Main analyses
Main analyses.
#cognitive data
fa = fa(data[1:5])
fa
## Factor Analysis using method = minres
## Call: fa(r = data[1:5])
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## T1 0.40 0.1568 0.84 1
## T2 0.10 0.0096 0.99 1
## T3 0.46 0.2077 0.79 1
## T4 0.93 0.8621 0.14 1
## T5 0.92 0.8399 0.16 1
##
## MR1
## SS loadings 2.08
## 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 10 and the objective function was 2.9 with Chi Square of 86
## The degrees of freedom for the model are 5 and the objective function was 1.1
##
## The root mean square of the residuals (RMSR) is 0.21
## The df corrected root mean square of the residuals is 0.29
##
## The harmonic number of observations is 33 with the empirical chi square 28 with prob < 3.3e-05
## The total number of observations was 33 with Likelihood Chi Square = 33 with prob < 3.4e-06
##
## Tucker Lewis Index of factoring reliability = 0.23
## RMSEA index = 0.18 and the 90 % confidence intervals are 0.18 0.55
## BIC = 16
## Fit based upon off diagonal values = 0.78
## Measures of factor score adequacy
## MR1
## Correlation of scores with factors 0.96
## Multiple R square of scores with factors 0.92
## Minimum correlation of possible factor scores 0.83
data["G"] = as.numeric(fa$scores)
#S data
fa2 = fa(data[7:14])
fa2
## Factor Analysis using method = minres
## Call: fa(r = data[7:14])
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## Lit 0.79 0.626 0.37 1
## II 0.36 0.130 0.87 1
## TI 0.89 0.799 0.20 1
## GDP 0.76 0.578 0.42 1
## IMR -0.92 0.850 0.15 1
## CMR -0.85 0.721 0.28 1
## FER -0.84 0.699 0.30 1
## LE 0.14 0.019 0.98 1
##
## MR1
## SS loadings 4.42
## Proportion Var 0.55
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 28 and the objective function was 6.2 with Chi Square of 177
## The degrees of freedom for the model are 20 and the objective function was 1.2
##
## The root mean square of the residuals (RMSR) is 0.09
## The df corrected root mean square of the residuals is 0.1
##
## The harmonic number of observations is 33 with the empirical chi square 13 with prob < 0.86
## The total number of observations was 33 with Likelihood Chi Square = 33 with prob < 0.038
##
## Tucker Lewis Index of factoring reliability = 0.88
## RMSEA index = 0.02 and the 90 % confidence intervals are 0.02 0.22
## BIC = -37
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## MR1
## Correlation of scores with factors 0.97
## Multiple R square of scores with factors 0.95
## Minimum correlation of possible factor scores 0.89
data["S"] = as.numeric(fa2$scores)
#Pearson results
(data_cors = wtd.cors(data))
## T1 T2 T3 T4 T5 CA Lit II TI GDP
## T1 1.000 0.049 0.411 0.352 0.344 0.65 0.51 0.525 0.276 0.503
## T2 0.049 1.000 0.640 -0.028 0.146 0.42 -0.19 0.092 -0.491 -0.365
## T3 0.411 0.640 1.000 0.411 0.376 0.73 0.29 0.242 0.023 0.195
## T4 0.352 -0.028 0.411 1.000 0.871 0.80 0.71 0.356 0.442 0.425
## T5 0.344 0.146 0.376 0.871 1.000 0.80 0.53 0.480 0.398 0.316
## CA 0.654 0.422 0.728 0.796 0.804 1.00 0.56 0.524 0.172 0.332
## Lit 0.507 -0.193 0.288 0.713 0.534 0.56 1.00 0.326 0.615 0.539
## II 0.525 0.092 0.242 0.356 0.480 0.52 0.33 1.000 0.277 0.422
## TI 0.276 -0.491 0.023 0.442 0.398 0.17 0.62 0.277 1.000 0.717
## GDP 0.503 -0.365 0.195 0.425 0.316 0.33 0.54 0.422 0.717 1.000
## IMR -0.359 0.337 -0.179 -0.638 -0.530 -0.40 -0.81 -0.277 -0.810 -0.719
## CMR -0.436 0.160 -0.270 -0.520 -0.511 -0.41 -0.66 -0.541 -0.786 -0.661
## FER -0.277 0.362 -0.093 -0.594 -0.513 -0.31 -0.69 -0.118 -0.798 -0.549
## LE -0.190 -0.044 0.066 0.021 0.011 -0.03 0.13 -0.147 0.154 0.037
## LAT -0.266 0.143 -0.142 -0.548 -0.478 -0.44 -0.31 -0.289 -0.308 -0.335
## CL -0.404 0.169 -0.224 -0.612 -0.600 -0.50 -0.33 -0.428 -0.497 -0.594
## MS -0.335 0.246 0.037 -0.282 -0.175 -0.33 -0.28 -0.264 -0.031 -0.230
## G 0.414 0.102 0.476 0.970 0.957 0.87 0.66 0.446 0.425 0.401
## S 0.421 -0.371 0.183 0.632 0.543 0.40 0.81 0.370 0.919 0.781
## IMR CMR FER LE LAT CL MS G S
## T1 -0.36 -0.436 -0.277 -0.190 -0.266 -0.404 -0.335 0.414 0.421
## T2 0.34 0.160 0.362 -0.044 0.143 0.169 0.246 0.102 -0.371
## T3 -0.18 -0.270 -0.093 0.066 -0.142 -0.224 0.037 0.476 0.183
## T4 -0.64 -0.520 -0.594 0.021 -0.548 -0.612 -0.282 0.970 0.632
## T5 -0.53 -0.511 -0.513 0.011 -0.478 -0.600 -0.175 0.957 0.543
## CA -0.40 -0.412 -0.315 -0.030 -0.436 -0.502 -0.325 0.867 0.402
## Lit -0.81 -0.657 -0.690 0.128 -0.309 -0.329 -0.282 0.661 0.813
## II -0.28 -0.541 -0.118 -0.147 -0.289 -0.428 -0.264 0.446 0.370
## TI -0.81 -0.786 -0.798 0.154 -0.308 -0.497 -0.031 0.425 0.919
## GDP -0.72 -0.661 -0.549 0.037 -0.335 -0.594 -0.230 0.401 0.781
## IMR 1.00 0.744 0.761 -0.176 0.342 0.473 0.118 -0.604 -0.947
## CMR 0.74 1.000 0.718 -0.074 0.287 0.542 -0.146 -0.543 -0.872
## FER 0.76 0.718 1.000 -0.059 0.227 0.425 0.016 -0.564 -0.859
## LE -0.18 -0.074 -0.059 1.000 0.036 0.154 -0.070 0.012 0.142
## LAT 0.34 0.287 0.227 0.036 1.000 0.785 0.198 -0.528 -0.348
## CL 0.47 0.542 0.425 0.154 0.785 1.000 0.009 -0.628 -0.541
## MS 0.12 -0.146 0.016 -0.070 0.198 0.009 1.000 -0.240 -0.086
## G -0.60 -0.543 -0.564 0.012 -0.528 -0.628 -0.240 1.000 0.610
## S -0.95 -0.872 -0.859 0.142 -0.348 -0.541 -0.086 0.610 1.000
(data_cors_spearman = cor_matrix(data, rank_order = T))
## T1 T2 T3 T4 T5 CA Lit II TI GDP
## T1 1.000 0.049 0.411 0.352 0.34 0.592 0.50 0.5158 0.309 0.53
## T2 0.049 1.000 0.640 -0.028 0.15 0.474 -0.16 -0.0239 -0.365 -0.38
## T3 0.411 0.640 1.000 0.411 0.38 0.719 0.31 0.1517 0.079 0.17
## T4 0.352 -0.028 0.411 1.000 0.87 0.788 0.73 0.3501 0.429 0.43
## T5 0.344 0.146 0.376 0.871 1.00 0.795 0.55 0.4686 0.438 0.39
## CA 0.592 0.474 0.719 0.788 0.80 1.000 0.55 0.3998 0.179 0.27
## Lit 0.500 -0.157 0.311 0.726 0.55 0.552 1.00 0.3570 0.561 0.53
## II 0.516 -0.024 0.152 0.350 0.47 0.400 0.36 1.0000 0.452 0.54
## TI 0.309 -0.365 0.079 0.429 0.44 0.179 0.56 0.4515 1.000 0.75
## GDP 0.527 -0.382 0.166 0.429 0.39 0.271 0.53 0.5404 0.754 1.00
## IMR -0.381 0.271 -0.243 -0.633 -0.54 -0.427 -0.79 -0.3934 -0.725 -0.69
## CMR -0.452 0.140 -0.288 -0.519 -0.51 -0.419 -0.68 -0.5650 -0.789 -0.68
## FER -0.409 0.223 -0.068 -0.528 -0.50 -0.382 -0.62 -0.2734 -0.693 -0.54
## LE 0.171 -0.203 0.169 0.476 0.38 0.274 0.70 0.1034 0.542 0.38
## LAT -0.251 0.077 -0.193 -0.523 -0.43 -0.429 -0.25 -0.2228 -0.246 -0.27
## CL -0.404 0.169 -0.224 -0.612 -0.60 -0.493 -0.33 -0.4400 -0.539 -0.62
## MS -0.033 0.227 -0.071 -0.217 -0.11 -0.038 -0.23 -0.0029 -0.097 -0.23
## G 0.380 0.069 0.444 0.971 0.94 0.840 0.67 0.4080 0.413 0.42
## S 0.486 -0.301 0.227 0.600 0.54 0.401 0.80 0.5511 0.875 0.81
## IMR CMR FER LE LAT CL MS G S
## T1 -0.38 -0.452 -0.409 0.171 -0.251 -0.40 -0.0330 0.380 0.49
## T2 0.27 0.140 0.223 -0.203 0.077 0.17 0.2272 0.069 -0.30
## T3 -0.24 -0.288 -0.068 0.169 -0.193 -0.22 -0.0711 0.444 0.23
## T4 -0.63 -0.519 -0.528 0.476 -0.523 -0.61 -0.2172 0.971 0.60
## T5 -0.54 -0.507 -0.503 0.376 -0.435 -0.60 -0.1062 0.937 0.54
## CA -0.43 -0.419 -0.382 0.274 -0.429 -0.49 -0.0383 0.840 0.40
## Lit -0.79 -0.682 -0.619 0.700 -0.248 -0.33 -0.2276 0.675 0.80
## II -0.39 -0.565 -0.273 0.103 -0.223 -0.44 -0.0029 0.408 0.55
## TI -0.73 -0.789 -0.693 0.542 -0.246 -0.54 -0.0968 0.413 0.88
## GDP -0.69 -0.676 -0.535 0.383 -0.274 -0.62 -0.2285 0.420 0.81
## IMR 1.00 0.704 0.612 -0.762 0.248 0.43 0.2949 -0.611 -0.90
## CMR 0.70 1.000 0.735 -0.481 0.249 0.54 -0.0881 -0.533 -0.88
## FER 0.61 0.735 1.000 -0.423 0.188 0.47 -0.0070 -0.509 -0.74
## LE -0.76 -0.481 -0.423 1.000 -0.034 -0.10 -0.3038 0.425 0.67
## LAT 0.25 0.249 0.188 -0.034 1.000 0.79 -0.1384 -0.546 -0.25
## CL 0.43 0.543 0.467 -0.103 0.787 1.00 -0.2018 -0.635 -0.50
## MS 0.29 -0.088 -0.007 -0.304 -0.138 -0.20 1.0000 -0.158 -0.20
## G -0.61 -0.533 -0.509 0.425 -0.546 -0.64 -0.1579 1.000 0.58
## S -0.90 -0.883 -0.743 0.669 -0.249 -0.50 -0.2009 0.584 1.00
#discrepancies
(r_disc = data_cors - data_cors_spearman)
## T1 T2 T3 T4 T5 CA Lit
## T1 1.7e-14 0.0e+00 0.0e+00 0.0e+00 0.0e+00 6.2e-02 7.1e-03
## T2 4.6e-14 1.3e-15 0.0e+00 0.0e+00 0.0e+00 -5.2e-02 -3.7e-02
## T3 4.9e-14 0.0e+00 -4.4e-14 0.0e+00 0.0e+00 9.0e-03 -2.3e-02
## T4 0.0e+00 0.0e+00 -7.2e-14 1.2e-14 0.0e+00 7.8e-03 -1.3e-02
## T5 4.6e-14 0.0e+00 0.0e+00 0.0e+00 -6.5e-14 8.5e-03 -1.2e-02
## CA 6.2e-02 -5.2e-02 9.0e-03 7.8e-03 8.5e-03 2.8e-14 1.1e-02
## Lit 7.1e-03 -3.7e-02 -2.3e-02 -1.3e-02 -1.2e-02 1.1e-02 -3.5e-14
## II 9.1e-03 1.2e-01 9.1e-02 6.2e-03 1.2e-02 1.2e-01 -3.1e-02
## TI -3.3e-02 -1.3e-01 -5.6e-02 1.3e-02 -4.0e-02 -7.2e-03 5.4e-02
## GDP -2.4e-02 1.7e-02 2.9e-02 -4.8e-03 -7.3e-02 6.1e-02 1.0e-02
## IMR 2.1e-02 6.6e-02 6.4e-02 -4.8e-03 8.5e-03 2.8e-02 -1.7e-02
## CMR 1.6e-02 2.0e-02 1.8e-02 -4.2e-04 -3.6e-03 7.3e-03 2.5e-02
## FER 1.3e-01 1.4e-01 -2.6e-02 -6.6e-02 -9.9e-03 6.7e-02 -7.1e-02
## LE -3.6e-01 1.6e-01 -1.0e-01 -4.6e-01 -3.6e-01 -3.0e-01 -5.7e-01
## LAT -1.5e-02 6.6e-02 5.1e-02 -2.6e-02 -4.3e-02 -6.7e-03 -6.1e-02
## CL 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 -9.0e-03 1.7e-03
## MS -3.0e-01 1.8e-02 1.1e-01 -6.5e-02 -6.8e-02 -2.9e-01 -5.4e-02
## G 3.3e-02 3.3e-02 3.2e-02 -1.5e-03 2.1e-02 2.7e-02 -1.3e-02
## S -6.5e-02 -7.1e-02 -4.4e-02 3.3e-02 5.3e-03 1.8e-03 1.3e-02
## II TI GDP IMR CMR FER LE
## T1 9.1e-03 -3.3e-02 -2.4e-02 2.1e-02 1.6e-02 1.3e-01 -3.6e-01
## T2 1.2e-01 -1.3e-01 1.7e-02 6.6e-02 2.0e-02 1.4e-01 1.6e-01
## T3 9.1e-02 -5.6e-02 2.9e-02 6.4e-02 1.8e-02 -2.6e-02 -1.0e-01
## T4 6.2e-03 1.3e-02 -4.8e-03 -4.8e-03 -4.2e-04 -6.6e-02 -4.6e-01
## T5 1.2e-02 -4.0e-02 -7.3e-02 8.5e-03 -3.6e-03 -9.9e-03 -3.6e-01
## CA 1.2e-01 -7.2e-03 6.1e-02 2.8e-02 7.3e-03 6.7e-02 -3.0e-01
## Lit -3.1e-02 5.4e-02 1.0e-02 -1.7e-02 2.5e-02 -7.1e-02 -5.7e-01
## II 2.2e-16 -1.7e-01 -1.2e-01 1.2e-01 2.4e-02 1.5e-01 -2.5e-01
## TI -1.7e-01 -5.1e-15 -3.6e-02 -8.5e-02 2.7e-03 -1.0e-01 -3.9e-01
## GDP -1.2e-01 -3.6e-02 -5.6e-16 -2.5e-02 1.5e-02 -1.3e-02 -3.5e-01
## IMR 1.2e-01 -8.5e-02 -2.5e-02 -2.7e-15 4.1e-02 1.5e-01 5.9e-01
## CMR 2.4e-02 2.7e-03 1.5e-02 4.1e-02 6.7e-16 -1.7e-02 4.1e-01
## FER 1.5e-01 -1.0e-01 -1.3e-02 1.5e-01 -1.7e-02 5.6e-15 3.6e-01
## LE -2.5e-01 -3.9e-01 -3.5e-01 5.9e-01 4.1e-01 3.6e-01 -1.2e-14
## LAT -6.6e-02 -6.2e-02 -6.1e-02 9.4e-02 3.8e-02 3.9e-02 7.0e-02
## CL 1.2e-02 4.3e-02 2.4e-02 4.3e-02 -5.7e-04 -4.3e-02 2.6e-01
## MS -2.6e-01 6.6e-02 -1.4e-03 -1.8e-01 -5.8e-02 2.3e-02 2.3e-01
## G 3.8e-02 1.2e-02 -1.9e-02 6.9e-03 -9.6e-03 -5.5e-02 -4.1e-01
## S -1.8e-01 4.3e-02 -3.2e-02 -4.5e-02 1.1e-02 -1.2e-01 -5.3e-01
## LAT CL MS G S
## T1 -1.5e-02 0.0e+00 -3.0e-01 3.3e-02 -0.0648
## T2 6.6e-02 0.0e+00 1.8e-02 3.3e-02 -0.0707
## T3 5.1e-02 0.0e+00 1.1e-01 3.2e-02 -0.0438
## T4 -2.6e-02 0.0e+00 -6.5e-02 -1.5e-03 0.0325
## T5 -4.3e-02 0.0e+00 -6.8e-02 2.1e-02 0.0053
## CA -6.7e-03 -9.0e-03 -2.9e-01 2.7e-02 0.0018
## Lit -6.1e-02 1.7e-03 -5.4e-02 -1.3e-02 0.0134
## II -6.6e-02 1.2e-02 -2.6e-01 3.8e-02 -0.1809
## TI -6.2e-02 4.3e-02 6.6e-02 1.2e-02 0.0433
## GDP -6.1e-02 2.4e-02 -1.4e-03 -1.9e-02 -0.0323
## IMR 9.4e-02 4.3e-02 -1.8e-01 6.9e-03 -0.0446
## CMR 3.8e-02 -5.7e-04 -5.8e-02 -9.6e-03 0.0107
## FER 3.9e-02 -4.3e-02 2.3e-02 -5.5e-02 -0.1161
## LE 7.0e-02 2.6e-01 2.3e-01 -4.1e-01 -0.5268
## LAT 2.2e-15 -2.1e-03 3.4e-01 1.7e-02 -0.0987
## CL -2.1e-03 4.4e-16 2.1e-01 7.1e-03 -0.0378
## MS 3.4e-01 2.1e-01 6.7e-16 -8.2e-02 0.1147
## G 1.7e-02 7.1e-03 -8.2e-02 2.2e-16 0.0258
## S -9.9e-02 -3.8e-02 1.1e-01 2.6e-02 0.0000
## MCV
#MCV on G
fa_Jensens_method(fa, data, criterion = "S", loading_reversing = F)
## Using Pearson correlations for the criterion-indicators relationships.
silence(ggsave("MCV_G.png"))
#MCV on S
fa_Jensens_method(fa2, data, criterion = "G", loading_reversing = F)
## Using Pearson correlations for the criterion-indicators relationships.
silence(ggsave("MCV_S.png"))
#Double MCV
#cor(results$r[1:14, 18], results$r[1:14, 19])
data_frame(
G_cors = data_cors[1:14, 18],
S_cors = data_cors[1:14, 19],
var = names(data)[1:14]
) %>%
GG_scatter("G_cors", "S_cors", case_names_vector = "var") +
xlab("G x variable correlation") +
ylab("S x variable correlation")
silence(ggsave("double_MCV.png"))
#Plots
GG_scatter(data, "G", "S") +
xlab("G, extracted from 5 indicators") +
ylab("S, extracted from 11 indicates") +
xlim(-2, 2)
## Warning: Removed 1 rows containing non-finite values (stat_smooth).
## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_text).
silence(ggsave("G_S.png"))