LET Youth CFA
Levi Brackman
28 July 2015
1.There is not enough purpose in my life. 2. To me, the things I do are all worthwhile. 3. Most of what I do seems trivial and unimportant to me. 4. I value my activities a lot. 5. I don’t care very much about the things I do. 2 6. I have lots of reasons for living.
library(lavaan)## This is lavaan 0.5-18
## lavaan is BETA software! Please report any bugs.library(semPlot)
library(dplyr)##
## Attaching package: 'dplyr'
##
## The following objects are masked from 'package:stats':
##
## filter, lag
##
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(GPArotation)
library(psych)
library(car)##
## Attaching package: 'car'
##
## The following object is masked from 'package:psych':
##
## logitlibrary(ggplot2)##
## Attaching package: 'ggplot2'
##
## The following object is masked from 'package:psych':
##
## %+%library(GGally)##
## Attaching package: 'GGally'
##
## The following object is masked from 'package:dplyr':
##
## nasaloadthedata
data <- read.csv("~/Psychometric_study_data/allsurveysYT1.csv")
LET<-select(data, LET_1, LET_2, LET_3, LET_4, LET_5, LET_6)
LET$LET_1 <- 6- LET$LET_1
LET$LET_3 <- 6- LET$LET_3
LET$LET_5 <- 6- LET$LET_5EFA Let
LET=na.omit(LET)#removes missing data
#LET<- LET[complete.cases(LET[,]),]EFA
number of factors
parallal analysis and scree plot
parallel<-fa.parallel(LET, fm="ml",fa="fa")
## Parallel analysis suggests that the number of factors = 2 and the number of components = NAthree factors are greater than one Eigenvalue scree plot says there are three factors.
Paralel analysis suggests 6 factors
eigenvalues (kaiser)
parallel$fa.values## [1] 1.927516975 0.836013102 -0.001708068 -0.022006275 -0.284535586
## [6] -0.547334193#over 1=1, over .7=2doign aprincipal components analysis to see how many factors there might be using that method
Deal with NA doing principle componant analysis
princomp(na.omit(LET), cor = TRUE)## Call:
## princomp(x = na.omit(LET), cor = TRUE)
##
## Standard deviations:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## 1.5484389 1.3143871 0.7992045 0.7099442 0.6511704 0.5549343
##
## 6 variables and 829 observations.parallel2<-princomp(na.omit(LET), cor = TRUE)
summary(parallel2)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.5484389 1.3143871 0.7992045 0.70994416 0.65117042
## Proportion of Variance 0.3996105 0.2879356 0.1064546 0.08400345 0.07067049
## Cumulative Proportion 0.3996105 0.6875461 0.7940007 0.87800417 0.94867466
## Comp.6
## Standard deviation 0.55493427
## Proportion of Variance 0.05132534
## Cumulative Proportion 1.00000000plot(parallel2)##results show at least two factors
#simple structure
twofactor<-fa(LET, nfactors=2, rotate="oblimin", fm="ml")
twofactor## Factor Analysis using method = ml
## Call: fa(r = LET, nfactors = 2, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 h2 u2 com
## LET_1 0.63 0.16 0.43 0.57 1.1
## LET_2 -0.02 0.75 0.56 0.44 1.0
## LET_3 0.88 -0.04 0.77 0.23 1.0
## LET_4 -0.07 0.73 0.53 0.47 1.0
## LET_5 0.78 -0.07 0.60 0.40 1.0
## LET_6 0.35 0.46 0.36 0.64 1.9
##
## ML1 ML2
## SS loadings 1.91 1.34
## Proportion Var 0.32 0.22
## Cumulative Var 0.32 0.54
## Proportion Explained 0.59 0.41
## Cumulative Proportion 0.59 1.00
##
## With factor correlations of
## ML1 ML2
## ML1 1.00 0.06
## ML2 0.06 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 1.75 with Chi Square of 1442.36
## The degrees of freedom for the model are 4 and the objective function was 0.02
##
## 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 number of observations is 829 with the empirical chi square 8.31 with prob < 0.081
## The total number of observations was 829 with MLE Chi Square = 16.06 with prob < 0.0029
##
## Tucker Lewis Index of factoring reliability = 0.968
## RMSEA index = 0.061 and the 90 % confidence intervals are 0.031 0.092
## BIC = -10.82
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML1 ML2
## Correlation of scores with factors 0.92 0.86
## Multiple R square of scores with factors 0.85 0.74
## Minimum correlation of possible factor scores 0.71 0.47LET_6 “I have lots of reasons for living.” loads on both factors so droping it
twofactorWO6<-fa(LET[,-6], nfactors=2, rotate="oblimin", fm="ml")
twofactorWO6## Factor Analysis using method = ml
## Call: fa(r = LET[, -6], nfactors = 2, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML2 ML1 h2 u2 com
## LET_1 0.63 0.17 0.43 0.570 1.1
## LET_2 0.01 1.00 1.00 0.005 1.0
## LET_3 0.88 -0.01 0.78 0.224 1.0
## LET_4 -0.05 0.54 0.30 0.705 1.0
## LET_5 0.77 -0.07 0.60 0.403 1.0
##
## ML2 ML1
## SS loadings 1.77 1.32
## Proportion Var 0.35 0.26
## Cumulative Var 0.35 0.62
## Proportion Explained 0.57 0.43
## Cumulative Proportion 0.57 1.00
##
## With factor correlations of
## ML2 ML1
## ML2 1.00 0.01
## ML1 0.01 1.00
##
## Mean item complexity = 1
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 1.42 with Chi Square of 1174.7
## The degrees of freedom for the model are 1 and the objective function was 0
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic number of observations is 829 with the empirical chi square 0.54 with prob < 0.46
## The total number of observations was 829 with MLE Chi Square = 1.1 with prob < 0.29
##
## Tucker Lewis Index of factoring reliability = 0.999
## RMSEA index = 0.011 and the 90 % confidence intervals are NA 0.094
## BIC = -5.62
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML2 ML1
## Correlation of scores with factors 0.92 1.00
## Multiple R square of scores with factors 0.85 1.00
## Minimum correlation of possible factor scores 0.70 0.99Finding Alpha
alpha(LET, na.rm = TRUE, check.keys=TRUE)##
## Reliability analysis
## Call: alpha(x = LET, na.rm = TRUE, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.69 0.68 0.74 0.26 2.1 0.024 3.9 0.75
##
## lower alpha upper 95% confidence boundaries
## 0.64 0.69 0.73
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## LET_1 0.60 0.60 0.68 0.23 1.5 0.030
## LET_2 0.69 0.67 0.70 0.29 2.0 0.026
## LET_3 0.60 0.61 0.64 0.24 1.6 0.030
## LET_4 0.70 0.69 0.71 0.31 2.2 0.026
## LET_5 0.63 0.63 0.67 0.26 1.7 0.029
## LET_6 0.62 0.60 0.69 0.23 1.5 0.029
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## LET_1 829 0.73 0.69 0.61 0.54 3.5 1.36
## LET_2 829 0.48 0.54 0.42 0.26 3.9 1.11
## LET_3 829 0.73 0.67 0.64 0.53 3.5 1.33
## LET_4 829 0.42 0.49 0.37 0.21 4.2 0.99
## LET_5 829 0.68 0.63 0.57 0.46 3.8 1.33
## LET_6 829 0.66 0.69 0.58 0.49 4.2 1.05Create the Models, As only one factor
one.factor = 'LET =~ LET_1 + LET_2 + LET_3 + LET_4 + LET_5 + LET_6
' Two Factor, Positive and Nagative Model
first.model= ' Negative =~ LET_1 + LET_3 + LET_5
Positive =~ LET_2 + LET_4 + LET_6
' Second order models
second.model = ' Negative =~ LET_1 + LET_3 + LET_5
Positive =~ LET_2 + LET_4 + LET_6
LET =~ NA*Positive + Negative
'
alternative.model = 'Negative =~ LET_1 + LET_3 + LET_5
Positive =~ LET_2 + LET_4 + LET_6
LET =~ NA*Positive + Negative
LET~~1*LET
'Bifactor Models (similar to Models 6, 7 & 8 in Marsh, Scalas & Nagengast, 2010)
bifactor.model = 'Negative =~ LET_1 + LET_3 + LET_5
Positive =~ LET_2 + LET_4 + LET_6
Life Satisfaction =~ LET_1 + LET_2 + LET_3 + LET_4 + LET_5 + LET_6
'Bifactor only with Negative questions protioned out (like model 7 in Marsh, Scalas & Nagengast, 2010)
bifactor.negative.model = 'Negative =~ LET_1 + LET_3 + LET_5
LET =~ LET_1 + LET_2 + LET_3 + LET_4 + LET_5 + LET_6
'Bifactor only with Positive questions protioned out (like model 8 in Marsh, Scalas & Nagengast, 2010)
bifactor.positive.model = 'Positive =~ LET_2 + LET_4 + LET_6
LET =~ LET_1 + LET_2 + LET_3 + LET_4 + LET_5 + LET_6
'Alternative method of writing bifactor model
bifactor.model1 = 'LET =~ LET_1 + LET_2 + LET_3 + LET_4 + LET_5 + LET_6
Negative =~ LET_1 + LET_3 + LET_5
Positive =~ LET_2 + LET_4 + LET_6
LET ~~ 0*Negative
LET ~~ 0*Positive
Negative~~0*Positive
'Running the models
one.fit=cfa(one.factor, data=LET, missing = "fiml", std.lv = T)
two.fit=cfa(first.model, data=LET, missing = "fiml", std.lv = T)
second.fit=cfa(second.model, data=LET, missing = "fiml", std.lv = T)
alt.fit=cfa(alternative.model, data=LET, missing = "fiml", std.lv = T)
bifactor.fit=cfa(bifactor.model, data=LET, missing = "fiml", orthogonal = TRUE, std.lv = T)
bifactor.fit1=cfa(bifactor.model1, data=LET, missing = "fiml", orthogonal = TRUE, std.lv = T)
bifactor.negative.fit=cfa(bifactor.negative.model, missing = "fiml", data=LET, orthogonal = TRUE, std.lv = T)
bifactor.positive.fit=cfa(bifactor.positive.model, missing = "fiml", data=LET, orthogonal = TRUE, std.lv = T)Create pictures of models
#One Factor
semPaths(one.fit, whatLabels = "std", layout = "tree", title=T)
#Two Factors Positive and Nagative
semPaths(two.fit, whatLabels = "std", layout = "tree")
#Second order factors
semPaths(second.fit, whatLabels = "std", layout = "tree")
semPaths(alt.fit, whatLabels = "std", layout = "tree")
#Bifactor Models (similar to Models 6, 7 & 8 in Marsh, Scalas & Nagengast, 2010)
semPaths(bifactor.fit, whatLabels = "std", layout = "tree")
semPaths(bifactor.fit1, whatLabels = "std", layout = "tree")
#Bifactor only with Negative questions protioned out (like model 7 in Marsh, Scalas & Nagengast, 2010)
semPaths(bifactor.negative.fit, whatLabels = "std", layout = "tree")
#Bifactor only with Negative questions protioned out (like model 7 in Marsh, Scalas & Nagengast, 2010)
semPaths(bifactor.positive.fit, whatLabels = "std", layout = "tree")
Summaries
summary(one.fit, standardized = TRUE, rsquare=TRUE)## lavaan (0.5-18) converged normally after 21 iterations
##
## Number of observations 829
##
## Number of missing patterns 1
##
## Estimator ML
## Minimum Function Test Statistic 502.067
## Degrees of freedom 9
## P-value (Chi-square) 0.000
##
## Parameter estimates:
##
## Information Observed
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## LET =~
## LET_1 0.866 0.046 18.678 0.000 0.866 0.636
## LET_2 0.045 0.042 1.058 0.290 0.045 0.041
## LET_3 1.168 0.043 27.162 0.000 1.168 0.878
## LET_4 -0.014 0.038 -0.365 0.715 -0.014 -0.014
## LET_5 1.025 0.044 23.469 0.000 1.025 0.768
## LET_6 0.396 0.039 10.228 0.000 0.396 0.376
##
## Intercepts:
## LET_1 3.521 0.047 74.410 0.000 3.521 2.584
## LET_2 3.906 0.038 101.752 0.000 3.906 3.534
## LET_3 3.486 0.046 75.452 0.000 3.486 2.621
## LET_4 4.163 0.034 121.180 0.000 4.163 4.209
## LET_5 3.807 0.046 82.172 0.000 3.807 2.854
## LET_6 4.230 0.037 115.560 0.000 4.230 4.014
## LET 0.000 0.000 0.000
##
## Variances:
## LET_1 1.106 0.064 1.106 0.596
## LET_2 1.220 0.060 1.220 0.998
## LET_3 0.406 0.058 0.406 0.230
## LET_4 0.978 0.048 0.978 1.000
## LET_5 0.729 0.054 0.729 0.410
## LET_6 0.954 0.049 0.954 0.859
## LET 1.000 1.000 1.000
##
## R-Square:
##
## LET_1 0.404
## LET_2 0.002
## LET_3 0.770
## LET_4 0.000
## LET_5 0.590
## LET_6 0.141summary(two.fit, standardized = TRUE, rsquare=TRUE)## lavaan (0.5-18) converged normally after 20 iterations
##
## Number of observations 829
##
## Number of missing patterns 1
##
## Estimator ML
## Minimum Function Test Statistic 182.290
## Degrees of freedom 8
## P-value (Chi-square) 0.000
##
## Parameter estimates:
##
## Information Observed
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## Negative =~
## LET_1 0.856 0.047 18.324 0.000 0.856 0.628
## LET_3 1.179 0.045 26.423 0.000 1.179 0.887
## LET_5 1.020 0.045 22.633 0.000 1.020 0.764
## Positive =~
## LET_2 0.810 0.047 17.066 0.000 0.810 0.732
## LET_4 0.721 0.043 16.886 0.000 0.721 0.729
## LET_6 0.505 0.042 12.019 0.000 0.505 0.479
##
## Covariances:
## Negative ~~
## Positive 0.070 0.046 1.512 0.130 0.070 0.070
##
## Intercepts:
## LET_1 3.521 0.047 74.410 0.000 3.521 2.584
## LET_3 3.486 0.046 75.452 0.000 3.486 2.621
## LET_5 3.807 0.046 82.172 0.000 3.807 2.854
## LET_2 3.906 0.038 101.752 0.000 3.906 3.534
## LET_4 4.163 0.034 121.180 0.000 4.163 4.209
## LET_6 4.230 0.037 115.560 0.000 4.230 4.014
## Negative 0.000 0.000 0.000
## Positive 0.000 0.000 0.000
##
## Variances:
## LET_1 1.124 0.065 1.124 0.605
## LET_3 0.379 0.065 0.379 0.214
## LET_5 0.739 0.059 0.739 0.416
## LET_2 0.566 0.062 0.566 0.463
## LET_4 0.458 0.050 0.458 0.468
## LET_6 0.856 0.049 0.856 0.770
## Negative 1.000 1.000 1.000
## Positive 1.000 1.000 1.000
##
## R-Square:
##
## LET_1 0.395
## LET_3 0.786
## LET_5 0.584
## LET_2 0.537
## LET_4 0.532
## LET_6 0.230summary(second.fit, standardized = TRUE, rsquare=TRUE)## lavaan (0.5-18) converged normally after 22 iterations
##
## Number of observations 829
##
## Number of missing patterns 1
##
## Estimator ML
## Minimum Function Test Statistic 182.290
## Degrees of freedom 7
## P-value (Chi-square) 0.000
##
## Parameter estimates:
##
## Information Observed
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## Negative =~
## LET_1 0.722 NA 0.856 0.628
## LET_3 0.995 NA 1.179 0.887
## LET_5 0.860 NA 1.020 0.764
## Positive =~
## LET_2 0.803 NA 0.810 0.732
## LET_4 0.715 NA 0.721 0.729
## LET_6 0.501 NA 0.505 0.479
## LET =~
## Positive 0.131 NA 0.130 0.130
## Negative 0.636 NA 0.537 0.537
##
## Intercepts:
## LET_1 3.521 0.047 74.410 0.000 3.521 2.584
## LET_3 3.486 0.046 75.452 0.000 3.486 2.621
## LET_5 3.807 0.046 82.172 0.000 3.807 2.854
## LET_2 3.906 0.038 101.752 0.000 3.906 3.534
## LET_4 4.163 0.034 121.180 0.000 4.163 4.209
## LET_6 4.230 0.037 115.560 0.000 4.230 4.014
## Negative 0.000 0.000 0.000
## Positive 0.000 0.000 0.000
## LET 0.000 0.000 0.000
##
## Variances:
## LET_1 1.124 0.065 1.124 0.605
## LET_3 0.379 0.065 0.379 0.214
## LET_5 0.739 0.059 0.739 0.416
## LET_2 0.566 0.062 0.566 0.463
## LET_4 0.458 0.050 0.458 0.468
## LET_6 0.856 0.049 0.856 0.770
## Negative 1.000 0.712 0.712
## Positive 1.000 0.983 0.983
## LET 1.000 1.000 1.000
##
## R-Square:
##
## LET_1 0.395
## LET_3 0.786
## LET_5 0.584
## LET_2 0.537
## LET_4 0.532
## LET_6 0.230
## Negative 0.288
## Positive 0.017summary(alt.fit, standardized = TRUE, rsquare=TRUE)## lavaan (0.5-18) converged normally after 22 iterations
##
## Number of observations 829
##
## Number of missing patterns 1
##
## Estimator ML
## Minimum Function Test Statistic 182.290
## Degrees of freedom 7
## P-value (Chi-square) 0.000
##
## Parameter estimates:
##
## Information Observed
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## Negative =~
## LET_1 0.722 NA 0.856 0.628
## LET_3 0.995 NA 1.179 0.887
## LET_5 0.860 NA 1.020 0.764
## Positive =~
## LET_2 0.803 NA 0.810 0.732
## LET_4 0.715 NA 0.721 0.729
## LET_6 0.501 NA 0.505 0.479
## LET =~
## Positive 0.131 NA 0.130 0.130
## Negative 0.636 NA 0.537 0.537
##
## Intercepts:
## LET_1 3.521 0.047 74.410 0.000 3.521 2.584
## LET_3 3.486 0.046 75.452 0.000 3.486 2.621
## LET_5 3.807 0.046 82.172 0.000 3.807 2.854
## LET_2 3.906 0.038 101.752 0.000 3.906 3.534
## LET_4 4.163 0.034 121.180 0.000 4.163 4.209
## LET_6 4.230 0.037 115.560 0.000 4.230 4.014
## Negative 0.000 0.000 0.000
## Positive 0.000 0.000 0.000
## LET 0.000 0.000 0.000
##
## Variances:
## LET 1.000 1.000 1.000
## LET_1 1.124 0.065 1.124 0.605
## LET_3 0.379 0.065 0.379 0.214
## LET_5 0.739 0.059 0.739 0.416
## LET_2 0.566 0.062 0.566 0.463
## LET_4 0.458 0.050 0.458 0.468
## LET_6 0.856 0.049 0.856 0.770
## Negative 1.000 0.712 0.712
## Positive 1.000 0.983 0.983
##
## R-Square:
##
## LET_1 0.395
## LET_3 0.786
## LET_5 0.584
## LET_2 0.537
## LET_4 0.532
## LET_6 0.230
## Negative 0.288
## Positive 0.017summary(bifactor.fit, standardized = TRUE, rsquare=TRUE)## lavaan (0.5-18) converged normally after 29 iterations
##
## Number of observations 829
##
## Number of missing patterns 1
##
## Estimator ML
## Minimum Function Test Statistic 50.515
## Degrees of freedom 3
## P-value (Chi-square) 0.000
##
## Parameter estimates:
##
## Information Observed
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## Negative =~
## LET_1 0.584 23.262 0.025 0.980 0.584 0.429
## LET_3 0.844 28.393 0.030 0.976 0.844 0.635
## LET_5 0.689 28.881 0.024 0.981 0.689 0.516
## Positive =~
## LET_2 0.759 3.136 0.242 0.809 0.759 0.687
## LET_4 0.778 3.343 0.233 0.816 0.778 0.787
## LET_6 0.508 0.961 0.529 0.597 0.508 0.482
## LifeSatisfaction =~
## LET_1 0.620 21.868 0.028 0.977 0.620 0.455
## LET_2 0.022 0.788 0.028 0.977 0.022 0.020
## LET_3 0.828 29.211 0.028 0.977 0.828 0.623
## LET_4 -0.063 2.220 -0.028 0.977 -0.063 -0.064
## LET_5 0.752 26.521 0.028 0.977 0.752 0.564
## LET_6 0.551 19.417 0.028 0.977 0.551 0.522
##
## Covariances:
## Negative ~~
## Positive 0.000 0.000 0.000
## LifeSatisfctn 0.000 0.000 0.000
## Positive ~~
## LifeSatisfctn 0.000 0.000 0.000
##
## Intercepts:
## LET_1 3.521 0.047 74.410 0.000 3.521 2.584
## LET_3 3.486 0.046 75.452 0.000 3.486 2.621
## LET_5 3.807 0.046 82.172 0.000 3.807 2.854
## LET_2 3.906 0.038 101.752 0.000 3.906 3.534
## LET_4 4.163 0.034 121.180 0.000 4.163 4.209
## LET_6 4.230 0.037 115.560 0.000 4.230 4.014
## Negative 0.000 0.000 0.000
## Positive 0.000 0.000 0.000
## LifeSatisfctn 0.000 0.000 0.000
##
## Variances:
## LET_1 1.130 0.088 1.130 0.609
## LET_3 0.370 0.454 0.370 0.209
## LET_5 0.739 0.128 0.739 0.415
## LET_2 0.644 4.728 0.644 0.527
## LET_4 0.369 5.481 0.369 0.377
## LET_6 0.550 22.360 0.550 0.495
## Negative 1.000 1.000 1.000
## Positive 1.000 1.000 1.000
## LifeSatisfctn 1.000 1.000 1.000
##
## R-Square:
##
## LET_1 0.391
## LET_3 0.791
## LET_5 0.585
## LET_2 0.473
## LET_4 0.623
## LET_6 0.505summary(bifactor.fit1, standardized = TRUE, rsquare=TRUE)## lavaan (0.5-18) converged normally after 29 iterations
##
## Number of observations 829
##
## Number of missing patterns 1
##
## Estimator ML
## Minimum Function Test Statistic 50.515
## Degrees of freedom 3
## P-value (Chi-square) 0.000
##
## Parameter estimates:
##
## Information Observed
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## LET =~
## LET_1 0.620 21.868 0.028 0.977 0.620 0.455
## LET_2 0.022 0.788 0.028 0.977 0.022 0.020
## LET_3 0.828 29.211 0.028 0.977 0.828 0.623
## LET_4 -0.063 2.220 -0.028 0.977 -0.063 -0.064
## LET_5 0.752 26.521 0.028 0.977 0.752 0.564
## LET_6 0.551 19.417 0.028 0.977 0.551 0.522
## Negative =~
## LET_1 0.584 23.262 0.025 0.980 0.584 0.429
## LET_3 0.844 28.393 0.030 0.976 0.844 0.635
## LET_5 0.689 28.881 0.024 0.981 0.689 0.516
## Positive =~
## LET_2 0.759 3.136 0.242 0.809 0.759 0.687
## LET_4 0.778 3.343 0.233 0.816 0.778 0.787
## LET_6 0.508 0.961 0.529 0.597 0.508 0.482
##
## Covariances:
## LET ~~
## Negative 0.000 0.000 0.000
## Positive 0.000 0.000 0.000
## Negative ~~
## Positive 0.000 0.000 0.000
##
## Intercepts:
## LET_1 3.521 0.047 74.410 0.000 3.521 2.584
## LET_2 3.906 0.038 101.752 0.000 3.906 3.534
## LET_3 3.486 0.046 75.452 0.000 3.486 2.621
## LET_4 4.163 0.034 121.180 0.000 4.163 4.209
## LET_5 3.807 0.046 82.172 0.000 3.807 2.854
## LET_6 4.230 0.037 115.560 0.000 4.230 4.014
## LET 0.000 0.000 0.000
## Negative 0.000 0.000 0.000
## Positive 0.000 0.000 0.000
##
## Variances:
## LET_1 1.130 0.088 1.130 0.609
## LET_2 0.644 4.728 0.644 0.527
## LET_3 0.370 0.454 0.370 0.209
## LET_4 0.369 5.481 0.369 0.377
## LET_5 0.739 0.128 0.739 0.415
## LET_6 0.550 22.360 0.550 0.495
## LET 1.000 1.000 1.000
## Negative 1.000 1.000 1.000
## Positive 1.000 1.000 1.000
##
## R-Square:
##
## LET_1 0.391
## LET_2 0.473
## LET_3 0.791
## LET_4 0.623
## LET_5 0.585
## LET_6 0.505summary(bifactor.negative.fit, standardized = TRUE, rsquare=TRUE)## lavaan (0.5-18) converged normally after 22 iterations
##
## Number of observations 829
##
## Number of missing patterns 1
##
## Estimator ML
## Minimum Function Test Statistic 144.351
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Parameter estimates:
##
## Information Observed
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## Negative =~
## LET_1 0.846 0.046 18.442 0.000 0.846 0.621
## LET_3 1.170 0.045 26.230 0.000 1.170 0.879
## LET_5 1.030 0.045 22.799 0.000 1.030 0.772
## LET =~
## LET_1 0.305 0.055 5.509 0.000 0.305 0.224
## LET_2 0.857 0.049 17.638 0.000 0.857 0.776
## LET_3 0.057 0.055 1.028 0.304 0.057 0.043
## LET_4 0.685 0.041 16.509 0.000 0.685 0.692
## LET_5 -0.009 0.056 -0.158 0.874 -0.009 -0.007
## LET_6 0.492 0.043 11.555 0.000 0.492 0.467
##
## Covariances:
## Negative ~~
## LET 0.000 0.000 0.000
##
## Intercepts:
## LET_1 3.521 0.047 74.410 0.000 3.521 2.584
## LET_3 3.486 0.046 75.452 0.000 3.486 2.621
## LET_5 3.807 0.046 82.172 0.000 3.807 2.854
## LET_2 3.906 0.038 101.752 0.000 3.906 3.534
## LET_4 4.163 0.034 121.180 0.000 4.163 4.209
## LET_6 4.230 0.037 115.560 0.000 4.230 4.014
## Negative 0.000 0.000 0.000
## LET 0.000 0.000 0.000
##
## Variances:
## LET_1 1.047 0.062 1.047 0.564
## LET_3 0.398 0.064 0.398 0.225
## LET_5 0.718 0.059 0.718 0.403
## LET_2 0.486 0.067 0.486 0.398
## LET_4 0.510 0.047 0.510 0.521
## LET_6 0.869 0.049 0.869 0.782
## Negative 1.000 1.000 1.000
## LET 1.000 1.000 1.000
##
## R-Square:
##
## LET_1 0.436
## LET_3 0.775
## LET_5 0.597
## LET_2 0.602
## LET_4 0.479
## LET_6 0.218summary(bifactor.positive.fit, standardized = TRUE, rsquare=TRUE)## lavaan (0.5-18) converged normally after 22 iterations
##
## Number of observations 829
##
## Number of missing patterns 1
##
## Estimator ML
## Minimum Function Test Statistic 50.899
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Parameter estimates:
##
## Information Observed
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## Positive =~
## LET_2 0.781 0.046 16.845 0.000 0.781 0.707
## LET_4 0.756 0.043 17.713 0.000 0.756 0.764
## LET_6 0.501 0.038 13.077 0.000 0.501 0.476
## LET =~
## LET_1 0.855 0.046 18.528 0.000 0.855 0.628
## LET_2 0.016 0.042 0.383 0.702 0.016 0.014
## LET_3 1.174 0.043 27.423 0.000 1.174 0.882
## LET_4 -0.047 0.037 -1.247 0.212 -0.047 -0.047
## LET_5 1.026 0.044 23.370 0.000 1.026 0.769
## LET_6 0.393 0.038 10.236 0.000 0.393 0.373
##
## Covariances:
## Positive ~~
## LET 0.000 0.000 0.000
##
## Intercepts:
## LET_2 3.906 0.038 101.752 0.000 3.906 3.534
## LET_4 4.163 0.034 121.180 0.000 4.163 4.209
## LET_6 4.230 0.037 115.560 0.000 4.230 4.014
## LET_1 3.521 0.047 74.410 0.000 3.521 2.584
## LET_3 3.486 0.046 75.452 0.000 3.486 2.621
## LET_5 3.807 0.046 82.172 0.000 3.807 2.854
## Positive 0.000 0.000 0.000
## LET 0.000 0.000 0.000
##
## Variances:
## LET_2 0.611 0.059 0.611 0.500
## LET_4 0.405 0.052 0.405 0.414
## LET_6 0.705 0.042 0.705 0.635
## LET_1 1.125 0.063 1.125 0.606
## LET_3 0.392 0.057 0.392 0.222
## LET_5 0.726 0.055 0.726 0.408
## Positive 1.000 1.000 1.000
## LET 1.000 1.000 1.000
##
## R-Square:
##
## LET_2 0.500
## LET_4 0.586
## LET_6 0.365
## LET_1 0.394
## LET_3 0.778
## LET_5 0.592Residual correlations
correl.1 = residuals(one.fit, type="cor")
correl.1## $type
## [1] "cor.bollen"
##
## $cor
## LET_1 LET_2 LET_3 LET_4 LET_5 LET_6
## LET_1 0.000
## LET_2 0.151 0.000
## LET_3 -0.002 -0.035 0.000
## LET_4 0.076 0.540 -0.044 0.000
## LET_5 -0.010 -0.087 0.005 -0.047 0.000
## LET_6 0.053 0.326 -0.012 0.351 -0.009 0.000
##
## $mean
## LET_1 LET_2 LET_3 LET_4 LET_5 LET_6
## 0 0 0 0 0 0#View(correl.1$cor)
correl = residuals(two.fit, type="cor")
correl## $type
## [1] "cor.bollen"
##
## $cor
## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## LET_1 0.000
## LET_3 -0.001 0.000
## LET_5 -0.002 0.001 0.000
## LET_2 0.145 -0.045 -0.095 0.000
## LET_4 0.035 -0.102 -0.097 0.005 0.000
## LET_6 0.271 0.288 0.254 -0.009 -0.004 0.000
##
## $mean
## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## 0 0 0 0 0 0#View(correl$cor)
correl1 = residuals(second.fit, type="cor")
correl1## $type
## [1] "cor.bollen"
##
## $cor
## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## LET_1 0.000
## LET_3 -0.001 0.000
## LET_5 -0.002 0.001 0.000
## LET_2 0.145 -0.045 -0.095 0.000
## LET_4 0.035 -0.102 -0.097 0.005 0.000
## LET_6 0.271 0.288 0.254 -0.009 -0.004 0.000
##
## $mean
## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## 0 0 0 0 0 0#View(correl1$cor)
correl2 = residuals(alt.fit, type="cor")
correl2## $type
## [1] "cor.bollen"
##
## $cor
## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## LET_1 0.000
## LET_3 -0.001 0.000
## LET_5 -0.002 0.001 0.000
## LET_2 0.145 -0.045 -0.095 0.000
## LET_4 0.035 -0.102 -0.097 0.005 0.000
## LET_6 0.271 0.288 0.254 -0.009 -0.004 0.000
##
## $mean
## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## 0 0 0 0 0 0#View(correl2$cor)
correl3 = residuals(bifactor.fit, type="cor")
correl3## $type
## [1] "cor.bollen"
##
## $cor
## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## LET_1 0.000
## LET_3 0.000 0.000
## LET_5 0.000 0.000 0.000
## LET_2 0.168 -0.012 -0.067 0.000
## LET_4 0.096 -0.017 -0.022 0.000 0.000
## LET_6 0.054 -0.008 -0.015 0.000 0.000 0.000
##
## $mean
## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## 0 0 0 0 0 0#View(correl3$cor)
correl4 = residuals(bifactor.fit1, type="cor")
correl4## $type
## [1] "cor.bollen"
##
## $cor
## LET_1 LET_2 LET_3 LET_4 LET_5 LET_6
## LET_1 0.000
## LET_2 0.168 0.000
## LET_3 0.000 -0.012 0.000
## LET_4 0.096 0.000 -0.017 0.000
## LET_5 0.000 -0.067 0.000 -0.022 0.000
## LET_6 0.054 0.000 -0.008 0.000 -0.015 0.000
##
## $mean
## LET_1 LET_2 LET_3 LET_4 LET_5 LET_6
## 0 0 0 0 0 0#View(correl4$cor)
correl5 = residuals(bifactor.negative.fit, type="cor")
correl5## $type
## [1] "cor.bollen"
##
## $cor
## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## LET_1 0.000
## LET_3 0.000 0.000
## LET_5 0.000 0.000 0.000
## LET_2 0.003 -0.032 -0.051 0.000
## LET_4 -0.088 -0.086 -0.053 0.002 0.000
## LET_6 0.187 0.298 0.283 -0.021 0.023 0.000
##
## $mean
## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## 0 0 0 0 0 0#View(correl5$cor)
correl6 = residuals(bifactor.positive.fit, type="cor")
correl6## $type
## [1] "cor.bollen"
##
## $cor
## LET_2 LET_4 LET_6 LET_1 LET_3 LET_5
## LET_2 0.000
## LET_4 0.000 0.000
## LET_6 0.000 0.000 0.000
## LET_1 0.168 0.096 0.058 0.000
## LET_3 -0.012 -0.015 -0.012 0.002 0.000
## LET_5 -0.067 -0.021 -0.007 -0.005 0.000 0.000
##
## $mean
## LET_2 LET_4 LET_6 LET_1 LET_3 LET_5
## 0 0 0 0 0 0#View(correl6$cor)zscore correlation anything over 1.96 is going to be statistically significant at the .05 level
zcorrels10 = residuals(one.fit, type = "standardized")
zcorrels10$cov## LET_1 LET_2 LET_3 LET_4 LET_5 LET_6
## LET_1 NA
## LET_2 5.963 0.000
## LET_3 -0.681 -4.114 NA
## LET_4 3.053 13.692 -5.303 0.000
## LET_5 -1.385 -4.733 NA -2.540 NA
## LET_6 2.346 9.700 -1.524 10.386 -0.596 NAzcorrels = residuals(two.fit, type = "standardized")
zcorrels$cov## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## LET_1 0.000
## LET_3 -1.064 0.000
## LET_5 -1.162 NA 0.000
## LET_2 5.186 -2.610 -4.135 NA
## LET_4 1.261 -5.606 -4.114 NA NA
## LET_6 8.168 9.507 8.060 -9.053 -1.217 NA#zcorrels1 = residuals(second.fit, type = "standardized")
#zcorrels1$cov
#zcorrels2 = residuals(alt.fit, type = "standardized")
#zcorrels2$cov
#zcorrels3 = residuals(bifactor.fit, type = "standardized")
#zcorrels3$cov
#zcorrels4 = residuals(bifactor1.fit, type = "standardized")
#zcorrels4$cov
zcorrels5 = residuals(bifactor.negative.fit, type = "standardized")
zcorrels5$cov## LET_1 LET_3 LET_5 LET_2 LET_4 LET_6
## LET_1 0.000
## LET_3 0.000 0.000
## LET_5 0.000 0.000 0.000
## LET_2 0.271 -2.535 -4.068 0.000
## LET_4 -4.719 -4.437 -2.745 NA 0.000
## LET_6 6.525 9.734 9.316 -2.568 NA 0.000zcorrels6 = residuals(bifactor.positive.fit, type = "standardized")
zcorrels6$cov## LET_2 LET_4 LET_6 LET_1 LET_3 LET_5
## LET_2 0.000
## LET_4 0.000 0.000
## LET_6 0.000 0.000 0.000
## LET_1 6.439 3.782 2.474 0.000
## LET_3 -1.254 -1.533 -1.384 0.603 0.000
## LET_5 -3.509 -1.119 -0.470 -0.593 0.208 0.000Modification indicies
modindices(one.fit, sort. = TRUE, minimum.value = 3.84)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 LET_2 ~~ LET_4 242.111 0.590 0.590 0.540 0.540
## 2 LET_4 ~~ LET_6 122.634 0.377 0.377 0.362 0.362
## 3 LET_2 ~~ LET_6 106.161 0.392 0.392 0.336 0.336
## 4 LET_1 ~~ LET_2 36.107 0.258 0.258 0.172 0.172
## 5 LET_2 ~~ LET_5 20.570 -0.172 -0.172 -0.117 -0.117
## 6 LET_3 ~~ LET_4 17.410 -0.144 -0.144 -0.109 -0.109
## 7 LET_2 ~~ LET_3 10.921 -0.127 -0.127 -0.086 -0.086
## 8 LET_3 ~~ LET_5 10.016 0.432 0.432 0.243 0.243
## 9 LET_1 ~~ LET_4 9.078 0.116 0.116 0.086 0.086
## 10 LET_4 ~~ LET_5 5.939 -0.083 -0.083 -0.063 -0.063
## 11 LET_1 ~~ LET_6 5.520 0.093 0.093 0.064 0.064modindices(two.fit, sort. = TRUE, minimum.value = 3.84)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 Negative =~ LET_6 119.522 0.406 0.406 0.385 0.385
## 2 LET_2 ~~ LET_4 119.518 6.688 6.688 6.118 6.118
## 3 LET_3 ~~ LET_5 33.970 5.389 5.389 3.037 3.037
## 4 Positive =~ LET_1 33.969 0.269 0.269 0.198 0.198
## 5 Negative =~ LET_4 26.307 -0.176 -0.176 -0.178 -0.178
## 6 LET_2 ~~ LET_6 26.307 -1.420 -1.420 -1.219 -1.219
## 7 LET_1 ~~ LET_2 25.260 0.178 0.178 0.118 0.118
## 8 LET_3 ~~ LET_6 18.559 0.132 0.132 0.094 0.094
## 9 LET_5 ~~ LET_2 14.361 -0.117 -0.117 -0.079 -0.079
## 10 LET_5 ~~ LET_6 9.908 0.102 0.102 0.073 0.073
## 11 LET_3 ~~ LET_4 8.503 -0.077 -0.077 -0.059 -0.059
## 12 Positive =~ LET_5 5.793 -0.098 -0.098 -0.073 -0.073
## 13 LET_1 ~~ LET_3 5.793 -1.380 -1.380 -0.761 -0.761#modindices(second.fit, sort. = TRUE, minimum.value = 3.84)
#modindices(alt.fit, sort. = TRUE, minimum.value = 3.84)
#modindices(bifactor.fit, sort. = TRUE, minimum.value = 3.84)
#modindices(bifactor.fit1, sort. = TRUE, minimum.value = 3.84)
modindices(bifactor.negative.fit, sort. = TRUE, minimum.value = 3.84)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 Negative =~ LET_6 117.026 0.402 0.402 0.381 0.381
## 2 LET_3 ~~ LET_6 20.307 0.140 0.140 0.100 0.100
## 3 Negative =~ LET_4 18.893 -0.145 -0.145 -0.146 -0.146
## 4 LET_5 ~~ LET_6 13.253 0.120 0.120 0.085 0.085
## 5 LET_2 ~~ LET_6 13.168 -0.279 -0.279 -0.240 -0.240
## 6 LET_5 ~~ LET_2 9.437 -0.109 -0.109 -0.074 -0.074
## 7 LET_1 ~~ LET_4 8.276 -0.104 -0.104 -0.077 -0.077
## 8 LET_4 ~~ LET_6 6.873 0.156 0.156 0.150 0.150
## 9 LET_1 ~~ LET_2 6.431 0.111 0.111 0.074 0.074
## 10 Negative =~ LET_2 6.275 -0.100 -0.100 -0.090 -0.090
## 11 LET_3 ~~ LET_4 4.916 -0.062 -0.062 -0.047 -0.047modindices(bifactor.positive.fit, sort. = TRUE, minimum.value = 3.84)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 Positive =~ LET_1 31.240 0.256 0.256 0.188 0.188
## 2 LET_2 ~~ LET_1 28.127 0.190 0.190 0.126 0.126
## 3 LET_2 ~~ LET_5 12.340 -0.110 -0.110 -0.075 -0.075
## 4 Positive =~ LET_5 5.134 -0.091 -0.091 -0.068 -0.068Fit Measures
fitmeasures(one.fit)## npar fmin chisq
## 18.000 0.303 502.067
## df pvalue baseline.chisq
## 9.000 0.000 1449.057
## baseline.df baseline.pvalue cfi
## 15.000 0.000 0.656
## tli nnfi rfi
## 0.427 0.427 0.423
## nfi pnfi ifi
## 0.654 0.392 0.658
## rni logl unrestricted.logl
## 0.656 -7433.656 -7182.623
## aic bic ntotal
## 14903.312 14988.276 829.000
## bic2 rmsea rmsea.ci.lower
## 14931.115 0.257 0.238
## rmsea.ci.upper rmsea.pvalue rmr
## 0.276 0.000 0.164
## rmr_nomean srmr srmr_bentler
## 0.185 0.145 0.145
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.164 0.145 0.164
## srmr_mplus srmr_mplus_nomean cn_05
## 0.145 0.164 28.936
## cn_01 gfi agfi
## 36.774 0.988 0.963
## pgfi mfi ecvi
## 0.329 0.743 NAfitmeasures(two.fit)## npar fmin chisq
## 19.000 0.110 182.290
## df pvalue baseline.chisq
## 8.000 0.000 1449.057
## baseline.df baseline.pvalue cfi
## 15.000 0.000 0.878
## tli nnfi rfi
## 0.772 0.772 0.764
## nfi pnfi ifi
## 0.874 0.466 0.879
## rni logl unrestricted.logl
## 0.878 -7273.768 -7182.623
## aic bic ntotal
## 14585.536 14675.220 829.000
## bic2 rmsea rmsea.ci.lower
## 14614.883 0.162 0.142
## rmsea.ci.upper rmsea.pvalue rmr
## 0.183 0.000 0.143
## rmr_nomean srmr srmr_bentler
## 0.162 0.101 0.101
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.114 0.101 0.114
## srmr_mplus srmr_mplus_nomean cn_05
## 0.101 0.114 71.522
## cn_01 gfi agfi
## 92.364 0.995 0.982
## pgfi mfi ecvi
## 0.295 0.900 NAfitmeasures(second.fit)## npar fmin chisq
## 20.000 0.110 182.290
## df pvalue baseline.chisq
## 7.000 0.000 1449.057
## baseline.df baseline.pvalue cfi
## 15.000 0.000 0.878
## tli nnfi rfi
## 0.738 0.738 0.730
## nfi pnfi ifi
## 0.874 0.408 0.878
## rni logl unrestricted.logl
## 0.878 -7273.768 -7182.623
## aic bic ntotal
## 14587.536 14681.940 829.000
## bic2 rmsea rmsea.ci.lower
## 14618.427 0.174 0.153
## rmsea.ci.upper rmsea.pvalue rmr
## 0.196 0.000 0.143
## rmr_nomean srmr srmr_bentler
## 0.162 0.101 0.101
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.114 0.101 0.114
## srmr_mplus srmr_mplus_nomean cn_05
## 0.101 0.114 64.973
## cn_01 gfi agfi
## 85.020 0.995 0.979
## pgfi mfi ecvi
## 0.258 0.900 NAfitmeasures(alt.fit)## npar fmin chisq
## 20.000 0.110 182.290
## df pvalue baseline.chisq
## 7.000 0.000 1449.057
## baseline.df baseline.pvalue cfi
## 15.000 0.000 0.878
## tli nnfi rfi
## 0.738 0.738 0.730
## nfi pnfi ifi
## 0.874 0.408 0.878
## rni logl unrestricted.logl
## 0.878 -7273.768 -7182.623
## aic bic ntotal
## 14587.536 14681.940 829.000
## bic2 rmsea rmsea.ci.lower
## 14618.427 0.174 0.153
## rmsea.ci.upper rmsea.pvalue rmr
## 0.196 0.000 0.143
## rmr_nomean srmr srmr_bentler
## 0.162 0.101 0.101
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.114 0.101 0.114
## srmr_mplus srmr_mplus_nomean cn_05
## 0.101 0.114 64.973
## cn_01 gfi agfi
## 85.020 0.995 0.979
## pgfi mfi ecvi
## 0.258 0.900 NAfitmeasures(bifactor.fit)## npar fmin chisq
## 24.000 0.030 50.515
## df pvalue baseline.chisq
## 3.000 0.000 1449.057
## baseline.df baseline.pvalue cfi
## 15.000 0.000 0.967
## tli nnfi rfi
## 0.834 0.834 0.826
## nfi pnfi ifi
## 0.965 0.193 0.967
## rni logl unrestricted.logl
## 0.967 -7207.880 -7182.623
## aic bic ntotal
## 14463.760 14577.046 829.000
## bic2 rmsea rmsea.ci.lower
## 14500.830 0.138 0.106
## rmsea.ci.upper rmsea.pvalue rmr
## 0.173 0.000 0.060
## rmr_nomean srmr srmr_bentler
## 0.068 0.041 0.041
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.047 0.041 0.047
## srmr_mplus srmr_mplus_nomean cn_05
## 0.041 0.047 129.247
## cn_01 gfi agfi
## 187.180 0.998 0.985
## pgfi mfi ecvi
## 0.111 0.972 NAfitmeasures(bifactor.fit1)## npar fmin chisq
## 24.000 0.030 50.515
## df pvalue baseline.chisq
## 3.000 0.000 1449.057
## baseline.df baseline.pvalue cfi
## 15.000 0.000 0.967
## tli nnfi rfi
## 0.834 0.834 0.826
## nfi pnfi ifi
## 0.965 0.193 0.967
## rni logl unrestricted.logl
## 0.967 -7207.880 -7182.623
## aic bic ntotal
## 14463.760 14577.046 829.000
## bic2 rmsea rmsea.ci.lower
## 14500.830 0.138 0.106
## rmsea.ci.upper rmsea.pvalue rmr
## 0.173 0.000 0.060
## rmr_nomean srmr srmr_bentler
## 0.068 0.041 0.041
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.047 0.041 0.047
## srmr_mplus srmr_mplus_nomean cn_05
## 0.041 0.047 129.247
## cn_01 gfi agfi
## 187.180 0.998 0.985
## pgfi mfi ecvi
## 0.111 0.972 NAfitmeasures(bifactor.negative.fit)## npar fmin chisq
## 21.000 0.087 144.351
## df pvalue baseline.chisq
## 6.000 0.000 1449.057
## baseline.df baseline.pvalue cfi
## 15.000 0.000 0.904
## tli nnfi rfi
## 0.759 0.759 0.751
## nfi pnfi ifi
## 0.900 0.360 0.904
## rni logl unrestricted.logl
## 0.904 -7254.798 -7182.623
## aic bic ntotal
## 14551.596 14650.721 829.000
## bic2 rmsea rmsea.ci.lower
## 14584.033 0.167 0.144
## rmsea.ci.upper rmsea.pvalue rmr
## 0.191 0.000 0.128
## rmr_nomean srmr srmr_bentler
## 0.146 0.092 0.092
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.104 0.092 0.104
## srmr_mplus srmr_mplus_nomean cn_05
## 0.092 0.104 73.313
## cn_01 gfi agfi
## 97.550 0.996 0.981
## pgfi mfi ecvi
## 0.221 0.920 NAfitmeasures(bifactor.positive.fit)## npar fmin chisq
## 21.000 0.031 50.899
## df pvalue baseline.chisq
## 6.000 0.000 1449.057
## baseline.df baseline.pvalue cfi
## 15.000 0.000 0.969
## tli nnfi rfi
## 0.922 0.922 0.912
## nfi pnfi ifi
## 0.965 0.386 0.969
## rni logl unrestricted.logl
## 0.969 -7208.072 -7182.623
## aic bic ntotal
## 14458.145 14557.269 829.000
## bic2 rmsea rmsea.ci.lower
## 14490.581 0.095 0.072
## rmsea.ci.upper rmsea.pvalue rmr
## 0.120 0.001 0.061
## rmr_nomean srmr srmr_bentler
## 0.069 0.041 0.041
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.047 0.041 0.047
## srmr_mplus srmr_mplus_nomean cn_05
## 0.041 0.047 206.080
## cn_01 gfi agfi
## 274.816 0.998 0.992
## pgfi mfi ecvi
## 0.222 0.973 NACreate dataset for Target rotation
LETTR<-select(LET, LET_1 , LET_2 , LET_3, LET_4 , LET_5 , LET_6)
colnames(LETTR) <- c("1","2", "3", "4", "5", "6")
#Target RorationTarg_key <- make.keys(6,list(f1=1:6))
Targ_key <- scrub(Targ_key,isvalue=1) #fix the 0s, allow the NAs to be estimated
Targ_key <- list(Targ_key)
out_targetQ <- fa(LETTR,1,rotate="TargetQ",Target=Targ_key) #TargetT for orthogonal rotation
out_targetQ[c("loadings", "score.cor", "TLI", "RMSEA","uniquenesses")]## $loadings
##
## Loadings:
## MR1
## 1 0.642
## 2
## 3 0.868
## 4
## 5 0.774
## 6 0.381
##
## MR1
## SS loadings 1.912
## Proportion Var 0.319
##
## $<NA>
## NULL
##
## $TLI
## [1] 0.4265872
##
## $RMSEA
## RMSEA lower upper confidence
## 0.2571571 0.2375846 0.2758252 0.1000000
##
## $uniquenesses
## 1 2 3 4 5 6
## 0.5883392 0.9979331 0.2470149 0.9999157 0.4002568 0.8545076out_targetQ## Factor Analysis using method = minres
## Call: fa(r = LETTR, nfactors = 1, rotate = "TargetQ", Target = Targ_key)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## 1 0.64 4.1e-01 0.59 1
## 2 0.05 2.1e-03 1.00 1
## 3 0.87 7.5e-01 0.25 1
## 4 -0.01 8.4e-05 1.00 1
## 5 0.77 6.0e-01 0.40 1
## 6 0.38 1.5e-01 0.85 1
##
## MR1
## SS loadings 1.91
## Proportion Var 0.32
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 1.75 with Chi Square of 1442.36
## The degrees of freedom for the model are 9 and the objective function was 0.61
##
## The root mean square of the residuals (RMSR) is 0.19
## The df corrected root mean square of the residuals is 0.25
##
## The harmonic number of observations is 829 with the empirical chi square 933.89 with prob < 3.1e-195
## The total number of observations was 829 with MLE Chi Square = 499.68 with prob < 6.7e-102
##
## Tucker Lewis Index of factoring reliability = 0.427
## RMSEA index = 0.257 and the 90 % confidence intervals are 0.238 0.276
## BIC = 439.2
## Fit based upon off diagonal values = 0.69
## Measures of factor score adequacy
## MR1
## Correlation of scores with factors 0.92
## Multiple R square of scores with factors 0.84
## Minimum correlation of possible factor scores 0.69CFI
1-((out_targetQ$STATISTIC - out_targetQ$dof)/(out_targetQ$null.chisq- out_targetQ$null.dof))## [1] 0.6562332As two Factor
data <- read.csv("~/Psychometric_study_data/allsurveysYT1.csv")
LETTR2<-select(data, LET_1, LET_3, LET_5, LET_2, LET_4, LET_6)
LETTR2$LET_1 <- 6- LETTR2$LET_1
LETTR2$LET_3 <- 6- LETTR2$LET_3
LETTR2$LET_5 <- 6- LETTR2$LET_5
colnames(LETTR2) <- c("1","2", "3", "4", "5", "6")
Targ_key <- make.keys(6,list(f1=1:3, f2=4:6))
Targ_key <- scrub(Targ_key,isvalue=1) #fix the 0s, allow the NAs to be estimated
Targ_key <- list(Targ_key)
LETTR2_cor <- corFiml(LETTR2)
out_targetQ <- fa(LETTR2_cor,2,rotate="TargetQ",Target=Targ_key) #TargetT for orthogonal rotation
out_targetQ[c("loadings", "score.cor", "TLI", "RMSEA","uniquenesses")]## $loadings
##
## Loadings:
## MR1 MR2
## 1 0.614 0.164
## 2 0.882
## 3 0.782
## 4 0.754
## 5 -0.126 0.733
## 6 0.321 0.466
##
## MR1 MR2
## SS loadings 1.890 1.355
## Proportion Var 0.315 0.226
## Cumulative Var 0.315 0.541
##
## $score.cor
## [,1] [,2]
## [1,] 1.0000000 0.1627735
## [2,] 0.1627735 1.0000000
##
## $<NA>
## NULL
##
## $<NA>
## NULL
##
## $uniquenesses
## 1 2 3 4 5 6
## 0.5698459 0.2292629 0.3975502 0.4406720 0.4704202 0.6413141out_targetQ## Factor Analysis using method = minres
## Call: fa(r = LETTR2_cor, nfactors = 2, rotate = "TargetQ", Target = Targ_key)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 h2 u2 com
## 1 0.61 0.16 0.43 0.57 1.1
## 2 0.88 -0.03 0.77 0.23 1.0
## 3 0.78 -0.07 0.60 0.40 1.0
## 4 -0.07 0.75 0.56 0.44 1.0
## 5 -0.13 0.73 0.53 0.47 1.1
## 6 0.32 0.47 0.36 0.64 1.8
##
## MR1 MR2
## SS loadings 1.89 1.36
## Proportion Var 0.32 0.23
## Cumulative Var 0.32 0.54
## Proportion Explained 0.58 0.42
## Cumulative Proportion 0.58 1.00
##
## With factor correlations of
## MR1 MR2
## MR1 1.00 0.13
## MR2 0.13 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 1.75
## The degrees of freedom for the model are 4 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.04
##
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2
## Correlation of scores with factors 0.92 0.86
## Multiple R square of scores with factors 0.85 0.74
## Minimum correlation of possible factor scores 0.71 0.48CFI
1-((out_targetQ$STATISTIC - out_targetQ$dof)/(out_targetQ$null.chisq- out_targetQ$null.dof))## numeric(0)