.0213 -0.01680 0.03016
## PA 0.0157 -0.01261 0.01565
## GIT 0.0115 0.02286 0.00467
## AFQT 0.0197 -0.00778 0.01066
## MED_MOTOR_NCV 0.0131 0.00251 0.00723
## MED_SENSORY_DL_NCV 0.1622 0.08351 0.13866
## MED_SENSORY_PL_NCV 0.1529 0.02179 0.03843
## ULN_SENSORY_NCV 0.2325 0.02129 0.17651
## PER_MOTOR_NCV 0.1252 -0.02479 0.00915
## SUR_SENSORY_NCV 1.0000 -0.00854 0.05507
## TEMP_ULIMB_SIDE_TEST -0.0085 1.00000 0.04846
## TEMP_ULIMB_PALM 0.0551 0.04846 1.00000
## TEMP_ULIMB_FOREARM 0.0545 0.02923 0.91602
## TEMP_LLIMB_SIDE_TEST -0.0291 0.61499 0.03422
## TEMP_LLIMB_FOOT 0.1470 0.03813 0.65816
## TEMP_LLIMB_UPPER_CALF 0.0839 0.04792 0.69984
## race NaN NaN NaN
## AGE -0.0097 0.00215 -0.00085
## test_time -0.0013 0.00126 0.08080
## TEMP_ULIMB_FOREARM TEMP_LLIMB_SIDE_TEST
## WRAT 0.0264 -0.0042
## CVLT 0.0187 -0.0141
## WCST -0.0038 -0.0385
## WAIS_BD 0.0040 -0.0220
## WAIS_Inf 0.0134 -0.0033
## copy_direct 0.0087 -0.0179
## copy_immediate -0.0042 -0.0232
## copy_delayed -0.0072 -0.0264
## PASAT 0.0099 -0.0086
## GPT_left 0.0065 0.0345
## GPT_right 0.0086 -0.0393
## WLGT 0.0200 0.0024
## ACB_verbal_early 0.0147 0.0240
## ACB_verbal_later 0.0160 0.0167
## ACB_arithmetic_early 0.0136 0.0104
## ACB_arithmetic_later 0.0243 0.0038
## PA 0.0132 -0.0002
## GIT 0.0045 0.0347
## AFQT 0.0126 0.0082
## MED_MOTOR_NCV 0.0105 -0.0095
## MED_SENSORY_DL_NCV 0.1350 0.0305
## MED_SENSORY_PL_NCV 0.0313 0.0207
## ULN_SENSORY_NCV 0.1687 0.0027
## PER_MOTOR_NCV 0.0063 -0.0276
## SUR_SENSORY_NCV 0.0545 -0.0291
## TEMP_ULIMB_SIDE_TEST 0.0292 0.6150
## TEMP_ULIMB_PALM 0.9160 0.0342
## TEMP_ULIMB_FOREARM 1.0000 0.0231
## TEMP_LLIMB_SIDE_TEST 0.0231 1.0000
## TEMP_LLIMB_FOOT 0.6620 0.0403
## TEMP_LLIMB_UPPER_CALF 0.7393 0.0523
## race NaN NaN
## AGE 0.0112 0.0032
## test_time 0.0823 0.0022
## TEMP_LLIMB_FOOT TEMP_LLIMB_UPPER_CALF race AGE
## WRAT 0.0183 0.01914 NaN 0.03953
## CVLT 0.0157 0.00287 NaN -0.05091
## WCST -0.0243 -0.00984 NaN -0.00814
## WAIS_BD -0.0115 0.00231 NaN 0.02279
## WAIS_Inf -0.0044 0.00409 NaN 0.14902
## copy_direct 0.0291 0.01309 NaN -0.02564
## copy_immediate 0.0015 0.00816 NaN -0.03669
## copy_delayed 0.0016 0.00653 NaN -0.03912
## PASAT -0.0094 0.00283 NaN 0.01614
## GPT_left -0.0038 0.01570 NaN -0.05237
## GPT_right -0.0176 0.00740 NaN -0.05849
## WLGT 0.0202 0.03731 NaN 0.01884
## ACB_verbal_early -0.0148 -0.00662 NaN 0.12448
## ACB_verbal_later 0.0091 0.00467 NaN 0.05516
## ACB_arithmetic_early -0.0152 -0.00705 NaN 0.12577
## ACB_arithmetic_later -0.0028 0.00366 NaN 0.05965
## PA -0.0083 0.00016 NaN 0.05648
## GIT -0.0183 -0.01424 NaN 0.13693
## AFQT -0.0120 -0.00120 NaN 0.11622
## MED_MOTOR_NCV 0.0214 -0.00374 NaN 0.00723
## MED_SENSORY_DL_NCV 0.1021 0.08719 NaN -0.01685
## MED_SENSORY_PL_NCV 0.0301 0.01741 NaN -0.06474
## ULN_SENSORY_NCV 0.1199 0.08506 NaN -0.02106
## PER_MOTOR_NCV 0.0290 0.02353 NaN -0.03743
## SUR_SENSORY_NCV 0.1470 0.08387 NaN -0.00968
## TEMP_ULIMB_SIDE_TEST 0.0381 0.04792 NaN 0.00215
## TEMP_ULIMB_PALM 0.6582 0.69984 NaN -0.00085
## TEMP_ULIMB_FOREARM 0.6620 0.73933 NaN 0.01125
## TEMP_LLIMB_SIDE_TEST 0.0403 0.05233 NaN 0.00319
## TEMP_LLIMB_FOOT 1.0000 0.75383 NaN -0.01064
## TEMP_LLIMB_UPPER_CALF 0.7538 1.00000 NaN 0.02621
## race NaN NaN NaN NaN
## AGE -0.0106 0.02621 NaN 1.00000
## test_time 0.0800 0.05461 NaN -0.02981
## test_time
## WRAT 0.00547
## CVLT 0.02119
## WCST 0.00290
## WAIS_BD -0.00869
## WAIS_Inf -0.00164
## copy_direct -0.02733
## copy_immediate 0.00101
## copy_delayed 0.00035
## PASAT -0.01545
## GPT_left 0.00802
## GPT_right -0.01357
## WLGT -0.00385
## ACB_verbal_early -0.00494
## ACB_verbal_later 0.00080
## ACB_arithmetic_early 0.00192
## ACB_arithmetic_later 0.00612
## PA 0.00095
## GIT -0.01389
## AFQT -0.00351
## MED_MOTOR_NCV 0.04002
## MED_SENSORY_DL_NCV 0.07048
## MED_SENSORY_PL_NCV 0.03901
## ULN_SENSORY_NCV 0.08973
## PER_MOTOR_NCV 0.01766
## SUR_SENSORY_NCV -0.00131
## TEMP_ULIMB_SIDE_TEST 0.00126
## TEMP_ULIMB_PALM 0.08080
## TEMP_ULIMB_FOREARM 0.08234
## TEMP_LLIMB_SIDE_TEST 0.00217
## TEMP_LLIMB_FOOT 0.07995
## TEMP_LLIMB_UPPER_CALF 0.05461
## race NaN
## AGE -0.02981
## test_time 1.00000#adjust
d_adj = do_adjust(d, vars = c(g_tests, ncv_tests), control_vars = control_vars)Exploratory factor analysis: 1 factor
We use exploratory factor analysis to extract the g factor, as well as a general NCV factor.
#GCA
(fa_g = fa(d_adj[g_tests]))## Factor Analysis using method = minres
## Call: fa(r = d_adj[g_tests])
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## WRAT 0.72 0.517 0.48 1
## CVLT 0.41 0.171 0.83 1
## WCST 0.42 0.180 0.82 1
## WAIS_BD 0.62 0.387 0.61 1
## WAIS_Inf 0.75 0.561 0.44 1
## copy_direct 0.44 0.194 0.81 1
## copy_immediate 0.52 0.272 0.73 1
## copy_delayed 0.52 0.275 0.73 1
## PASAT 0.53 0.282 0.72 1
## GPT_left 0.31 0.098 0.90 1
## GPT_right 0.31 0.098 0.90 1
## WLGT 0.51 0.257 0.74 1
## ACB_verbal_early 0.80 0.633 0.37 1
## ACB_verbal_later 0.80 0.639 0.36 1
## ACB_arithmetic_early 0.78 0.613 0.39 1
## ACB_arithmetic_later 0.79 0.617 0.38 1
## PA 0.67 0.450 0.55 1
## GIT 0.63 0.403 0.60 1
## AFQT 0.83 0.682 0.32 1
##
## MR1
## SS loadings 7.33
## Proportion Var 0.39
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 171 and the objective function was 11 with Chi Square of 50769
## The degrees of freedom for the model are 152 and the objective function was 3.8
##
## The root mean square of the residuals (RMSR) is 0.1
## The df corrected root mean square of the residuals is 0.1
##
## The harmonic number of observations is 4462 with the empirical chi square 14178 with prob < 0
## The total number of observations was 4462 with Likelihood Chi Square = 17030 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.62
## RMSEA index = 0.16 and the 90 % confidence intervals are 0.16 0.16
## BIC = 15752
## Fit based upon off diagonal values = 0.94
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.97
## Multiple R square of scores with factors 0.94
## Minimum correlation of possible factor scores 0.88d_adj$g = fa_g$scores %>% as.vector %>% standardize
fa_g$loadings %>% as.vector %>% describe## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 19 0.6 0.17 0.62 0.6 0.24 0.31 0.83 0.51 -0.2 -1.4
## se
## X1 0.04GG_denhist(d_adj$g)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
describe(d_adj$g)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 4462 0 1 0.04 0.03 1.1 -3.3 3.1 6.4 -0.23 -0.34 0.01#factor method variance
fa_all_methods(d_adj[g_tests], messages = F) %>% `[[`("scores") %>% wtd.cors %>% MAT_half %>% averages## arithmetic geometric harmonic mode median trimmed
## 1.00 1.00 1.00 1.00 1.00 1.00
## midrange
## 0.99#PNCV
(fa_ncv = fa(d_adj[ncv_tests]))## Factor Analysis using method = minres
## Call: fa(r = d_adj[ncv_tests])
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## MED_MOTOR_NCV 0.07 0.0046 1.00 1
## MED_SENSORY_DL_NCV 0.40 0.1627 0.84 1
## MED_SENSORY_PL_NCV 0.24 0.0561 0.94 1
## ULN_SENSORY_NCV 0.73 0.5340 0.47 1
## PER_MOTOR_NCV 0.19 0.0374 0.96 1
## SUR_SENSORY_NCV 0.35 0.1230 0.88 1
##
## MR1
## SS loadings 0.92
## Proportion Var 0.15
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 0.26 with Chi Square of 1157
## The degrees of freedom for the model are 9 and the objective function was 0.04
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 4462 with the empirical chi square 220 with prob < 2.1e-42
## The total number of observations was 4462 with Likelihood Chi Square = 157 with prob < 3.8e-29
##
## Tucker Lewis Index of factoring reliability = 0.78
## RMSEA index = 0.061 and the 90 % confidence intervals are 0.053 0.069
## BIC = 81
## Fit based upon off diagonal values = 0.91
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.78
## Multiple R square of scores with factors 0.61
## Minimum correlation of possible factor scores 0.23d_adj$ncv = fa_ncv$scores %>% as.vector %>% standardize
fa_ncv$loadings %>% as.vector %>% describe## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 6 0.33 0.23 0.29 0.33 0.16 0.07 0.73 0.66 0.6 -1.1 0.09GG_denhist(d_adj$ncv)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
describe(d_adj$ncv)## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 4462 0 1 0.01 0.02 0.92 -7.8 8.3 16 -0.26 3.2
## se
## X1 0.01#factor method variance
fa_all_methods(d_adj[ncv_tests], messages = F) %>% `[[`("scores") %>% wtd.cors %>% MAT_half %>% averages## arithmetic geometric harmonic mode median trimmed
## 0.66 0.44 0.25 1.00 0.95 0.68
## midrange
## 0.54Relationships if we use the scores from exploratory analyses
Then we analyze the relationships between NCV, g and education.
#cors
wtd.cors(d_adj[c("education", "g", "ncv")])## education g ncv
## education 1.00 0.57 0.12
## g 0.57 1.00 0.10
## ncv 0.12 0.10 1.00#plot
GG_scatter(d_adj, "ncv", "g", case_names = F) +
geom_smooth() +
xlab("Peripheral nerve conduction velocity\n(factor score from 6 indicators)") +
ylab("General cognitive abiliy\n(factor score from 19 indicators)")## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
silence(ggsave("figures/ncv_g.png"))
#Jensen's method based on EFAs
fa_Jensens_method(fa_g, d_adj, criterion = "ncv", loading_reversing = F, indicator_criterion_method = "pearson", text_pos = "tl") +
xlim(NA, .90)## Using Pearson correlations for the criterion-indicators relationships.
silence(ggsave("figures/Jensen_method_g_ncv.png"))
fa_Jensens_method(fa_ncv, d_adj, criterion = "g", loading_reversing = F, indicator_criterion_method = "pearson", text_pos = "br") +
xlim(0, .8)## Using Pearson correlations for the criterion-indicators relationships.
silence(ggsave("figures/Jensen_method_ncv_g.png"))Without GPT tests
#extract g
(fa_g_noGPT = fa(d_adj[g_tests_noGPT]))## Factor Analysis using method = minres
## Call: fa(r = d_adj[g_tests_noGPT])
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## WRAT 0.72 0.53 0.47 1
## CVLT 0.41 0.17 0.83 1
## WCST 0.42 0.18 0.82 1
## WAIS_BD 0.61 0.37 0.63 1
## WAIS_Inf 0.76 0.57 0.43 1
## copy_direct 0.43 0.19 0.81 1
## copy_immediate 0.52 0.27 0.73 1
## copy_delayed 0.52 0.27 0.73 1
## PASAT 0.53 0.28 0.72 1
## WLGT 0.51 0.26 0.74 1
## ACB_verbal_early 0.80 0.64 0.36 1
## ACB_verbal_later 0.80 0.65 0.35 1
## ACB_arithmetic_early 0.79 0.62 0.38 1
## ACB_arithmetic_later 0.79 0.62 0.38 1
## PA 0.67 0.44 0.56 1
## GIT 0.64 0.41 0.59 1
## AFQT 0.83 0.68 0.32 1
##
## MR1
## SS loadings 7.15
## Proportion Var 0.42
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 136 and the objective function was 11 with Chi Square of 47858
## The degrees of freedom for the model are 119 and the objective function was 3.3
##
## The root mean square of the residuals (RMSR) is 0.09
## The df corrected root mean square of the residuals is 0.1
##
## The harmonic number of observations is 4462 with the empirical chi square 10932 with prob < 0
## The total number of observations was 4462 with Likelihood Chi Square = 14733 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.65
## RMSEA index = 0.17 and the 90 % confidence intervals are 0.16 0.17
## BIC = 13733
## Fit based upon off diagonal values = 0.95
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.97
## Multiple R square of scores with factors 0.94
## Minimum correlation of possible factor scores 0.88d_adj$g_noGPT = fa_g$scores %>% as.vector
#factor method variance
fa_all_methods(d_adj[g_tests_noGPT], messages = F) %>% `[[`("scores") %>% wtd.cors %>% MAT_half %>% averages## arithmetic geometric harmonic mode median trimmed
## 1 1 1 1 1 1
## midrange
## 1#cors
wtd.cors(d_adj[c("g", "g_noGPT", "ncv")])## g g_noGPT ncv
## g 1.0 1.0 0.1
## g_noGPT 1.0 1.0 0.1
## ncv 0.1 0.1 1.0#plot
GG_scatter(d_adj, "ncv", "g", case_names = F) +
geom_smooth()## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
silence(ggsave("figures/ncv_g_noGPT.png"))
#Jensen's method based on EFA
fa_Jensens_method(fa_g_noGPT, d_adj, criterion = "ncv", loading_reversing = F, indicator_criterion_method = "pearson", text_pos = "tl")## Using Pearson correlations for the criterion-indicators relationships.
silence(ggsave("figures/Jensen_method_ncv_noGPT.png"))SEM approach
Usually produces about the same relationship as EFA.
#SEM
g_part = "g =~ " + str_c(g_tests, collapse = " + ")
ncv_part = "ncv =~ " + str_c(ncv_tests, collapse = " + ")
model_str = g_part + "\n" + ncv_part + "\n" +
"g ~~ ncv"
cat(model_str)## g =~ WRAT + CVLT + WCST + WAIS_BD + WAIS_Inf + copy_direct + copy_immediate + copy_delayed + PASAT + GPT_left + GPT_right + WLGT + ACB_verbal_early + ACB_verbal_later + ACB_arithmetic_early + ACB_arithmetic_later + PA + GIT + AFQT
## ncv =~ MED_MOTOR_NCV + MED_SENSORY_DL_NCV + MED_SENSORY_PL_NCV + ULN_SENSORY_NCV + PER_MOTOR_NCV + SUR_SENSORY_NCV
## g ~~ ncv#fit
fit = sem(model_str, data = d_adj, std.ov = T, std.lv = T)
parameterestimates(fit)## lhs op rhs est se z pvalue
## 1 g =~ WRAT 0.756 0.013 58.6 0.000
## 2 g =~ CVLT 0.398 0.015 27.0 0.000
## 3 g =~ WCST 0.409 0.015 27.8 0.000
## 4 g =~ WAIS_BD 0.579 0.014 41.4 0.000
## 5 g =~ WAIS_Inf 0.772 0.013 60.4 0.000
## 6 g =~ copy_direct 0.400 0.015 27.1 0.000
## 7 g =~ copy_immediate 0.455 0.015 31.2 0.000
## 8 g =~ copy_delayed 0.457 0.015 31.4 0.000
## 9 g =~ PASAT 0.520 0.014 36.4 0.000
## 10 g =~ GPT_left 0.278 0.015 18.4 0.000
## 11 g =~ GPT_right 0.280 0.015 18.5 0.000
## 12 g =~ WLGT 0.512 0.014 35.7 0.000
## 13 g =~ ACB_verbal_early 0.836 0.012 68.1 0.000
## 14 g =~ ACB_verbal_later 0.833 0.012 67.6 0.000
## 15 g =~ ACB_arithmetic_early 0.797 0.013 63.3 0.000
## 16 g =~ ACB_arithmetic_later 0.785 0.013 61.9 0.000
## 17 g =~ PA 0.645 0.014 47.3 0.000
## 18 g =~ GIT 0.658 0.014 48.5 0.000
## 19 g =~ AFQT 0.816 0.012 65.6 0.000
## 20 ncv =~ MED_MOTOR_NCV 0.063 0.019 3.3 0.001
## 21 ncv =~ MED_SENSORY_DL_NCV 0.424 0.021 19.8 0.000
## 22 ncv =~ MED_SENSORY_PL_NCV 0.240 0.019 12.4 0.000
## 23 ncv =~ ULN_SENSORY_NCV 0.744 0.029 25.4 0.000
## 24 ncv =~ PER_MOTOR_NCV 0.177 0.019 9.3 0.000
## 25 ncv =~ SUR_SENSORY_NCV 0.319 0.020 16.0 0.000
## 26 g ~~ ncv 0.137 0.019 7.1 0.000
## 27 WRAT ~~ WRAT 0.428 0.010 43.5 0.000
## 28 CVLT ~~ CVLT 0.841 0.018 46.7 0.000
## 29 WCST ~~ WCST 0.833 0.018 46.7 0.000
## 30 WAIS_BD ~~ WAIS_BD 0.664 0.014 45.8 0.000
## 31 WAIS_Inf ~~ WAIS_Inf 0.403 0.009 43.0 0.000
## 32 copy_direct ~~ copy_direct 0.840 0.018 46.7 0.000
## 33 copy_immediate ~~ copy_immediate 0.793 0.017 46.5 0.000
## 34 copy_delayed ~~ copy_delayed 0.791 0.017 46.5 0.000
## 35 PASAT ~~ PASAT 0.730 0.016 46.2 0.000
## 36 GPT_left ~~ GPT_left 0.923 0.020 47.0 0.000
## 37 GPT_right ~~ GPT_right 0.922 0.020 47.0 0.000
## 38 WLGT ~~ WLGT 0.738 0.016 46.2 0.000
## 39 ACB_verbal_early ~~ ACB_verbal_early 0.300 0.007 40.6 0.000
## 40 ACB_verbal_later ~~ ACB_verbal_later 0.307 0.008 40.8 0.000
## 41 ACB_arithmetic_early ~~ ACB_arithmetic_early 0.365 0.009 42.3 0.000
## 42 ACB_arithmetic_later ~~ ACB_arithmetic_later 0.383 0.009 42.7 0.000
## 43 PA ~~ PA 0.584 0.013 45.2 0.000
## 44 GIT ~~ GIT 0.567 0.013 45.1 0.000
## 45 AFQT ~~ AFQT 0.334 0.008 41.6 0.000
## 46 MED_MOTOR_NCV ~~ MED_MOTOR_NCV 0.996 0.021 47.1 0.000
## 47 MED_SENSORY_DL_NCV ~~ MED_SENSORY_DL_NCV 0.820 0.022 37.2 0.000
## 48 MED_SENSORY_PL_NCV ~~ MED_SENSORY_PL_NCV 0.942 0.021 45.2 0.000
## 49 ULN_SENSORY_NCV ~~ ULN_SENSORY_NCV 0.446 0.040 11.1 0.000
## 50 PER_MOTOR_NCV ~~ PER_MOTOR_NCV 0.968 0.021 46.2 0.000
## 51 SUR_SENSORY_NCV ~~ SUR_SENSORY_NCV 0.898 0.021 43.0 0.000
## 52 g ~~ g 1.000 0.000 NA NA
## 53 ncv ~~ ncv 1.000 0.000 NA NA
## ci.lower ci.upper
## 1 0.731 0.78
## 2 0.369 0.43
## 3 0.380 0.44
## 4 0.552 0.61
## 5 0.747 0.80
## 6 0.371 0.43
## 7 0.426 0.48
## 8 0.429 0.49
## 9 0.492 0.55
## 10 0.248 0.31
## 11 0.250 0.31
## 12 0.484 0.54
## 13 0.812 0.86
## 14 0.808 0.86
## 15 0.772 0.82
## 16 0.761 0.81
## 17 0.618 0.67
## 18 0.631 0.69
## 19 0.792 0.84
## 20 0.026 0.10
## 21 0.382 0.47
## 22 0.203 0.28
## 23 0.687 0.80
## 24 0.140 0.21
## 25 0.280 0.36
## 26 0.099 0.17
## 27 0.409 0.45
## 28 0.806 0.88
## 29 0.798 0.87
## 30 0.636 0.69
## 31 0.385 0.42
## 32 0.805 0.88
## 33 0.760 0.83
## 34 0.758 0.82
## 35 0.699 0.76
## 36 0.884 0.96
## 37 0.883 0.96
## 38 0.707 0.77
## 39 0.286 0.32
## 40 0.292 0.32
## 41 0.348 0.38
## 42 0.365 0.40
## 43 0.558 0.61
## 44 0.542 0.59
## 45 0.318 0.35
## 46 0.954 1.04
## 47 0.777 0.86
## 48 0.901 0.98
## 49 0.367 0.53
## 50 0.927 1.01
## 51 0.857 0.94
## 52 1.000 1.00
## 53 1.000 1.00As expected, this produced roughly the same result as the EFA approach.
EFA: multi-factor
Given that the two outlying tests are variants by hand, perhaps variance from non-g factors are obscuring the relationship. We try extracting more factors.
#determine number of factors
nFactors::nScree(d_adj[g_tests] %>% as.data.frame)## noc naf nparallel nkaiser
## 1 3 1 3 3#g bifactor efa
fa_bi3 = fa(d_adj[g_tests], nfactors = 3, rotate = "bifactor")## Loading required namespace: GPArotationfa_plot_loadings(fa_bi3)## Warning: Some components of ... were not used: fun
fa_bi4 = fa(d_adj[g_tests], nfactors = 4, rotate = "bifactor")
fa_plot_loadings(fa_bi4)## Warning: Some components of ... were not used: fun
#Jensen's method for bifactor
fa_Jensens_method(fa_bi3, df = d_adj, criterion = "ncv", n_factor = 1, loading_reversing = F)## Using Pearson correlations for the criterion-indicators relationships.
fa_Jensens_method(fa_bi3, df = d_adj, criterion = "ncv", n_factor = 2, loading_reversing = F)## Using Pearson correlations for the criterion-indicators relationships.
fa_Jensens_method(fa_bi3, df = d_adj, criterion = "ncv", n_factor = 3, loading_reversing = F)## Using Pearson correlations for the criterion-indicators relationships.
#Jensen's method regression
#construct data frame with test level data
d_test = data_frame(
test = g_tests,
g = fa_bi3$loadings %>% `[`(, 1),
F1 = fa_bi3$loadings %>% `[`(, 2),
F2 = fa_bi3$loadings %>% `[`(, 3),
criterion_r = wtd.cors(d_adj[c("ncv", g_tests)]) %>% `[`(-1, 1)
)## Warning: `data_frame()` is deprecated, use `tibble()`.
## This warning is displayed once per session.d_test## # A tibble: 19 x 5
## test g F1 F2 criterion_r
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 WRAT 0.653 0.444 -0.00777 0.0758
## 2 CVLT 0.420 0.0183 -0.00737 0.0231
## 3 WCST 0.411 0.0444 0.104 0.0651
## 4 WAIS_BD 0.637 -0.0903 0.189 0.0580
## 5 WAIS_Inf 0.704 0.334 -0.0302 0.108
## 6 copy_direct 0.484 -0.198 0.116 0.0446
## 7 copy_immediate 0.704 -0.591 -0.00922 0.0315
## 8 copy_delayed 0.709 -0.595 -0.00730 0.0245
## 9 PASAT 0.497 0.152 0.112 0.0762
## 10 GPT_left 0.255 -0.0152 0.705 0.0755
## 11 GPT_right 0.245 0.0144 0.778 0.0662
## 12 WLGT 0.463 0.237 0.0520 0.0721
## 13 ACB_verbal_early 0.731 0.472 -0.0263 0.103
## 14 ACB_verbal_later 0.731 0.461 0.00328 0.0981
## 15 ACB_arithmetic_early 0.734 0.315 0.0131 0.0775
## 16 ACB_arithmetic_later 0.742 0.255 0.0561 0.0912
## 17 PA 0.673 -0.00773 0.126 0.0415
## 18 GIT 0.594 0.274 -0.00463 0.0461
## 19 AFQT 0.796 0.178 0.0713 0.0506lm("criterion_r ~ g + F1 + F2", data = d_test) %>% MOD_summary(kfold = F)##
## ---- Model summary ----
## Model coefficients
## Beta SE CI_lower CI_upper
## g 0.29 0.23 -0.21 0.79
## F1 0.77 0.16 0.43 1.11
## F2 0.36 0.23 -0.13 0.86
##
##
## Model meta-data
## outcome N df R2 R2-adj. R2-cv
## 1 criterion_r 19 15 0.64 0.56 NA
##
##
## Etas from analysis of variance
## Eta Eta_partial
## g 0.19 0.31
## F1 0.76 0.78
## F2 0.24 0.38#case-level
d_adj$bi_g = fa_bi3$scores %>% `[`(, 1)
d_adj$bi_F1 = fa_bi3$scores %>% `[`(, 2)
d_adj$bi_F2 = fa_bi3$scores %>% `[`(, 3)
#model
lm("ncv ~ bi_g + bi_F1 + bi_F2", data = d_adj) %>% MOD_summary(progress = F)##
## ---- Model summary ----
## Model coefficients
## Beta SE CI_lower CI_upper
## bi_g 0.084 0.015 0.055 0.114
## bi_F1 0.060 0.015 0.031 0.090
## bi_F2 0.053 0.015 0.023 0.082
##
##
## Model meta-data
## outcome N df R2 R2-adj. R2-cv
## 1 ncv 4462 4458 0.014 0.013 NA
##
##
## Etas from analysis of variance
## Eta Eta_partial
## bi_g 0.084 0.085
## bi_F1 0.060 0.061
## bi_F2 0.053 0.053These results are similar to the previous ones.
Whites only
Perhaps we should not control for SIRE and instead just use the White subsample.
#subset, adjust
d_white_adj = d %>%
filter(race == "White") %>%
do_adjust(vars = c(g_tests, ncv_tests), control_vars = control_vars_noSIRE)
#extract g
(fa_g = fa(d_white_adj[g_tests]))## Factor Analysis using method = minres
## Call: fa(r = d_white_adj[g_tests])
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## WRAT 0.73 0.53 0.47 1
## CVLT 0.42 0.18 0.82 1
## WCST 0.42 0.18 0.82 1
## WAIS_BD 0.63 0.40 0.60 1
## WAIS_Inf 0.75 0.57 0.43 1
## copy_direct 0.45 0.20 0.80 1
## copy_immediate 0.53 0.28 0.72 1
## copy_delayed 0.54 0.29 0.71 1
## PASAT 0.54 0.29 0.71 1
## GPT_left 0.33 0.11 0.89 1
## GPT_right 0.32 0.10 0.90 1
## WLGT 0.51 0.26 0.74 1
## ACB_verbal_early 0.80 0.64 0.36 1
## ACB_verbal_later 0.81 0.65 0.35 1
## ACB_arithmetic_early 0.79 0.63 0.37 1
## ACB_arithmetic_later 0.79 0.63 0.37 1
## PA 0.69 0.48 0.52 1
## GIT 0.65 0.43 0.57 1
## AFQT 0.84 0.71 0.29 1
##
## MR1
## SS loadings 7.6
## Proportion Var 0.4
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 171 and the objective function was 12 with Chi Square of 43230
## The degrees of freedom for the model are 152 and the objective function was 3.9
##
## The root mean square of the residuals (RMSR) is 0.09
## The df corrected root mean square of the residuals is 0.1
##
## The harmonic number of observations is 3654 with the empirical chi square 11257 with prob < 0
## The total number of observations was 3654 with Likelihood Chi Square = 14080 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.64
## RMSEA index = 0.16 and the 90 % confidence intervals are 0.16 0.16
## BIC = 12833
## Fit based upon off diagonal values = 0.95
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.97
## Multiple R square of scores with factors 0.94
## Minimum correlation of possible factor scores 0.88d_white_adj$g = fa_g$scores %>% as.vector
#factor method variance
fa_all_methods(d_white_adj[g_tests], messages = F) %>% `[[`("scores") %>% wtd.cors %>% MAT_half %>% averages## arithmetic geometric harmonic mode median trimmed
## 1.00 1.00 1.00 1.00 1.00 1.00
## midrange
## 0.99#extract ncv
(fa_ncv = fa(d_white_adj[ncv_tests]))## Factor Analysis using method = minres
## Call: fa(r = d_white_adj[ncv_tests])
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## MED_MOTOR_NCV 0.09 0.0082 0.99 1
## MED_SENSORY_DL_NCV 0.34 0.1153 0.88 1
## MED_SENSORY_PL_NCV 0.25 0.0628 0.94 1
## ULN_SENSORY_NCV 0.87 0.7530 0.25 1
## PER_MOTOR_NCV 0.17 0.0273 0.97 1
## SUR_SENSORY_NCV 0.28 0.0765 0.92 1
##
## MR1
## SS loadings 1.04
## Proportion Var 0.17
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 0.29 with Chi Square of 1064
## The degrees of freedom for the model are 9 and the objective function was 0.06
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.07
##
## The harmonic number of observations is 3654 with the empirical chi square 310 with prob < 2.1e-61
## The total number of observations was 3654 with Likelihood Chi Square = 229 with prob < 2.1e-44
##
## Tucker Lewis Index of factoring reliability = 0.65
## RMSEA index = 0.082 and the 90 % confidence intervals are 0.073 0.091
## BIC = 156
## Fit based upon off diagonal values = 0.85
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.88
## Multiple R square of scores with factors 0.77
## Minimum correlation of possible factor scores 0.55d_white_adj$ncv = fa_ncv$scores %>% as.vector
#factor method variance
fa_all_methods(d_white_adj[ncv_tests], messages = F) %>% `[[`("scores") %>% wtd.cors %>% MAT_half %>% averages## arithmetic geometric harmonic mode median trimmed
## 0.65 0.48 0.30 1.00 0.88 0.67
## midrange
## 0.53#cors
wtd.cors(d_white_adj[c("education", "g", "ncv")])## education g ncv
## education 1.00 0.586 0.102
## g 0.59 1.000 0.095
## ncv 0.10 0.095 1.000#plot
GG_scatter(d_white_adj, "ncv", "g", case_names = F) +
geom_smooth()## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
silence(ggsave("figures/ncv_g_white.png"))
#Jensen's method based on EFA
fa_Jensens_method(fa_g, d_white_adj, criterion = "ncv", loading_reversing = F, indicator_criterion_method = "pearson", text_pos = "tr")## Using Pearson correlations for the criterion-indicators relationships.
silence(ggsave("figures/Jensen_method_ncv_white.png"))However, these results are quite similar to the others.
Without controls
Perhaps we are overcontrolling the data in some way. We can examine the relationships if we don’t control for possible confounders.
#extract g
(fa_g = fa(d[g_tests]))## Factor Analysis using method = minres
## Call: fa(r = d[g_tests])
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## WRAT 0.73 0.53 0.47 1
## CVLT 0.42 0.18 0.82 1
## WCST 0.46 0.21 0.79 1
## WAIS_BD 0.67 0.45 0.55 1
## WAIS_Inf 0.76 0.58 0.42 1
## copy_direct 0.47 0.22 0.78 1
## copy_immediate 0.55 0.30 0.70 1
## copy_delayed 0.55 0.30 0.70 1
## PASAT 0.57 0.32 0.68 1
## GPT_left 0.34 0.12 0.88 1
## GPT_right 0.33 0.11 0.89 1
## WLGT 0.49 0.24 0.76 1
## ACB_verbal_early 0.82 0.67 0.33 1
## ACB_verbal_later 0.82 0.67 0.33 1
## ACB_arithmetic_early 0.81 0.66 0.34 1
## ACB_arithmetic_later 0.82 0.67 0.33 1
## PA 0.71 0.50 0.50 1
## GIT 0.69 0.48 0.52 1
## AFQT 0.85 0.73 0.27 1
##
## MR1
## SS loadings 7.94
## Proportion Var 0.42
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 171 and the objective function was 13 with Chi Square of 56112
## The degrees of freedom for the model are 152 and the objective function was 3.9
##
## The root mean square of the residuals (RMSR) is 0.09
## The df corrected root mean square of the residuals is 0.1
##
## The harmonic number of observations is 4462 with the empirical chi square 13128 with prob < 0
## The total number of observations was 4462 with Likelihood Chi Square = 17325 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.66
## RMSEA index = 0.16 and the 90 % confidence intervals are 0.16 0.16
## BIC = 16047
## Fit based upon off diagonal values = 0.95
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.97
## Multiple R square of scores with factors 0.95
## Minimum correlation of possible factor scores 0.89d$g = fa_g$scores %>% as.vector
#factor method variance
fa_all_methods(d[g_tests], messages = F) %>% `[[`("scores") %>% wtd.cors %>% MAT_half %>% averages## arithmetic geometric harmonic mode median trimmed
## 1 1 1 1 1 1
## midrange
## 1#extract ncv
(fa_ncv = fa(d[ncv_tests]))## Factor Analysis using method = minres
## Call: fa(r = d[ncv_tests])
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## MED_MOTOR_NCV 0.07 0.0049 1.00 1
## MED_SENSORY_DL_NCV 0.42 0.1777 0.82 1
## MED_SENSORY_PL_NCV 0.25 0.0633 0.94 1
## ULN_SENSORY_NCV 0.76 0.5706 0.43 1
## PER_MOTOR_NCV 0.19 0.0363 0.96 1
## SUR_SENSORY_NCV 0.36 0.1298 0.87 1
##
## MR1
## SS loadings 0.98
## Proportion Var 0.16
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 0.29 with Chi Square of 1307
## The degrees of freedom for the model are 9 and the objective function was 0.04
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 4462 with the empirical chi square 220 with prob < 2.2e-42
## The total number of observations was 4462 with Likelihood Chi Square = 161 with prob < 3.9e-30
##
## Tucker Lewis Index of factoring reliability = 0.8
## RMSEA index = 0.062 and the 90 % confidence intervals are 0.053 0.07
## BIC = 86
## Fit based upon off diagonal values = 0.92
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.80
## Multiple R square of scores with factors 0.64
## Minimum correlation of possible factor scores 0.29d$ncv = fa_ncv$scores %>% as.vector
#factor method variance
fa_all_methods(d[ncv_tests], messages = F) %>% `[[`("scores") %>% wtd.cors %>% MAT_half %>% averages## arithmetic geometric harmonic mode median trimmed
## 0.66 0.45 0.26 1.00 0.95 0.69
## midrange
## 0.54#cors
wtd.cors(d[c("education", "g", "ncv")])## education g ncv
## education 1.00 0.55 0.12
## g 0.55 1.00 0.15
## ncv 0.12 0.15 1.00#plot
GG_scatter(d, "ncv", "g", case_names = F) +
geom_smooth()## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
silence(ggsave("figures/ncv_g_noAdj.png"))
#Jensen's method based on EFA
fa_Jensens_method(fa_g, d, criterion = "ncv", loading_reversing = F, indicator_criterion_method = "pearson", text_pos = "tr")## Using Pearson correlations for the criterion-indicators relationships.
silence(ggsave("figures/Jensen_method_ncv_noAdj.png"))Early and later g
#extract early and later g
fa_g_early = fa(d_adj[g_tests_early])
d_adj$g_early = fa_g_early$scores %>% as.vector
fa_g_later = fa(d_adj[g_tests_later])
d_adj$g_later = fa_g_later$scores %>% as.vector
#correlate
cor_matrix(d_adj[c("g", "g_early", "g_later", "ncv")], CI = .95)## g g_early g_later
## g "1" "0.94 [0.93 0.94]" "0.97 [0.97 0.97]"
## g_early "0.94 [0.93 0.94]" "1" "0.82 [0.82 0.83]"
## g_later "0.97 [0.97 0.97]" "0.82 [0.82 0.83]" "1"
## ncv "0.10 [0.07 0.13]" "0.07 [0.05 0.10]" "0.11 [0.08 0.14]"
## ncv
## g "0.10 [0.07 0.13]"
## g_early "0.07 [0.05 0.10]"
## g_later "0.11 [0.08 0.14]"
## ncv "1"Height as confounding factor
d_orig$ncv = d_adj$ncv
GG_scatter(d_orig, "g", "ncv")
GG_scatter(d_orig, "height", "g")
GG_scatter(d_orig, "height", "ncv")
Other correlates
Which other variables are related to PNCV?
#overview of correlates
wtd.cors(d_adj[c("g_early", "g_later", exploratory_vars)])## g_early g_later education income unemployment_3yrs
## g_early 1.000 0.8248 0.517 0.310 -0.127
## g_later 0.825 1.0000 0.545 0.338 -0.173
## education 0.517 0.5454 1.000 0.349 -0.152
## income 0.310 0.3380 0.349 1.000 -0.487
## unemployment_3yrs -0.127 -0.1725 -0.152 -0.487 1.000
## height 0.118 0.1064 0.091 0.092 -0.027
## weight 0.017 0.0032 0.025 0.062 -0.031
## BMI -0.045 -0.0549 -0.021 0.021 -0.020
## height weight BMI
## g_early 0.1184 0.0174 -0.0446
## g_later 0.1064 0.0032 -0.0549
## education 0.0908 0.0251 -0.0205
## income 0.0917 0.0625 0.0211
## unemployment_3yrs -0.0268 -0.0306 -0.0203
## height 1.0000 0.4808 -0.0056
## weight 0.4808 1.0000 0.8707
## BMI -0.0056 0.8707 1.0000#models
ols(ncv ~ g + education, data = d_adj)## Linear Regression Model
##
## ols(formula = ncv ~ g + education, data = d_adj)
##
## Model Likelihood Discrimination
## Ratio Test Indexes
## Obs 4462 LR chi2 71.41 R2 0.016
## sigma0.9923 d.f. 2 R2 adj 0.015
## d.f. 4459 Pr(> chi2) 0.0000 g 0.142
##
## Residuals
##
## Min 1Q Median 3Q Max
## -7.84130 -0.59625 0.03094 0.64452 8.30186
##
##
## Coef S.E. t Pr(>|t|)
## Intercept -0.5310 0.1053 -5.04 <0.0001
## g 0.0489 0.0180 2.71 0.0067
## education 0.0400 0.0078 5.09 <0.0001
## ols(ncv ~ g + education, data = d)## Linear Regression Model
##
## ols(formula = ncv ~ g + education, data = d)
##
## Model Likelihood Discrimination
## Ratio Test Indexes
## Obs 4462 LR chi2 108.92 R2 0.024
## sigma0.7927 d.f. 2 R2 adj 0.024
## d.f. 4459 Pr(> chi2) 0.0000 g 0.142
##
## Residuals
##
## Min 1Q Median 3Q Max
## -5.38008 -0.48226 0.02194 0.51100 6.23856
##
##
## Coef S.E. t Pr(>|t|)
## Intercept -0.2790 0.0828 -3.37 0.0008
## g 0.0941 0.0146 6.47 <0.0001
## education 0.0210 0.0062 3.40 0.0007
## ols(ncv ~ g + education, data = d_white_adj)## Linear Regression Model
##
## ols(formula = ncv ~ g + education, data = d_white_adj)
##
## Model Likelihood Discrimination
## Ratio Test Indexes
## Obs 3654 LR chi2 44.97 R2 0.012
## sigma0.8740 d.f. 2 R2 adj 0.012
## d.f. 3651 Pr(> chi2) 0.0000 g 0.110
##
## Residuals
##
## Min 1Q Median 3Q Max
## -4.47049 -0.53475 0.02179 0.56756 4.19471
##
##
## Coef S.E. t Pr(>|t|)
## Intercept -0.3524 0.1025 -3.44 0.0006
## g 0.0484 0.0184 2.63 0.0085
## education 0.0264 0.0076 3.47 0.0005
## #path model for mediation
med_model = "
ncv ~ g + education
education ~ g"
#estimate
sem(med_model, data = d) %>% parameterestimates()## lhs op rhs est se z pvalue ci.lower ci.upper
## 1 ncv ~ g 0.094 0.015 6.5 0.000 0.066 0.123
## 2 ncv ~ education 0.021 0.006 3.4 0.001 0.009 0.033
## 3 education ~ g 1.287 0.030 43.5 0.000 1.229 1.345
## 4 ncv ~~ ncv 0.628 0.013 47.2 0.000 0.602 0.654
## 5 education ~~ education 3.702 0.078 47.2 0.000 3.548 3.856
## 6 g ~~ g 0.947 0.000 NA NA 0.947 0.947sem(med_model, data = d_adj) %>% parameterestimates()## lhs op rhs est se z pvalue ci.lower ci.upper
## 1 ncv ~ g 0.049 0.018 2.7 0.007 0.014 0.084
## 2 ncv ~ education 0.040 0.008 5.1 0.000 0.025 0.055
## 3 education ~ g 1.298 0.028 45.8 0.000 1.242 1.353
## 4 ncv ~~ ncv 0.984 0.021 47.2 0.000 0.943 1.025
## 5 education ~~ education 3.587 0.076 47.2 0.000 3.438 3.735
## 6 g ~~ g 1.000 0.000 NA NA 1.000 1.000sem(med_model, data = d_white_adj) %>% parameterestimates()## lhs op rhs est se z pvalue ci.lower ci.upper
## 1 ncv ~ g 0.048 0.018 2.6 0.008 0.012 0.084
## 2 ncv ~ education 0.026 0.008 3.5 0.001 0.012 0.041
## 3 education ~ g 1.414 0.032 43.7 0.000 1.351 1.478
## 4 ncv ~~ ncv 0.763 0.018 42.7 0.000 0.728 0.798
## 5 education ~~ education 3.607 0.084 42.7 0.000 3.441 3.772
## 6 g ~~ g 0.942 0.000 NA NA 0.942 0.942Export data
#complete data as RDS
readr::write_rds(d, "data/VES_NCV.rds", compress = "gz")
#CSVs
write_csv(d, "data/d.csv", na = "")
write_csv(d_adj, "data/d_adj.csv", na = "")Versions
write_sessioninfo()## R version 3.5.3 (2019-03-11)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Linux Mint 19.1
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] rms_5.1-3 SparseM_1.77 lavaan_0.6-3
## [4] haven_2.1.0 kirkegaard_2018.05 metafor_2.0-0
## [7] Matrix_1.2-17 psych_1.8.12 magrittr_1.5
## [10] assertthat_0.2.1 weights_1.0 mice_3.4.0
## [13] gdata_2.18.0 Hmisc_4.2-0 Formula_1.2-3
## [16] survival_2.43-3 lattice_0.20-38 forcats_0.4.0
## [19] stringr_1.4.0 dplyr_0.8.0.1 purrr_0.3.2
## [22] readr_1.3.1 tidyr_0.8.3 tibble_2.1.1
## [25] ggplot2_3.1.1 tidyverse_1.2.1 pacman_0.5.0
##
## loaded via a namespace (and not attached):
## [1] TH.data_1.0-10 minqa_1.2.4 colorspace_1.4-1
## [4] ellipsis_0.1.0 nFactors_2.3.3 class_7.3-15
## [7] rio_0.5.16 htmlTable_1.13.1 base64enc_0.1-3
## [10] rstudioapi_0.10 MatrixModels_0.4-1 fansi_0.4.0
## [13] mvtnorm_1.0-10 lubridate_1.7.4 ranger_0.11.1
## [16] xml2_1.2.0 codetools_0.2-16 splines_3.5.3
## [19] mnormt_1.5-5 robustbase_0.93-3 knitr_1.22
## [22] jsonlite_1.6 lsr_0.5 nloptr_1.2.1
## [25] broom_0.5.2 cluster_2.0.8 compiler_3.5.3
## [28] httr_1.4.0 backports_1.1.4 lazyeval_0.2.2
## [31] cli_1.1.0 acepack_1.4.1 htmltools_0.3.6
## [34] quantreg_5.38 tools_3.5.3 gtable_0.3.0
## [37] glue_1.3.1 Rcpp_1.0.1 carData_3.0-2
## [40] cellranger_1.1.0 nlme_3.1-139 multilevel_2.6
## [43] lmtest_0.9-36 laeken_0.5.0 xfun_0.6
## [46] Rcsdp_0.1.55 openxlsx_4.1.0 lme4_1.1-21
## [49] rvest_0.3.3 gtools_3.8.1 polspline_1.1.14
## [52] pan_1.6 DEoptimR_1.0-8 MASS_7.3-51.1
## [55] zoo_1.8-4 scales_1.0.0 VIM_4.8.0
## [58] hms_0.4.2 parallel_3.5.3 sandwich_2.5-0
## [61] RColorBrewer_1.1-2 psychometric_2.2 yaml_2.2.0
## [64] curl_3.3 gridExtra_2.3 rpart_4.1-13
## [67] latticeExtra_0.6-28 stringi_1.4.3 e1071_1.7-0.1
## [70] checkmate_1.9.1 zip_1.0.0 boot_1.3-20
## [73] rlang_0.3.4 pkgconfig_2.0.2 evaluate_0.13
## [76] htmlwidgets_1.3 labeling_0.3 tidyselect_0.2.5
## [79] plyr_1.8.4 R6_2.4.0 generics_0.0.2
## [82] mitml_0.3-7 multcomp_1.4-10 mgcv_1.8-28
## [85] pillar_1.3.1 foreign_0.8-70 withr_2.1.2
## [88] abind_1.4-5 sp_1.3-1 nnet_7.3-12
## [91] modelr_0.1.4 crayon_1.3.4 car_3.0-2
## [94] jomo_2.6-7 utf8_1.1.4 rmarkdown_1.12
## [97] grid_3.5.3 readxl_1.3.1 data.table_1.12.2
## [100] pbivnorm_0.6.0 vcd_1.4-4 digest_0.6.18
## [103] GPArotation_2014.11-1 stats4_3.5.3 munsell_0.5.0