Warne et al 2019’s retest of Army Beta World War 1 military test
Reanalyze some data from:
- Warne RT, Burton JZ, Gibbons A, Melendez DA. Stephen Jay Gould’s Analysis of the Army Beta Test in The Mismeasure of Man: Distortions and Misconceptions Regarding a Pioneering Mental Test. Journal of Intelligence. 2019; 7(1):6. https://www.mdpi.com/2079-3200/7/1/6
Init
library(pacman)
p_load(kirkegaard, haven, osfr, rms)Data
Download
#download data files
osf_download(osf_retrieve_file("https://osf.io/utvsb/"), path = "data/data.sav", overwrite = T)Read
#read data
army = haven::read_sav("data/data.sav")Recode
#items end with a digit
items = army[str_detect(names(army), "\\d$")]
names(items)## [1] "Maze1" "Maze2" "Maze3" "Maze4"
## [5] "Maze5" "Cube1" "Cube2" "Cube3"
## [9] "Cube4" "Cube5" "Cube6" "Cube7"
## [13] "Cube8" "Cube9" "Cube10" "Cube11"
## [17] "Cube12" "Cube13" "Cube14" "Cube15"
## [21] "Cube16" "XO1" "XO2" "XO3"
## [25] "XO4" "XO5" "XO6" "XO7"
## [29] "XO8" "XO9" "XO10" "XO11"
## [33] "XO12" "DigitSymbol1" "DigitSymbol2" "DigitSymbol3"
## [37] "DigitSymbol4" "DigitSymbol5" "DigitSymbol6" "NumbCheck1"
## [41] "NumbCheck2" "NumbCheck3" "NumbCheck4" "NumbCheck5"
## [45] "NumbCheck6" "NumbCheck7" "NumbCheck8" "NumbCheck9"
## [49] "NumbCheck10" "NumbCheck11" "NumbCheck12" "NumbCheck13"
## [53] "NumbCheck14" "NumbCheck15" "NumbCheck16" "NumbCheck17"
## [57] "NumbCheck18" "NumbCheck19" "NumbCheck20" "NumbCheck21"
## [61] "NumbCheck22" "NumbCheck23" "NumbCheck24" "NumbCheck25"
## [65] "NumbCheck26" "NumbCheck27" "NumbCheck28" "NumbCheck29"
## [69] "NumbCheck30" "NumbCheck31" "NumbCheck32" "NumbCheck33"
## [73] "NumbCheck34" "NumbCheck35" "NumbCheck36" "NumbCheck37"
## [77] "NumbCheck38" "NumbCheck39" "NumbCheck40" "NumbCheck41"
## [81] "NumbCheck42" "NumbCheck43" "NumbCheck44" "NumbCheck45"
## [85] "NumbCheck46" "NumbCheck47" "NumbCheck48" "NumbCheck49"
## [89] "NumbCheck50" "Picture1" "Picture2" "Picture3"
## [93] "Picture4" "Picture5" "Picture6" "Picture7"
## [97] "Picture8" "Picture9" "Picture10" "Picture11"
## [101] "Picture12" "Picture13" "Picture14" "Picture15"
## [105] "Picture16" "Picture17" "Picture18" "Picture19"
## [109] "Picture20" "Geometric1" "Geometric2" "Geometric3"
## [113] "Geometric4" "Geometric5" "Geometric6" "Geometric7"
## [117] "Geometric8" "Geometric9" "Geometric10"#recode to 1/0 format
items_10 = map_df(items, ~as.numeric(. == 1))
#how much missing?
miss_amount(items_10)## cases with missing data vars with missing data cells with missing data
## 0.96000000 0.48000000 0.05862345IRT
#subset without digitsymbol -- not binary-ish
items_10_noDS = items_10 %>% select(-starts_with("Digit"))
names(items_10_noDS)## [1] "Maze1" "Maze2" "Maze3" "Maze4" "Maze5"
## [6] "Cube1" "Cube2" "Cube3" "Cube4" "Cube5"
## [11] "Cube6" "Cube7" "Cube8" "Cube9" "Cube10"
## [16] "Cube11" "Cube12" "Cube13" "Cube14" "Cube15"
## [21] "Cube16" "XO1" "XO2" "XO3" "XO4"
## [26] "XO5" "XO6" "XO7" "XO8" "XO9"
## [31] "XO10" "XO11" "XO12" "NumbCheck1" "NumbCheck2"
## [36] "NumbCheck3" "NumbCheck4" "NumbCheck5" "NumbCheck6" "NumbCheck7"
## [41] "NumbCheck8" "NumbCheck9" "NumbCheck10" "NumbCheck11" "NumbCheck12"
## [46] "NumbCheck13" "NumbCheck14" "NumbCheck15" "NumbCheck16" "NumbCheck17"
## [51] "NumbCheck18" "NumbCheck19" "NumbCheck20" "NumbCheck21" "NumbCheck22"
## [56] "NumbCheck23" "NumbCheck24" "NumbCheck25" "NumbCheck26" "NumbCheck27"
## [61] "NumbCheck28" "NumbCheck29" "NumbCheck30" "NumbCheck31" "NumbCheck32"
## [66] "NumbCheck33" "NumbCheck34" "NumbCheck35" "NumbCheck36" "NumbCheck37"
## [71] "NumbCheck38" "NumbCheck39" "NumbCheck40" "NumbCheck41" "NumbCheck42"
## [76] "NumbCheck43" "NumbCheck44" "NumbCheck45" "NumbCheck46" "NumbCheck47"
## [81] "NumbCheck48" "NumbCheck49" "NumbCheck50" "Picture1" "Picture2"
## [86] "Picture3" "Picture4" "Picture5" "Picture6" "Picture7"
## [91] "Picture8" "Picture9" "Picture10" "Picture11" "Picture12"
## [96] "Picture13" "Picture14" "Picture15" "Picture16" "Picture17"
## [101] "Picture18" "Picture19" "Picture20" "Geometric1" "Geometric2"
## [106] "Geometric3" "Geometric4" "Geometric5" "Geometric6" "Geometric7"
## [111] "Geometric8" "Geometric9" "Geometric10"#fit IRT 2PN
irt_fit = irt.fa(items_10_noDS)## Warning in tetrachoric(x, correct = correct): Item = Maze1 had no variance
## and was deleted## Warning in tetrachoric(x, correct = correct): Item = Cube1 had no variance
## and was deleted## Warning in tetrachoric(x, correct = correct): Item = Cube2 had no variance
## and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck2 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck5 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck7 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck8 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck9 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck12 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck14 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck15 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck19 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck21 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck22 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck23 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck27 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck28 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck30 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck31 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck32 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck35 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck36 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck38 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck39 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck40 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck42 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck46 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck47 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = NumbCheck50 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = Picture1 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = Picture2 had no
## variance and was deleted## Warning in tetrachoric(x, correct = correct): Item = Picture14 had no
## variance and was deleted## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs
## = np.obs, : The estimated weights for the factor scores are probably
## incorrect. Try a different factor extraction method.
irt_fit$fa## Factor Analysis using method = minres
## Call: fa(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate,
## fm = fm)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## Maze2 0.46 0.21490 0.79 1
## Maze3 0.35 0.12529 0.87 1
## Maze4 0.24 0.05710 0.94 1
## Maze5 0.24 0.05732 0.94 1
## Cube3 0.77 0.59480 0.41 1
## Cube4 0.73 0.53654 0.46 1
## Cube5 0.52 0.27194 0.73 1
## Cube6 0.32 0.10340 0.90 1
## Cube7 0.25 0.06068 0.94 1
## Cube8 0.39 0.14938 0.85 1
## Cube9 0.28 0.07967 0.92 1
## Cube10 0.22 0.04746 0.95 1
## Cube11 0.26 0.06839 0.93 1
## Cube12 0.11 0.01143 0.99 1
## Cube13 0.26 0.06622 0.93 1
## Cube14 0.36 0.13063 0.87 1
## Cube15 0.15 0.02318 0.98 1
## Cube16 0.11 0.01240 0.99 1
## XO1 0.85 0.72389 0.28 1
## XO2 0.32 0.10272 0.90 1
## XO3 0.93 0.87063 0.13 1
## XO4 0.31 0.09652 0.90 1
## XO5 0.32 0.10255 0.90 1
## XO6 0.73 0.53827 0.46 1
## XO7 0.91 0.82671 0.17 1
## XO8 0.91 0.82671 0.17 1
## XO9 0.33 0.10982 0.89 1
## XO10 0.62 0.38487 0.62 1
## XO11 0.36 0.12659 0.87 1
## XO12 0.29 0.08565 0.91 1
## NumbCheck1 0.84 0.70478 0.30 1
## NumbCheck3 0.54 0.29445 0.71 1
## NumbCheck4 0.65 0.42559 0.57 1
## NumbCheck6 0.55 0.30624 0.69 1
## NumbCheck10 0.55 0.30169 0.70 1
## NumbCheck11 0.80 0.63980 0.36 1
## NumbCheck13 0.38 0.14471 0.86 1
## NumbCheck16 0.57 0.32524 0.67 1
## NumbCheck17 0.49 0.23633 0.76 1
## NumbCheck18 0.89 0.79081 0.21 1
## NumbCheck20 0.61 0.36815 0.63 1
## NumbCheck24 0.51 0.26317 0.74 1
## NumbCheck25 0.51 0.25589 0.74 1
## NumbCheck26 0.44 0.19406 0.81 1
## NumbCheck29 0.37 0.13449 0.87 1
## NumbCheck33 0.38 0.14114 0.86 1
## NumbCheck34 0.38 0.14648 0.85 1
## NumbCheck37 0.21 0.04407 0.96 1
## NumbCheck41 0.18 0.03188 0.97 1
## NumbCheck43 0.19 0.03703 0.96 1
## NumbCheck44 0.16 0.02655 0.97 1
## NumbCheck45 0.14 0.02069 0.98 1
## NumbCheck48 0.02 0.00045 1.00 1
## NumbCheck49 -0.01 0.00011 1.00 1
## Picture3 0.83 0.68159 0.32 1
## Picture4 0.28 0.07601 0.92 1
## Picture5 0.13 0.01776 0.98 1
## Picture6 0.82 0.68060 0.32 1
## Picture7 0.44 0.19135 0.81 1
## Picture8 -0.05 0.00239 1.00 1
## Picture9 0.46 0.21526 0.78 1
## Picture10 -0.22 0.04840 0.95 1
## Picture11 0.21 0.04346 0.96 1
## Picture12 0.59 0.34560 0.65 1
## Picture13 0.12 0.01421 0.99 1
## Picture15 0.27 0.07464 0.93 1
## Picture16 0.76 0.57864 0.42 1
## Picture17 0.79 0.62274 0.38 1
## Picture18 0.18 0.03326 0.97 1
## Picture19 0.38 0.14367 0.86 1
## Picture20 0.24 0.05913 0.94 1
## Geometric1 0.75 0.56568 0.43 1
## Geometric2 0.55 0.30458 0.70 1
## Geometric3 0.48 0.23001 0.77 1
## Geometric4 0.33 0.10605 0.89 1
## Geometric5 0.63 0.39741 0.60 1
## Geometric6 0.09 0.00774 0.99 1
## Geometric7 0.36 0.12657 0.87 1
## Geometric8 0.37 0.13431 0.87 1
## Geometric9 0.38 0.14813 0.85 1
## Geometric10 0.26 0.06706 0.93 1
##
## MR1
## SS loadings 19.16
## Proportion Var 0.24
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 3240 and the objective function was 726.64 with Chi Square of 131642.5
## The degrees of freedom for the model are 3159 and the objective function was 702.16
##
## The root mean square of the residuals (RMSR) is 0.14
## The df corrected root mean square of the residuals is 0.14
##
## The harmonic number of observations is 210 with the empirical chi square 26654.69 with prob < 0
## The total number of observations was 210 with Likelihood Chi Square = 126739.9 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.009
## RMSEA index = 0.466 and the 90 % confidence intervals are 0.431 NA
## BIC = 109848.4
## Fit based upon off diagonal values = 0.74#remove bad items -- negative loadings or no variance
items_10_noDS_ok = items_10_noDS[(irt_fit$fa$loadings > 0) %>% as.data.frame() %>% subset(MR1) %>% rownames()]
names(items_10_noDS_ok)## [1] "Maze2" "Maze3" "Maze4" "Maze5" "Cube3"
## [6] "Cube4" "Cube5" "Cube6" "Cube7" "Cube8"
## [11] "Cube9" "Cube10" "Cube11" "Cube12" "Cube13"
## [16] "Cube14" "Cube15" "Cube16" "XO1" "XO2"
## [21] "XO3" "XO4" "XO5" "XO6" "XO7"
## [26] "XO8" "XO9" "XO10" "XO11" "XO12"
## [31] "NumbCheck1" "NumbCheck3" "NumbCheck4" "NumbCheck6" "NumbCheck10"
## [36] "NumbCheck11" "NumbCheck13" "NumbCheck16" "NumbCheck17" "NumbCheck18"
## [41] "NumbCheck20" "NumbCheck24" "NumbCheck25" "NumbCheck26" "NumbCheck29"
## [46] "NumbCheck33" "NumbCheck34" "NumbCheck37" "NumbCheck41" "NumbCheck43"
## [51] "NumbCheck44" "NumbCheck45" "NumbCheck48" "Picture3" "Picture4"
## [56] "Picture5" "Picture6" "Picture7" "Picture9" "Picture11"
## [61] "Picture12" "Picture13" "Picture15" "Picture16" "Picture17"
## [66] "Picture18" "Picture19" "Picture20" "Geometric1" "Geometric2"
## [71] "Geometric3" "Geometric4" "Geometric5" "Geometric6" "Geometric7"
## [76] "Geometric8" "Geometric9" "Geometric10"#refit
irt_fit = irt.fa(items_10_noDS_ok)## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs
## = np.obs, : The estimated weights for the factor scores are probably
## incorrect. Try a different factor extraction method.
irt_fit$fa## Factor Analysis using method = minres
## Call: fa(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate,
## fm = fm)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## Maze2 0.47 0.21632 0.78 1
## Maze3 0.35 0.12397 0.88 1
## Maze4 0.24 0.05732 0.94 1
## Maze5 0.24 0.05782 0.94 1
## Cube3 0.77 0.59587 0.40 1
## Cube4 0.73 0.53567 0.46 1
## Cube5 0.52 0.27324 0.73 1
## Cube6 0.32 0.10418 0.90 1
## Cube7 0.25 0.06160 0.94 1
## Cube8 0.39 0.14974 0.85 1
## Cube9 0.28 0.08022 0.92 1
## Cube10 0.22 0.04938 0.95 1
## Cube11 0.27 0.07191 0.93 1
## Cube12 0.11 0.01167 0.99 1
## Cube13 0.26 0.06621 0.93 1
## Cube14 0.37 0.13459 0.87 1
## Cube15 0.16 0.02489 0.98 1
## Cube16 0.11 0.01303 0.99 1
## XO1 0.85 0.72736 0.27 1
## XO2 0.32 0.10273 0.90 1
## XO3 0.93 0.87295 0.13 1
## XO4 0.31 0.09708 0.90 1
## XO5 0.32 0.10285 0.90 1
## XO6 0.73 0.53864 0.46 1
## XO7 0.91 0.82604 0.17 1
## XO8 0.91 0.82604 0.17 1
## XO9 0.33 0.10971 0.89 1
## XO10 0.62 0.38808 0.61 1
## XO11 0.37 0.13395 0.87 1
## XO12 0.30 0.08738 0.91 1
## NumbCheck1 0.84 0.71009 0.29 1
## NumbCheck3 0.54 0.29279 0.71 1
## NumbCheck4 0.66 0.42934 0.57 1
## NumbCheck6 0.55 0.30790 0.69 1
## NumbCheck10 0.55 0.30727 0.69 1
## NumbCheck11 0.80 0.63937 0.36 1
## NumbCheck13 0.38 0.14465 0.86 1
## NumbCheck16 0.57 0.32746 0.67 1
## NumbCheck17 0.49 0.24045 0.76 1
## NumbCheck18 0.89 0.79629 0.20 1
## NumbCheck20 0.61 0.37206 0.63 1
## NumbCheck24 0.52 0.26602 0.73 1
## NumbCheck25 0.51 0.26298 0.74 1
## NumbCheck26 0.45 0.20051 0.80 1
## NumbCheck29 0.37 0.13905 0.86 1
## NumbCheck33 0.38 0.14271 0.86 1
## NumbCheck34 0.38 0.14771 0.85 1
## NumbCheck37 0.21 0.04459 0.96 1
## NumbCheck41 0.18 0.03318 0.97 1
## NumbCheck43 0.20 0.03841 0.96 1
## NumbCheck44 0.17 0.02731 0.97 1
## NumbCheck45 0.14 0.02099 0.98 1
## NumbCheck48 0.02 0.00048 1.00 1
## Picture3 0.83 0.68408 0.32 1
## Picture4 0.28 0.07605 0.92 1
## Picture5 0.13 0.01725 0.98 1
## Picture6 0.83 0.68277 0.32 1
## Picture7 0.44 0.19339 0.81 1
## Picture9 0.46 0.21372 0.79 1
## Picture11 0.21 0.04346 0.96 1
## Picture12 0.59 0.34585 0.65 1
## Picture13 0.12 0.01527 0.98 1
## Picture15 0.27 0.07381 0.93 1
## Picture16 0.76 0.57527 0.42 1
## Picture17 0.79 0.62822 0.37 1
## Picture18 0.18 0.03326 0.97 1
## Picture19 0.38 0.14599 0.85 1
## Picture20 0.25 0.06078 0.94 1
## Geometric1 0.75 0.56240 0.44 1
## Geometric2 0.55 0.30645 0.69 1
## Geometric3 0.48 0.22915 0.77 1
## Geometric4 0.33 0.10869 0.89 1
## Geometric5 0.63 0.39460 0.61 1
## Geometric6 0.10 0.00903 0.99 1
## Geometric7 0.36 0.12990 0.87 1
## Geometric8 0.38 0.14262 0.86 1
## Geometric9 0.39 0.14939 0.85 1
## Geometric10 0.26 0.06884 0.93 1
##
## MR1
## SS loadings 19.22
## Proportion Var 0.25
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 3003 and the objective function was 716.28 with Chi Square of 130482.7
## The degrees of freedom for the model are 2925 and the objective function was 691.67
##
## The root mean square of the residuals (RMSR) is 0.14
## The df corrected root mean square of the residuals is 0.14
##
## The harmonic number of observations is 210 with the empirical chi square 24318.55 with prob < 0
## The total number of observations was 210 with Likelihood Chi Square = 125538.1 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.009
## RMSEA index = 0.481 and the 90 % confidence intervals are 0.446 NA
## BIC = 109897.9
## Fit based upon off diagonal values = 0.76#score
irt_fit_score = scoreIrt(irt_fit, items_10_noDS_ok)
army$g_irt = irt_fit_score$theta1 %>% standardize()
#plot
army$g_irt %>% GG_denhist()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#recode far outliers
army$g_irt[army$g_irt < -3] = NARegular FA
#extract (sub)test scores
tests = army %>% select(contains("total_score"), -Beta_total_score)
names(tests)## [1] "Maze_total_score" "Cube_total_score"
## [3] "XO_total_score" "DigitSymbol_total_score"
## [5] "NumbCheck_total_score" "Picture_total_score"
## [7] "Geometric_total_score"#impute missing
tests_imp = miss_impute(tests)
#fit
fa_fit = fa(tests_imp)
fa_fit## Factor Analysis using method = minres
## Call: fa(r = tests_imp)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## Maze_total_score 0.40 0.16 0.84 1
## Cube_total_score 0.60 0.36 0.64 1
## XO_total_score 0.34 0.11 0.89 1
## DigitSymbol_total_score 0.43 0.19 0.81 1
## NumbCheck_total_score 0.56 0.31 0.69 1
## Picture_total_score 0.41 0.16 0.84 1
## Geometric_total_score 0.55 0.30 0.70 1
##
## MR1
## SS loadings 1.60
## Proportion Var 0.23
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 21 and the objective function was 0.78 with Chi Square of 160.5
## The degrees of freedom for the model are 14 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.06
##
## The harmonic number of observations is 209 with the empirical chi square 19.45 with prob < 0.15
## The total number of observations was 210 with Likelihood Chi Square = 16.06 with prob < 0.31
##
## Tucker Lewis Index of factoring reliability = 0.978
## RMSEA index = 0.028 and the 90 % confidence intervals are 0 0.074
## BIC = -58.8
## Fit based upon off diagonal values = 0.96
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.83
## Multiple R square of scores with factors 0.69
## Minimum correlation of possible factor scores 0.38army$g_fa = fa_fit$scores[, 1] %>% standardize()Regressions
Which is better, IRT or FA scores? Note that IRT scores do not include some of the items: Digit Symbol or the problematic ones.
#scatter of scores
GG_scatter(army, "g_irt", "g_fa")
#correlations
wtd.cors(army[c("g_irt", "g_fa", "Beta_total_score", "ACT_Comp", "College_GPA")])## g_irt g_fa Beta_total_score ACT_Comp
## g_irt 1.0000000 0.6083543 0.6132354 0.24285061
## g_fa 0.6083543 1.0000000 0.9649016 0.38802341
## Beta_total_score 0.6132354 0.9649016 1.0000000 0.36558426
## ACT_Comp 0.2428506 0.3880234 0.3655843 1.00000000
## College_GPA 0.1148794 0.1104303 0.1239335 0.08832275
## College_GPA
## g_irt 0.11487945
## g_fa 0.11043025
## Beta_total_score 0.12393350
## ACT_Comp 0.08832275
## College_GPA 1.00000000#groups
ols(g_fa ~ Male + White + Hispanic + Black + Asian, data = army)## Frequencies of Missing Values Due to Each Variable
## g_fa Male White Hispanic Black Asian
## 1 4 3 2 2 2
##
## Linear Regression Model
##
## ols(formula = g_fa ~ Male + White + Hispanic + Black + Asian,
## data = army)
##
##
## Model Likelihood Discrimination
## Ratio Test Indexes
## Obs 203 LR chi2 23.24 R2 0.108
## sigma0.9396 d.f. 5 R2 adj 0.086
## d.f. 197 Pr(> chi2) 0.0003 g 0.263
##
## Residuals
##
## Min 1Q Median 3Q Max
## -2.72600 -0.54600 0.09526 0.64434 2.15791
##
##
## Coef S.E. t Pr(>|t|)
## Intercept -0.7818 0.2730 -2.86 0.0046
## Male 0.1202 0.1339 0.90 0.3702
## White 0.8407 0.2625 3.20 0.0016
## Hispanic -0.1720 0.1982 -0.87 0.3865
## Black -0.6733 0.4265 -1.58 0.1160
## Asian 0.3886 0.3908 0.99 0.3213
## Seems that the ordinary factor analysis ones are better here, perhaps due to item coding issues. Group differences seem normal and we can see some correlations to criterion variables as expected – small due to range restriction perhaps / low effort.