EFA analysis, Examiner
Mark Sanderson-cimino
2023-04-20
Outline
- Descriptives (raw data)
- Binning (regular + transformed)
- EFA models (regular + transformed)
- IRT models (regular + transformed)
- CFA models
1. Descriptives (raw data)
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 289 15 5 15 15 4 0 27 27 0 0 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 227 7334 1378 7630 7460 1260 4000 9820 5820 -1 0 91
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 297 7051 1505 7360 7183 1245 0 10000 10000 -1 2 87
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1228 41 13 44 43 10 0 68 68 -1 1 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 839 18 7 18 18 7 1 38 37 0 0 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 805 12 5 13 12 6 1 33 32 0 0 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 794 13 6 13 13 6 1 35 34 0 0 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 789 12 5 13 12 6 1 28 27 0 0 0Skewness
Provides skew parameter for each variable. “|minimum|” designates the lowest skew value after transformation
## raw square.root log+10 1/x+100 squared exp |minimum|
## rundots -0.94 -2.59 -3.47 3.42 0.42 NaN 0.42
## dotcount -0.23 -1.77 -1.11 0.52 0.71 12.03 0.23
## flanker -0.76 -0.90 -1.04 1.33 -0.33 NaN 0.33
## setshift -1.08 -2.53 -10.33 16.89 -0.28 NaN 0.28
## match -1.02 -1.84 -2.06 1.57 -0.07 28.90 0.07
## animals -0.07 -0.67 -0.76 0.38 0.92 23.28 0.07
## veg 0.09 -0.46 -0.46 0.13 1.24 28.25 0.09
## fwords 0.09 -0.53 -0.55 0.17 1.37 27.38 0.09
## lwords 0.09 -0.51 -0.50 0.15 1.16 13.70 0.092. Binning (regular + transformed))
A. Regular data
Lookup table for Binned data. Provides the boundaries for each bin (row) for each variable (column)
## recode_score min_rundots max_rundots min_dotcount max_dotcount min_flanker
## 1 1 0 70 0 4 4000.0
## 2 2 95 140 5 6 4687.5
## 3 3 145 210 7 7 5116.0
## 4 4 215 285 8 9 5620.0
## 5 5 290 390 10 11 6135.0
## 6 6 NA NA 12 13 6680.0
## 7 7 NA NA 14 15 7230.0
## 8 8 NA NA 16 17 7737.7
## 9 9 NA NA 18 19 8290.0
## 10 10 NA NA 20 21 8810.0
## 11 11 NA NA 22 22 NA
## 12 12 NA NA 23 27 NA
## max_flanker min_setshift max_setshift min_match max_match min_animals
## 1 4380.0 0.0 2500.0 0 5 1
## 2 5049.8 2968.8 3780.0 6 10 4
## 3 5592.7 3860.0 4840.0 11 15 7
## 4 6090.0 4889.7 5950.0 16 20 10
## 5 6650.0 6015.2 7017.7 21 25 13
## 6 7180.0 7035.5 8090.0 26 31 16
## 7 7730.0 8113.1 10000.0 32 36 18
## 8 8260.0 NA NA 37 41 21
## 9 8790.0 NA NA 42 46 24
## 10 9820.0 NA NA 47 51 27
## 11 NA NA NA 52 57 30
## 12 NA NA NA 58 68 33
## max_animals min_veg max_veg min_fwords max_fwords min_lwords max_lwords
## 1 3 1 3 1 3 1 3
## 2 6 4 5 4 5 4 5
## 3 9 6 7 6 7 6 7
## 4 12 8 9 8 9 8 9
## 5 15 10 11 10 11 10 11
## 6 17 12 13 12 13 12 13
## 7 20 14 15 14 15 14 15
## 8 23 16 17 16 18 16 17
## 9 26 18 19 19 20 18 19
## 10 29 20 21 21 22 20 21
## 11 32 22 23 23 24 22 23
## 12 38 24 33 25 35 24 28B. Transformed data
Lookup table for Binned data. Provides the boundaries for each bin (row) for each variable (column)
## recode_score min_rundots max_rundots min_dotcount max_dotcount min_flanker
## 1 1 0 9025 0 4 16000000
## 2 2 12100 21025 5 6 21972656
## 3 3 22500 30625 7 7 27220219
## 4 4 32400 42025 8 9 33062500
## 5 5 44100 50625 10 11 38539264
## 6 6 52900 62500 12 13 44089600
## 7 7 65025 72900 14 15 49674304
## 8 8 75625 84100 16 17 55204900
## 9 9 87025 93025 18 19 60840000
## 10 10 96100 105625 20 21 66292164
## 11 11 108900 115600 22 22 72127652
## 12 12 119025 152100 23 27 77616100
## max_flanker min_setshift max_setshift min_match max_match min_animals
## 1 19184400 0 6250000 0 289 1
## 2 26173456 8813773 14899600 324 625 4
## 3 32718400 15444900 20531773 676 961 7
## 4 37638225 22929732 30140100 1024 1225 10
## 5 43644521 30360100 37318659 1296 1600 13
## 6 49446211 38047925 45292900 1681 1849 16
## 7 54789604 46313469 52963462 1936 2209 18
## 8 60217600 53058113 60528400 2304 2500 21
## 9 66259600 60637369 67909136 2601 2809 24
## 10 71402500 68724100 75516100 2916 3136 27
## 11 77264100 75961683 100000000 3249 3481 30
## 12 96432400 NA NA 3600 4624 33
## max_animals min_veg max_veg min_fwords max_fwords min_lwords max_lwords
## 1 3 1 3 1 3 1 3
## 2 6 4 5 4 5 4 5
## 3 9 6 7 6 7 6 7
## 4 12 8 9 8 9 8 9
## 5 15 10 11 10 11 10 11
## 6 17 12 13 12 13 12 13
## 7 20 14 15 14 15 14 15
## 8 23 16 17 16 18 16 17
## 9 26 18 19 19 20 18 19
## 10 29 20 21 21 22 20 21
## 11 32 22 23 23 24 22 23
## 12 38 24 33 25 35 24 283. EFA models (regular + transformed)
A. Regular Data
Skree plot + parallel plot
## Parallel analysis suggests that the number of factors = 4 and the number of components = 2## Call: fa.parallel(x = EFA.data)
## Parallel analysis suggests that the number of factors = 4 and the number of components = 2
##
## Eigen Values of
## Original factors Resampled data Simulated data Original components
## 1 4.11 1.01 0.43 4.61
## 2 0.77 0.28 0.10 1.32
## 3 0.23 0.17 0.06 0.87
## 4 0.13 0.10 0.04 0.68
## Resampled components Simulated components
## 1 1.44 1.13
## 2 1.25 1.09
## 3 1.13 1.05
## 4 1.06 1.02EFA model (2 factor, 3 factor, 4 factor) + path diagram
## Factor Analysis using method = pa
## Call: fa(r = EFA.data, nfactors = 2, rotate = "promax", max.iter = 100,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## rundots_r 0.65 -0.08 0.36 0.64 1.0
## dotcount_r 0.31 0.27 0.27 0.73 2.0
## flanker_r 0.89 -0.12 0.67 0.33 1.0
## match_r 0.83 0.15 0.87 0.13 1.1
## setshift_r 0.71 0.02 0.53 0.47 1.0
## animals_r 0.18 0.67 0.63 0.37 1.1
## veg_r 0.17 0.56 0.46 0.54 1.2
## fwords_r -0.15 0.92 0.69 0.31 1.1
## lwords_r -0.15 0.92 0.70 0.30 1.1
##
## PA1 PA2
## SS loadings 2.61 2.57
## Proportion Var 0.29 0.29
## Cumulative Var 0.29 0.58
## Proportion Explained 0.50 0.50
## Cumulative Proportion 0.50 1.00
##
## With factor correlations of
## PA1 PA2
## PA1 1.00 0.63
## PA2 0.63 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## df null model = 36 with the objective function = 5.25 with Chi Square = 6932.02
## df of the model are 19 and the objective function was 0.78
##
## The root mean square of the residuals (RMSR) is 0.09
## The df corrected root mean square of the residuals is 0.12
##
## The harmonic n.obs is 185 with the empirical chi square 96.4 with prob < 2.4e-12
## The total n.obs was 1326 with Likelihood Chi Square = 1032.7 with prob < 5.5e-207
##
## Tucker Lewis Index of factoring reliability = 0.721
## RMSEA index = 0.201 and the 90 % confidence intervals are 0.19 0.211
## BIC = 896.09
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1 PA2
## Correlation of (regression) scores with factors 0.96 0.95
## Multiple R square of scores with factors 0.92 0.89
## Minimum correlation of possible factor scores 0.84 0.79
## Factor Analysis using method = pa
## Call: fa(r = EFA.data, nfactors = 3, rotate = "promax", max.iter = 100,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA3 PA2 h2 u2 com
## rundots_r 0.37 0.36 -0.16 0.36 0.639 2.4
## dotcount_r 0.57 0.01 -0.01 0.33 0.672 1.0
## flanker_r -0.21 1.06 0.10 0.93 0.067 1.1
## match_r 0.63 0.43 -0.06 0.88 0.124 1.8
## setshift_r 0.06 0.65 0.12 0.54 0.457 1.1
## animals_r 0.67 -0.07 0.28 0.68 0.320 1.3
## veg_r 0.66 -0.10 0.19 0.53 0.469 1.2
## fwords_r 0.12 0.03 0.76 0.71 0.288 1.1
## lwords_r -0.01 0.09 0.89 0.83 0.166 1.0
##
## PA1 PA3 PA2
## SS loadings 2.05 2.01 1.74
## Proportion Var 0.23 0.22 0.19
## Cumulative Var 0.23 0.45 0.64
## Proportion Explained 0.35 0.35 0.30
## Cumulative Proportion 0.35 0.70 1.00
##
## With factor correlations of
## PA1 PA3 PA2
## PA1 1.00 0.64 0.57
## PA3 0.64 1.00 0.31
## PA2 0.57 0.31 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 36 with the objective function = 5.25 with Chi Square = 6932.02
## df of the model are 12 and the objective function was 0.45
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.08
##
## The harmonic n.obs is 185 with the empirical chi square 30.65 with prob < 0.0022
## The total n.obs was 1326 with Likelihood Chi Square = 587.28 with prob < 5.5e-118
##
## Tucker Lewis Index of factoring reliability = 0.749
## RMSEA index = 0.19 and the 90 % confidence intervals are 0.177 0.203
## BIC = 501
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA3 PA2
## Correlation of (regression) scores with factors 0.94 0.99 0.94
## Multiple R square of scores with factors 0.89 0.98 0.89
## Minimum correlation of possible factor scores 0.78 0.95 0.77
## Factor Analysis using method = pa
## Call: fa(r = EFA.data, nfactors = 4, rotate = "promax", max.iter = 100,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA4 PA2 PA3 h2 u2 com
## rundots_r -0.16 0.00 -0.02 1.03 0.90 0.10 1.0
## dotcount_r 0.30 -0.04 0.08 0.32 0.32 0.68 2.1
## flanker_r -0.08 0.80 0.00 0.15 0.71 0.29 1.1
## match_r 0.46 0.50 -0.10 0.16 0.83 0.17 2.3
## setshift_r -0.03 0.94 0.05 -0.15 0.74 0.26 1.1
## animals_r 1.01 -0.03 -0.02 -0.13 0.83 0.17 1.0
## veg_r 0.78 -0.02 0.00 -0.04 0.55 0.45 1.0
## fwords_r -0.14 0.00 1.14 0.04 1.13 -0.13 1.0
## lwords_r 0.27 0.05 0.57 -0.06 0.61 0.39 1.5
##
## PA1 PA4 PA2 PA3
## SS loadings 1.96 1.86 1.62 1.18
## Proportion Var 0.22 0.21 0.18 0.13
## Cumulative Var 0.22 0.42 0.60 0.74
## Proportion Explained 0.30 0.28 0.24 0.18
## Cumulative Proportion 0.30 0.58 0.82 1.00
##
## With factor correlations of
## PA1 PA4 PA2 PA3
## PA1 1.00 0.62 0.66 0.57
## PA4 0.62 1.00 0.41 0.59
## PA2 0.66 0.41 1.00 0.33
## PA3 0.57 0.59 0.33 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 36 with the objective function = 5.25 with Chi Square = 6932.02
## df of the model are 6 and the objective function was 0.18
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic n.obs is 185 with the empirical chi square 4.89 with prob < 0.56
## The total n.obs was 1326 with Likelihood Chi Square = 238.01 with prob < 1.5e-48
##
## Tucker Lewis Index of factoring reliability = 0.798
## RMSEA index = 0.171 and the 90 % confidence intervals are 0.153 0.19
## BIC = 194.87
## Fit based upon off diagonal values = 1
A. Transformed Data
Skree plot + parallel plot
## Parallel analysis suggests that the number of factors = 4 and the number of components = 2## Call: fa.parallel(x = EFA.data)
## Parallel analysis suggests that the number of factors = 4 and the number of components = 2
##
## Eigen Values of
## Original factors Resampled data Simulated data Original components
## 1 3.98 0.90 0.39 4.49
## 2 0.82 0.25 0.10 1.40
## 3 0.25 0.16 0.07 0.91
## 4 0.12 0.09 0.04 0.68
## Resampled components Simulated components
## 1 1.35 1.13
## 2 1.22 1.09
## 3 1.13 1.05
## 4 1.06 1.03EFA model (2 factor, 3 factor, 4 factor) + path diagram
#------------------# EFA #------------------#
fa.none <- fa(r=EFA.data,
nfactors = 2,
# covar = FALSE, SMC = TRUE,
fm= "pa", # type of factor analysis we want to use (“pa” is principal axis factoring)
max.iter=100, # (50 is the default, but we have changed it to 100
rotate= "promax") # none rotation
print(fa.none)## Factor Analysis using method = pa
## Call: fa(r = EFA.data, nfactors = 2, rotate = "promax", max.iter = 100,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## rundots_r -0.17 0.68 0.35 0.65 1.1
## dotcount_r 0.27 0.30 0.26 0.74 2.0
## flanker_r -0.06 0.82 0.61 0.39 1.0
## match_r 0.17 0.81 0.86 0.14 1.1
## setshift_r 0.07 0.67 0.51 0.49 1.0
## animals_r 0.67 0.19 0.64 0.36 1.2
## veg_r 0.57 0.17 0.46 0.54 1.2
## fwords_r 0.93 -0.17 0.71 0.29 1.1
## lwords_r 0.93 -0.16 0.71 0.29 1.1
##
## PA1 PA2
## SS loadings 2.66 2.46
## Proportion Var 0.30 0.27
## Cumulative Var 0.30 0.57
## Proportion Explained 0.52 0.48
## Cumulative Proportion 0.52 1.00
##
## With factor correlations of
## PA1 PA2
## PA1 1.0 0.6
## PA2 0.6 1.0
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## df null model = 36 with the objective function = 5.05 with Chi Square = 6669.3
## df of the model are 19 and the objective function was 0.72
##
## The root mean square of the residuals (RMSR) is 0.09
## The df corrected root mean square of the residuals is 0.12
##
## The harmonic n.obs is 185 with the empirical chi square 96.96 with prob < 1.9e-12
## The total n.obs was 1326 with Likelihood Chi Square = 955.78 with prob < 1.4e-190
##
## Tucker Lewis Index of factoring reliability = 0.732
## RMSEA index = 0.193 and the 90 % confidence intervals are 0.183 0.203
## BIC = 819.17
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1 PA2
## Correlation of (regression) scores with factors 0.95 0.95
## Multiple R square of scores with factors 0.90 0.91
## Minimum correlation of possible factor scores 0.79 0.81fa.diagram(fa.none)
fa.none <- fa(r=EFA.data,
nfactors = 3,
# covar = FALSE, SMC = TRUE,
fm= "pa", # type of factor analysis we want to use (“pa” is principal axis factoring)
max.iter=100, # (50 is the default, but we have changed it to 100
rotate= "promax") # none rotation
print(fa.none)## Factor Analysis using method = pa
## Call: fa(r = EFA.data, nfactors = 3, rotate = "promax", max.iter = 100,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA3 PA2 h2 u2 com
## rundots_r -0.26 0.30 0.47 0.38 0.62 2.3
## dotcount_r 0.05 -0.06 0.60 0.35 0.65 1.0
## flanker_r 0.06 0.90 -0.07 0.78 0.22 1.0
## match_r 0.04 0.44 0.56 0.85 0.15 1.9
## setshift_r 0.17 0.74 -0.05 0.61 0.39 1.1
## animals_r 0.41 -0.05 0.57 0.69 0.31 1.8
## veg_r 0.33 -0.07 0.53 0.51 0.49 1.7
## fwords_r 0.82 0.05 0.02 0.72 0.28 1.0
## lwords_r 0.87 0.10 -0.05 0.78 0.22 1.0
##
## PA1 PA3 PA2
## SS loadings 2.04 1.85 1.78
## Proportion Var 0.23 0.21 0.20
## Cumulative Var 0.23 0.43 0.63
## Proportion Explained 0.36 0.33 0.31
## Cumulative Proportion 0.36 0.69 1.00
##
## With factor correlations of
## PA1 PA3 PA2
## PA1 1.00 0.31 0.52
## PA3 0.31 1.00 0.62
## PA2 0.52 0.62 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 36 with the objective function = 5.05 with Chi Square = 6669.3
## df of the model are 12 and the objective function was 0.4
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.09
##
## The harmonic n.obs is 185 with the empirical chi square 35.07 with prob < 0.00046
## The total n.obs was 1326 with Likelihood Chi Square = 530.71 with prob < 6.4e-106
##
## Tucker Lewis Index of factoring reliability = 0.765
## RMSEA index = 0.181 and the 90 % confidence intervals are 0.168 0.194
## BIC = 444.43
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1 PA3 PA2
## Correlation of (regression) scores with factors 0.94 0.94 0.92
## Multiple R square of scores with factors 0.88 0.89 0.85
## Minimum correlation of possible factor scores 0.75 0.77 0.70fa.diagram(fa.none)
fa.none <- fa(r=EFA.data,
nfactors = 4,
# covar = FALSE, SMC = TRUE,
fm= "pa", # type of factor analysis we want to use (“pa” is principal axis factoring)
max.iter=100, # (50 is the default, but we have changed it to 100
rotate= "promax") # none rotation
print(fa.none)## Factor Analysis using method = pa
## Call: fa(r = EFA.data, nfactors = 4, rotate = "promax", max.iter = 100,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA4 PA2 PA3 h2 u2 com
## rundots_r -0.18 0.05 -0.06 0.98 0.84 0.16 1.1
## dotcount_r 0.28 -0.09 0.11 0.37 0.34 0.66 2.2
## flanker_r -0.05 0.76 0.00 0.14 0.66 0.34 1.1
## match_r 0.46 0.49 -0.11 0.16 0.82 0.18 2.3
## setshift_r -0.05 0.92 0.07 -0.12 0.75 0.25 1.0
## animals_r 1.01 -0.03 -0.03 -0.12 0.84 0.16 1.0
## veg_r 0.77 0.00 0.00 -0.06 0.55 0.45 1.0
## fwords_r -0.15 0.01 1.14 0.03 1.12 -0.12 1.0
## lwords_r 0.26 0.06 0.58 -0.09 0.61 0.39 1.5
##
## PA1 PA4 PA2 PA3
## SS loadings 1.95 1.81 1.64 1.13
## Proportion Var 0.22 0.20 0.18 0.13
## Cumulative Var 0.22 0.42 0.60 0.73
## Proportion Explained 0.30 0.28 0.25 0.17
## Cumulative Proportion 0.30 0.58 0.83 1.00
##
## With factor correlations of
## PA1 PA4 PA2 PA3
## PA1 1.00 0.60 0.67 0.54
## PA4 0.60 1.00 0.39 0.55
## PA2 0.67 0.39 1.00 0.28
## PA3 0.54 0.55 0.28 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 36 with the objective function = 5.05 with Chi Square = 6669.3
## df of the model are 6 and the objective function was 0.14
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic n.obs is 185 with the empirical chi square 4.07 with prob < 0.67
## The total n.obs was 1326 with Likelihood Chi Square = 179.63 with prob < 4.1e-36
##
## Tucker Lewis Index of factoring reliability = 0.843
## RMSEA index = 0.148 and the 90 % confidence intervals are 0.13 0.167
## BIC = 136.49
## Fit based upon off diagonal values = 1fa.diagram(fa.none)
5. CFA models
3 factor model: Fluency factor: animals and vegitables, fwords and lwords Procesing speed/inhib: set shifting, flanker, match Working memory: running dots, dot count
Results: standard model, no covariance between fluency items
## lavaan 0.6.15 ended normally after 102 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 32
##
## Used Total
## Number of observations 1324 1326
## Number of missing patterns 71
##
## Model Test User Model:
##
## Test statistic 43.062
## Degrees of freedom 22
## P-value (Chi-square) 0.005## lavaan 0.6.15 ended normally after 88 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 30
##
## Used Total
## Number of observations 1324 1326
## Number of missing patterns 71
##
## Model Test User Model:
##
## Test statistic 366.351
## Degrees of freedom 24
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2646.284
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.869
## Tucker-Lewis Index (TLI) 0.803
##
## Robust Comparative Fit Index (CFI) 0.894
## Robust Tucker-Lewis Index (TLI) 0.842
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11454.478
## Loglikelihood unrestricted model (H1) -11271.303
##
## Akaike (AIC) 22968.957
## Bayesian (BIC) 23124.609
## Sample-size adjusted Bayesian (SABIC) 23029.313
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.104
## 90 Percent confidence interval - lower 0.095
## 90 Percent confidence interval - upper 0.113
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Robust RMSEA 0.153
## 90 Percent confidence interval - lower 0.121
## 90 Percent confidence interval - upper 0.187
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.059
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## Flu.factor =~
## animals_r 1.000
## veg_r 0.910 0.040 22.971 0.000
## fwords_r 0.938 0.051 18.541 0.000
## lwords_r 0.980 0.052 18.989 0.000
## PSinhib.factor =~
## flanker_r 1.000
## match_r 1.070 0.080 13.455 0.000
## setshift_r 0.542 0.044 12.390 0.000
## Wrkmem.facotr =~
## rundots_r 1.000
## dotcount_r 2.188 0.306 7.146 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## Flu.factor ~~
## PSinhib.factor 3.356 0.315 10.658 0.000
## Wrkmem.facotr 0.964 0.143 6.757 0.000
## PSinhib.factor ~~
## Wrkmem.facotr 1.393 0.179 7.801 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .animals_r 6.745 0.082 82.167 0.000
## .veg_r 6.000 0.086 69.638 0.000
## .fwords_r 6.335 0.086 74.001 0.000
## .lwords_r 6.083 0.088 69.430 0.000
## .flanker_r 6.481 0.130 49.785 0.000
## .match_r 8.449 0.070 120.046 0.000
## .setshift_r 5.251 0.066 79.570 0.000
## .rundots_r 3.580 0.056 63.871 0.000
## .dotcount_r 6.999 0.137 51.028 0.000
## Flu.factor 0.000
## PSinhib.factor 0.000
## Wrkmem.facotr 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .animals_r 1.968 0.181 10.852 0.000
## .veg_r 3.041 0.202 15.031 0.000
## .fwords_r 2.727 0.223 12.210 0.000
## .lwords_r 2.701 0.231 11.693 0.000
## .flanker_r 2.254 0.322 6.998 0.000
## .match_r 1.004 0.225 4.461 0.000
## .setshift_r 0.728 0.089 8.186 0.000
## .rundots_r 0.533 0.080 6.700 0.000
## .dotcount_r 3.911 0.447 8.747 0.000
## Flu.factor 4.392 0.320 13.745 0.000
## PSinhib.factor 4.667 0.629 7.422 0.000
## Wrkmem.facotr 0.542 0.110 4.950 0.000Results: covaraince model, covariance between fluency items (animal + vegitable; l words + f words)
## lavaan 0.6.15 ended normally after 102 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 32
##
## Used Total
## Number of observations 1324 1326
## Number of missing patterns 71
##
## Model Test User Model:
##
## Test statistic 43.062
## Degrees of freedom 22
## P-value (Chi-square) 0.005## lavaan 0.6.15 ended normally after 102 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 32
##
## Used Total
## Number of observations 1324 1326
## Number of missing patterns 71
##
## Model Test User Model:
##
## Test statistic 43.062
## Degrees of freedom 22
## P-value (Chi-square) 0.005
##
## Model Test Baseline Model:
##
## Test statistic 2646.284
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.992
## Tucker-Lewis Index (TLI) 0.987
##
## Robust Comparative Fit Index (CFI) 0.968
## Robust Tucker-Lewis Index (TLI) 0.948
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11292.833
## Loglikelihood unrestricted model (H1) -11271.303
##
## Akaike (AIC) 22649.667
## Bayesian (BIC) 22815.696
## Sample-size adjusted Bayesian (SABIC) 22714.047
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.027
## 90 Percent confidence interval - lower 0.015
## 90 Percent confidence interval - upper 0.039
## P-value H_0: RMSEA <= 0.050 1.000
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.088
## 90 Percent confidence interval - lower 0.045
## 90 Percent confidence interval - upper 0.129
## P-value H_0: Robust RMSEA <= 0.050 0.070
## P-value H_0: Robust RMSEA >= 0.080 0.652
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.040
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## Flu.factor =~
## animals_r 1.000
## veg_r 0.888 0.038 23.477 0.000
## fwords_r 0.707 0.044 16.151 0.000
## lwords_r 0.744 0.045 16.477 0.000
## PSinhib.factor =~
## flanker_r 1.000
## match_r 1.076 0.080 13.508 0.000
## setshift_r 0.538 0.044 12.264 0.000
## Wrkmem.facotr =~
## rundots_r 1.000
## dotcount_r 2.199 0.307 7.169 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .animals_r ~~
## .veg_r -0.202 0.220 -0.920 0.357
## .fwords_r ~~
## .lwords_r 2.552 0.207 12.346 0.000
## Flu.factor ~~
## PSinhib.factor 3.754 0.331 11.352 0.000
## Wrkmem.facotr 1.079 0.151 7.139 0.000
## PSinhib.factor ~~
## Wrkmem.facotr 1.396 0.179 7.810 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .animals_r 6.767 0.080 84.283 0.000
## .veg_r 6.003 0.085 70.401 0.000
## .fwords_r 6.322 0.087 72.615 0.000
## .lwords_r 6.066 0.089 68.174 0.000
## .flanker_r 6.474 0.130 49.685 0.000
## .match_r 8.448 0.070 120.142 0.000
## .setshift_r 5.249 0.066 79.328 0.000
## .rundots_r 3.579 0.056 63.976 0.000
## .dotcount_r 6.994 0.137 50.984 0.000
## Flu.factor 0.000
## PSinhib.factor 0.000
## Wrkmem.facotr 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .animals_r 1.072 0.245 4.373 0.000
## .veg_r 2.552 0.270 9.444 0.000
## .fwords_r 3.971 0.232 17.093 0.000
## .lwords_r 3.999 0.240 16.652 0.000
## .flanker_r 2.298 0.322 7.133 0.000
## .match_r 0.939 0.216 4.351 0.000
## .setshift_r 0.749 0.088 8.466 0.000
## .rundots_r 0.534 0.079 6.747 0.000
## .dotcount_r 3.906 0.447 8.744 0.000
## Flu.factor 5.248 0.375 13.991 0.000
## PSinhib.factor 4.668 0.631 7.393 0.000
## Wrkmem.facotr 0.542 0.109 4.964 0.000Results: model comparison; Covaraince model has better fit
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit.cov 22 22650 22816 43.062
## fit.a 24 22969 23125 366.351 323.29 0.34833 2 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1