Infos
Datenaufbereitung
- Einlesen der Datenfiles im SPSS-Format.
- Spaltennamen zu Kleinbuchstaben konvertieren
- Daten im Tab-delimited Format wegschreiben
- Einlesen der konvertierten Daten
require(foreign)
df <- read.spss("/Users/pzezula/lehre/lehre_ss_2016/unit/fa/example_bfi/data/bfi-unique-3-exploratory.sav", to.data.frame=T)
names(df) <- tolower(names(df))
write.table(df, file="bfi-expl.txt", quote=F, sep="\t", row.names=F)
df <- read.spss("/Users/pzezula/lehre/lehre_ss_2016/unit/fa/example_bfi/data/bfi-unique-3-confirmatory.sav", to.data.frame=T)
names(df) <- tolower(names(df))
write.table(df, file="bfi-conf.txt", quote=F, sep="\t", row.names=F)
# we find the files written to the current directory
getwd()
# for convenience reasons we can read the data from our data server
df <- read.delim("http://md.psych.bio.uni-goettingen.de/mv/data/div/bfi-expl.txt")
- Berechnen einer explorativen Maximum-Likelihood-Faktoranalyse
- die Konzeption der big-five legt 5 Faktoren nahe, also suchen wir nach einer 5-Faktoren-Lösung
- wie gut passt diese Lösung?
- woran erkenne ich das?
df <- read.delim("http://md.psych.bio.uni-goettingen.de/mv/data/div/bfi-expl.txt")
head(df)
## a1 a2 a3 a4 a5 c1 c2 c3 c4 c5 e1 e2 e3 e4 e5 n1 n2 n3 n4 n5 o1 o2 o3 o4 o5
## 1 1 5 5 5 6 6 6 1 1 1 6 1 1 5 1 1 1 1 6 1 6 6 6 1 1
## 2 3 1 1 2 1 6 4 2 6 5 6 5 4 6 5 1 4 6 6 6 6 5 1 6 1
## 3 1 6 6 4 1 1 6 5 4 2 6 1 3 5 1 5 5 5 6 4 6 1 6 6 6
## 4 4 6 1 6 6 1 1 6 6 6 4 6 4 1 1 4 3 6 5 6 1 6 2 6 2
## 5 6 5 6 5 6 1 1 1 6 6 6 1 6 3 1 6 6 6 6 6 6 1 6 2 2
## 6 3 3 5 5 5 1 6 6 2 1 1 1 1 5 2 5 5 5 4 3 5 1 1 1 1
## gender education age id missing_count mahal_items dataset a1r
## 1 Female some college 40 62092 1 91.92642 Exploratory 5
## 2 Male graduate degree 21 65439 0 86.72993 Exploratory 3
## 3 Female some college 41 63763 0 83.05337 Exploratory 5
## 4 Female HS 20 64341 0 79.19262 Exploratory 2
## 5 Female some college 20 64192 0 78.37850 Exploratory 0
## 6 Female <NA> 13 65170 0 73.75773 Exploratory 3
## a2r a3r a4r a5r c1r c2r c3r c4r c5r e1r e2r e3r e4r e5r n1r n2r n3r n4r n5r
## 1 5 5 5 6 6 6 1 5 5 0 5 1 5 1 1 1 1 6 1
## 2 1 1 2 1 6 4 2 0 1 0 1 4 6 5 1 4 6 6 6
## 3 6 6 4 1 1 6 5 2 4 0 5 3 5 1 5 5 5 6 4
## 4 6 1 6 6 1 1 6 0 0 2 0 4 1 1 4 3 6 5 6
## 5 5 6 5 6 1 1 1 0 0 0 5 6 3 1 6 6 6 6 6
## 6 3 5 5 5 1 6 6 4 5 5 5 1 5 2 5 5 5 4 3
## o1r o2r o3r o4r o5r neuroticism extraversion openness agreeableness
## 1 6 0 6 1 5 2.0 2.75 4.25 5.2
## 2 6 1 1 6 5 4.6 3.00 3.25 1.6
## 3 6 5 6 6 0 5.0 2.75 4.25 4.4
## 4 1 0 2 6 4 4.8 1.00 1.75 4.2
## 5 6 5 6 2 4 6.0 2.25 5.25 4.4
## 6 5 5 1 1 5 4.4 4.25 4.00 4.2
## conscientiousness
## 1 4.6
## 2 2.6
## 3 3.6
## 4 1.6
## 5 0.6
## 6 4.4
v <- list()
v$items <- names(df[,1:25])
# v$items
# we do a screeplot to have an idea of the number of factors, the data suggest
require(psych)
## Loading required package: psych
psych::scree(df[,v$items])
# or via fa.parallel
psych::fa.parallel(df[,v$items])
## Parallel analysis suggests that the number of factors = 6 and the number of components = 5
# we extract 5 factors due to the concept of the big five
f.1 <- factanal(df[,v$items], factors=5, rotation="promax")
# we set cutoff in order to show us factor loadings above .3 only
print(f.1, cutoff=.3)
##
## Call:
## factanal(x = df[, v$items], factors = 5, rotation = "promax")
##
## Uniquenesses:
## a1 a2 a3 a4 a5 c1 c2 c3 c4 c5 e1 e2 e3
## 0.824 0.582 0.460 0.702 0.549 0.679 0.590 0.697 0.505 0.547 0.589 0.453 0.546
## e4 e5 n1 n2 n3 n4 n5 o1 o2 o3 o4 o5
## 0.460 0.590 0.301 0.341 0.475 0.468 0.640 0.611 0.775 0.491 0.747 0.796
##
## Loadings:
## Factor1 Factor2 Factor3 Factor4 Factor5
## a1 -0.424
## a2 0.600
## a3 0.666
## a4 0.467
## a5 0.554
## c1 0.534
## c2 0.637
## c3 0.582
## c4 -0.700
## c5 -0.609
## e1 0.685
## e2 0.685
## e3 -0.424 0.351
## e4 -0.609 0.342
## e5 -0.438
## n1 0.890
## n2 0.862
## n3 0.683
## n4 0.407 0.418
## n5 0.473
## o1 0.600
## o2 -0.413
## o3 0.683
## o4 0.351 0.372
## o5 -0.420
##
## Factor1 Factor2 Factor3 Factor4 Factor5
## SS loadings 2.599 2.252 2.071 1.841 1.595
## Proportion Var 0.104 0.090 0.083 0.074 0.064
## Cumulative Var 0.104 0.194 0.277 0.350 0.414
##
## Factor Correlations:
## Factor1 Factor2 Factor3 Factor4 Factor5
## Factor1 1.000 -0.38256 0.337 0.24772 0.1812
## Factor2 -0.383 1.00000 -0.299 -0.00192 -0.0176
## Factor3 0.337 -0.29870 1.000 0.26534 0.3560
## Factor4 0.248 -0.00192 0.265 1.00000 0.2421
## Factor5 0.181 -0.01756 0.356 0.24212 1.0000
##
## Test of the hypothesis that 5 factors are sufficient.
## The chi square statistic is 857 on 185 degrees of freedom.
## The p-value is 5.26e-87
- Die Ladungsmatrix zeigt nicht allzu viele cross-loadings
Ein globales Modell anpassen - Ein-Faktor-Modell
- Modell spezifizieren
- Modell anpassen
- Fit bewerten
- unstandardisierte und standardisierte Estimates ausgeben lassen
df <- read.delim("http://md.psych.bio.uni-goettingen.de/mv/data/div/bfi-expl.txt")
v <- list()
v$items <- names(df[,1:25])
# to help us to produce the model syntax
# paste(v$items, collapse = ' + ')
require(lavaan)
## Loading required package: lavaan
## This is lavaan 0.6-8
## lavaan is FREE software! Please report any bugs.
##
## Attaching package: 'lavaan'
## The following object is masked from 'package:psych':
##
## cor2cov
# default item to put contstraint on is the first in the model
# we can put that to another item, here a3 by making it the first item
m.g <- '
global =~ a3 + a1 + a2 + a4 + a5 + c1 + c2 + c3 + c4 + c5 + e1 + e2 + e3 + e4 + e5 + n1 + n2 + n3 + n4 + n5 + o1 + o2 + o3 + o4 + o5
'
fit.g <- lavaan::cfa(m.g, data=df)
summary(fit.g, fit.measures=T)
## lavaan 0.6-8 ended normally after 39 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 50
##
## Number of observations 1236
##
## Model Test User Model:
##
## Test statistic 5411.707
## Degrees of freedom 275
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 9406.973
## Degrees of freedom 300
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.436
## Tucker-Lewis Index (TLI) 0.385
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -52356.738
## Loglikelihood unrestricted model (H1) -49650.884
##
## Akaike (AIC) 104813.476
## Bayesian (BIC) 105069.458
## Sample-size adjusted Bayesian (BIC) 104910.636
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.123
## 90 Percent confidence interval - lower 0.120
## 90 Percent confidence interval - upper 0.126
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.114
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## global =~
## a3 1.000
## a1 -0.426 0.061 -6.978 0.000
## a2 0.795 0.061 13.125 0.000
## a4 0.846 0.071 12.003 0.000
## a5 0.990 0.066 15.107 0.000
## c1 0.552 0.058 9.589 0.000
## c2 0.540 0.059 9.084 0.000
## c3 0.506 0.059 8.585 0.000
## c4 -0.841 0.067 -12.602 0.000
## c5 -1.103 0.081 -13.624 0.000
## e1 -0.926 0.078 -11.890 0.000
## e2 -1.427 0.087 -16.407 0.000
## e3 1.064 0.070 15.228 0.000
## e4 1.236 0.077 16.016 0.000
## e5 1.036 0.070 14.830 0.000
## n1 -0.822 0.074 -11.129 0.000
## n2 -0.787 0.072 -10.990 0.000
## n3 -0.804 0.075 -10.744 0.000
## n4 -1.196 0.081 -14.713 0.000
## n5 -0.826 0.076 -10.905 0.000
## o1 0.556 0.053 10.438 0.000
## o2 -0.437 0.069 -6.365 0.000
## o3 0.686 0.058 11.912 0.000
## o4 -0.167 0.052 -3.198 0.001
## o5 -0.415 0.059 -7.075 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .a3 1.200 0.052 23.099 0.000
## .a1 1.808 0.073 24.647 0.000
## .a2 1.206 0.051 23.754 0.000
## .a4 1.812 0.075 24.025 0.000
## .a5 1.111 0.048 22.993 0.000
## .c1 1.424 0.058 24.408 0.000
## .c2 1.558 0.064 24.466 0.000
## .c3 1.576 0.064 24.516 0.000
## .c4 1.540 0.064 23.890 0.000
## .c5 2.045 0.087 23.604 0.000
## .e1 2.231 0.093 24.048 0.000
## .e2 1.560 0.071 22.098 0.000
## .e3 1.239 0.054 22.928 0.000
## .e4 1.325 0.059 22.421 0.000
## .e5 1.312 0.057 23.131 0.000
## .n1 2.126 0.088 24.189 0.000
## .n2 2.018 0.083 24.212 0.000
## .n3 2.245 0.093 24.251 0.000
## .n4 1.805 0.078 23.186 0.000
## .n5 2.275 0.094 24.226 0.000
## .o1 1.159 0.048 24.297 0.000
## .o2 2.334 0.095 24.687 0.000
## .o3 1.216 0.051 24.044 0.000
## .o4 1.445 0.058 24.819 0.000
## .o5 1.660 0.067 24.641 0.000
## global 0.514 0.053 9.725 0.000
# we get the standardized estimates
standardizedSolution(fit.g)
## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 global =~ a3 0.548 0.022 24.452 0.000 0.504 0.591
## 2 global =~ a1 -0.222 0.029 -7.559 0.000 -0.279 -0.164
## 3 global =~ a2 0.460 0.025 18.563 0.000 0.412 0.509
## 4 global =~ a4 0.411 0.026 15.803 0.000 0.360 0.462
## 5 global =~ a5 0.559 0.022 25.333 0.000 0.515 0.602
## 6 global =~ c1 0.315 0.028 11.263 0.000 0.260 0.369
## 7 global =~ c2 0.296 0.028 10.474 0.000 0.241 0.351
## 8 global =~ c3 0.278 0.029 9.732 0.000 0.222 0.334
## 9 global =~ c4 -0.437 0.025 -17.209 0.000 -0.487 -0.387
## 10 global =~ c5 -0.484 0.024 -19.990 0.000 -0.531 -0.436
## 11 global =~ e1 -0.406 0.026 -15.555 0.000 -0.457 -0.355
## 12 global =~ e2 -0.634 0.020 -32.264 0.000 -0.672 -0.595
## 13 global =~ e3 0.565 0.022 25.867 0.000 0.522 0.608
## 14 global =~ e4 0.610 0.020 29.859 0.000 0.570 0.650
## 15 global =~ e5 0.544 0.022 24.180 0.000 0.500 0.588
## 16 global =~ n1 -0.375 0.027 -13.984 0.000 -0.427 -0.322
## 17 global =~ n2 -0.369 0.027 -13.715 0.000 -0.422 -0.316
## 18 global =~ n3 -0.359 0.027 -13.253 0.000 -0.412 -0.306
## 19 global =~ n4 -0.538 0.023 -23.716 0.000 -0.582 -0.493
## 20 global =~ n5 -0.366 0.027 -13.553 0.000 -0.418 -0.313
## 21 global =~ o1 0.347 0.027 12.697 0.000 0.294 0.401
## 22 global =~ o2 -0.201 0.030 -6.798 0.000 -0.259 -0.143
## 23 global =~ o3 0.407 0.026 15.603 0.000 0.356 0.458
## 24 global =~ o4 -0.099 0.030 -3.250 0.001 -0.159 -0.039
## 25 global =~ o5 -0.225 0.029 -7.682 0.000 -0.282 -0.168
## 26 a3 ~~ a3 0.700 0.025 28.556 0.000 0.652 0.748
## 27 a1 ~~ a1 0.951 0.013 73.125 0.000 0.925 0.976
## 28 a2 ~~ a2 0.788 0.023 34.499 0.000 0.743 0.833
## 29 a4 ~~ a4 0.831 0.021 38.906 0.000 0.789 0.873
## 30 a5 ~~ a5 0.688 0.025 27.912 0.000 0.640 0.736
## 31 c1 ~~ c1 0.901 0.018 51.245 0.000 0.867 0.935
## 32 c2 ~~ c2 0.912 0.017 54.554 0.000 0.880 0.945
## 33 c3 ~~ c3 0.923 0.016 58.181 0.000 0.892 0.954
## 34 c4 ~~ c4 0.809 0.022 36.474 0.000 0.766 0.853
## 35 c5 ~~ c5 0.766 0.023 32.722 0.000 0.720 0.812
## 36 e1 ~~ e1 0.835 0.021 39.385 0.000 0.794 0.877
## 37 e2 ~~ e2 0.599 0.025 24.049 0.000 0.550 0.647
## 38 e3 ~~ e3 0.680 0.025 27.543 0.000 0.632 0.729
## 39 e4 ~~ e4 0.628 0.025 25.195 0.000 0.579 0.677
## 40 e5 ~~ e5 0.704 0.024 28.765 0.000 0.656 0.752
## 41 n1 ~~ n1 0.860 0.020 42.831 0.000 0.820 0.899
## 42 n2 ~~ n2 0.864 0.020 43.505 0.000 0.825 0.903
## 43 n3 ~~ n3 0.871 0.019 44.732 0.000 0.833 0.909
## 44 n4 ~~ n4 0.711 0.024 29.132 0.000 0.663 0.759
## 45 n5 ~~ n5 0.866 0.020 43.927 0.000 0.828 0.905
## 46 o1 ~~ o1 0.879 0.019 46.335 0.000 0.842 0.917
## 47 o2 ~~ o2 0.960 0.012 80.708 0.000 0.936 0.983
## 48 o3 ~~ o3 0.834 0.021 39.290 0.000 0.793 0.876
## 49 o4 ~~ o4 0.990 0.006 164.545 0.000 0.978 1.002
## 50 o5 ~~ o5 0.949 0.013 72.043 0.000 0.924 0.975
## 51 global ~~ global 1.000 0.000 NA NA 1.000 1.000
- Fit globales Modell ist nicht gut
Modell mit den vermuteten 5 Faktoren anpassen - mit und ohne Korrelation der Faktoren
- Modelle spezifizieren
- Modell anpassen
- Fits bewerten
- unstandardisierte und standardisierte Estimates ausgeben lassen
df <- read.delim("http://md.psych.bio.uni-goettingen.de/mv/data/div/bfi-expl.txt")
v <- list()
v$items <- names(df[,1:25])
# to help us to produce the model syntax
# paste(v$items, collapse = ' + ')
require(lavaan)
# default item to put contstraint on is the first in the model
# we can put that to another item, here a3 by making it the first item
m.g <- '
global =~ a3 + a1 + a2 + a4 + a5 + c1 + c2 + c3 + c4 + c5 + e1 + e2 + e3 + e4 + e5 + n1 + n2 + n3 + n4 + n5 + o1 + o2 + o3 + o4 + o5
'
fit.g <- lavaan::cfa(m.g, data=df)
summary(fit.g, fit.measures=T)
## lavaan 0.6-8 ended normally after 39 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 50
##
## Number of observations 1236
##
## Model Test User Model:
##
## Test statistic 5411.707
## Degrees of freedom 275
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 9406.973
## Degrees of freedom 300
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.436
## Tucker-Lewis Index (TLI) 0.385
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -52356.738
## Loglikelihood unrestricted model (H1) -49650.884
##
## Akaike (AIC) 104813.476
## Bayesian (BIC) 105069.458
## Sample-size adjusted Bayesian (BIC) 104910.636
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.123
## 90 Percent confidence interval - lower 0.120
## 90 Percent confidence interval - upper 0.126
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.114
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## global =~
## a3 1.000
## a1 -0.426 0.061 -6.978 0.000
## a2 0.795 0.061 13.125 0.000
## a4 0.846 0.071 12.003 0.000
## a5 0.990 0.066 15.107 0.000
## c1 0.552 0.058 9.589 0.000
## c2 0.540 0.059 9.084 0.000
## c3 0.506 0.059 8.585 0.000
## c4 -0.841 0.067 -12.602 0.000
## c5 -1.103 0.081 -13.624 0.000
## e1 -0.926 0.078 -11.890 0.000
## e2 -1.427 0.087 -16.407 0.000
## e3 1.064 0.070 15.228 0.000
## e4 1.236 0.077 16.016 0.000
## e5 1.036 0.070 14.830 0.000
## n1 -0.822 0.074 -11.129 0.000
## n2 -0.787 0.072 -10.990 0.000
## n3 -0.804 0.075 -10.744 0.000
## n4 -1.196 0.081 -14.713 0.000
## n5 -0.826 0.076 -10.905 0.000
## o1 0.556 0.053 10.438 0.000
## o2 -0.437 0.069 -6.365 0.000
## o3 0.686 0.058 11.912 0.000
## o4 -0.167 0.052 -3.198 0.001
## o5 -0.415 0.059 -7.075 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .a3 1.200 0.052 23.099 0.000
## .a1 1.808 0.073 24.647 0.000
## .a2 1.206 0.051 23.754 0.000
## .a4 1.812 0.075 24.025 0.000
## .a5 1.111 0.048 22.993 0.000
## .c1 1.424 0.058 24.408 0.000
## .c2 1.558 0.064 24.466 0.000
## .c3 1.576 0.064 24.516 0.000
## .c4 1.540 0.064 23.890 0.000
## .c5 2.045 0.087 23.604 0.000
## .e1 2.231 0.093 24.048 0.000
## .e2 1.560 0.071 22.098 0.000
## .e3 1.239 0.054 22.928 0.000
## .e4 1.325 0.059 22.421 0.000
## .e5 1.312 0.057 23.131 0.000
## .n1 2.126 0.088 24.189 0.000
## .n2 2.018 0.083 24.212 0.000
## .n3 2.245 0.093 24.251 0.000
## .n4 1.805 0.078 23.186 0.000
## .n5 2.275 0.094 24.226 0.000
## .o1 1.159 0.048 24.297 0.000
## .o2 2.334 0.095 24.687 0.000
## .o3 1.216 0.051 24.044 0.000
## .o4 1.445 0.058 24.819 0.000
## .o5 1.660 0.067 24.641 0.000
## global 0.514 0.053 9.725 0.000
# we get the standardized estimates
standardizedSolution(fit.g)
## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 global =~ a3 0.548 0.022 24.452 0.000 0.504 0.591
## 2 global =~ a1 -0.222 0.029 -7.559 0.000 -0.279 -0.164
## 3 global =~ a2 0.460 0.025 18.563 0.000 0.412 0.509
## 4 global =~ a4 0.411 0.026 15.803 0.000 0.360 0.462
## 5 global =~ a5 0.559 0.022 25.333 0.000 0.515 0.602
## 6 global =~ c1 0.315 0.028 11.263 0.000 0.260 0.369
## 7 global =~ c2 0.296 0.028 10.474 0.000 0.241 0.351
## 8 global =~ c3 0.278 0.029 9.732 0.000 0.222 0.334
## 9 global =~ c4 -0.437 0.025 -17.209 0.000 -0.487 -0.387
## 10 global =~ c5 -0.484 0.024 -19.990 0.000 -0.531 -0.436
## 11 global =~ e1 -0.406 0.026 -15.555 0.000 -0.457 -0.355
## 12 global =~ e2 -0.634 0.020 -32.264 0.000 -0.672 -0.595
## 13 global =~ e3 0.565 0.022 25.867 0.000 0.522 0.608
## 14 global =~ e4 0.610 0.020 29.859 0.000 0.570 0.650
## 15 global =~ e5 0.544 0.022 24.180 0.000 0.500 0.588
## 16 global =~ n1 -0.375 0.027 -13.984 0.000 -0.427 -0.322
## 17 global =~ n2 -0.369 0.027 -13.715 0.000 -0.422 -0.316
## 18 global =~ n3 -0.359 0.027 -13.253 0.000 -0.412 -0.306
## 19 global =~ n4 -0.538 0.023 -23.716 0.000 -0.582 -0.493
## 20 global =~ n5 -0.366 0.027 -13.553 0.000 -0.418 -0.313
## 21 global =~ o1 0.347 0.027 12.697 0.000 0.294 0.401
## 22 global =~ o2 -0.201 0.030 -6.798 0.000 -0.259 -0.143
## 23 global =~ o3 0.407 0.026 15.603 0.000 0.356 0.458
## 24 global =~ o4 -0.099 0.030 -3.250 0.001 -0.159 -0.039
## 25 global =~ o5 -0.225 0.029 -7.682 0.000 -0.282 -0.168
## 26 a3 ~~ a3 0.700 0.025 28.556 0.000 0.652 0.748
## 27 a1 ~~ a1 0.951 0.013 73.125 0.000 0.925 0.976
## 28 a2 ~~ a2 0.788 0.023 34.499 0.000 0.743 0.833
## 29 a4 ~~ a4 0.831 0.021 38.906 0.000 0.789 0.873
## 30 a5 ~~ a5 0.688 0.025 27.912 0.000 0.640 0.736
## 31 c1 ~~ c1 0.901 0.018 51.245 0.000 0.867 0.935
## 32 c2 ~~ c2 0.912 0.017 54.554 0.000 0.880 0.945
## 33 c3 ~~ c3 0.923 0.016 58.181 0.000 0.892 0.954
## 34 c4 ~~ c4 0.809 0.022 36.474 0.000 0.766 0.853
## 35 c5 ~~ c5 0.766 0.023 32.722 0.000 0.720 0.812
## 36 e1 ~~ e1 0.835 0.021 39.385 0.000 0.794 0.877
## 37 e2 ~~ e2 0.599 0.025 24.049 0.000 0.550 0.647
## 38 e3 ~~ e3 0.680 0.025 27.543 0.000 0.632 0.729
## 39 e4 ~~ e4 0.628 0.025 25.195 0.000 0.579 0.677
## 40 e5 ~~ e5 0.704 0.024 28.765 0.000 0.656 0.752
## 41 n1 ~~ n1 0.860 0.020 42.831 0.000 0.820 0.899
## 42 n2 ~~ n2 0.864 0.020 43.505 0.000 0.825 0.903
## 43 n3 ~~ n3 0.871 0.019 44.732 0.000 0.833 0.909
## 44 n4 ~~ n4 0.711 0.024 29.132 0.000 0.663 0.759
## 45 n5 ~~ n5 0.866 0.020 43.927 0.000 0.828 0.905
## 46 o1 ~~ o1 0.879 0.019 46.335 0.000 0.842 0.917
## 47 o2 ~~ o2 0.960 0.012 80.708 0.000 0.936 0.983
## 48 o3 ~~ o3 0.834 0.021 39.290 0.000 0.793 0.876
## 49 o4 ~~ o4 0.990 0.006 164.545 0.000 0.978 1.002
## 50 o5 ~~ o5 0.949 0.013 72.043 0.000 0.924 0.975
## 51 global ~~ global 1.000 0.000 NA NA 1.000 1.000
# we choose a non negativ item to be the reference item: a3 and e3
m.5f <- '
agree =~ a3 + a1 + a2 + a4 + a5
consc =~ c1 + c2 + c3 + c4 + c5
extra =~ e3 + e1 + e2 + e4 + e5
neuro =~ n1 + n2 + n3 + n4 + n5
openn =~ o1 + o2 + o3 + o4 + o5
'
fit.5f.o <- lavaan::cfa(m.5f, data=df, orthogonal=T)
fit.5f.c <- lavaan::cfa(m.5f, data=df, orthogonal=F)
fitmeasures(fit.5f.o)
## npar fmin chisq df
## 50.000 1.222 3021.448 275.000
## pvalue baseline.chisq baseline.df baseline.pvalue
## 0.000 9406.973 300.000 0.000
## cfi tli nnfi rfi
## 0.698 0.671 0.671 0.650
## nfi pnfi ifi rni
## 0.679 0.622 0.699 0.698
## logl unrestricted.logl aic bic
## -51161.608 -49650.884 102423.217 102679.198
## ntotal bic2 rmsea rmsea.ci.lower
## 1236.000 102520.377 0.090 0.087
## rmsea.ci.upper rmsea.pvalue rmr rmr_nomean
## 0.093 0.000 0.291 0.291
## srmr srmr_bentler srmr_bentler_nomean crmr
## 0.143 0.143 0.143 0.148
## crmr_nomean srmr_mplus srmr_mplus_nomean cn_05
## 0.148 0.143 0.143 129.727
## cn_01 gfi agfi pgfi
## 137.009 0.815 0.781 0.689
## mfi ecvi
## 0.329 2.525
#dput(names(fitmeasures(fit.g)))
fit.indices <- c("npar", "chisq", "df", "pvalue", "cfi", "rmsea", "rmsea.ci.lower", "rmsea.ci.upper", "srmr")
# we compare the models by inspecting certain indices
round(fitmeasures(fit.g)[fit.indices], 3)
## npar chisq df pvalue cfi
## 50.000 5411.707 275.000 0.000 0.436
## rmsea rmsea.ci.lower rmsea.ci.upper srmr
## 0.123 0.120 0.126 0.114
round(fitmeasures(fit.5f.o)[fit.indices], 3)
## npar chisq df pvalue cfi
## 50.000 3021.448 275.000 0.000 0.698
## rmsea rmsea.ci.lower rmsea.ci.upper srmr
## 0.090 0.087 0.093 0.143
round(fitmeasures(fit.5f.c)[fit.indices], 3)
## npar chisq df pvalue cfi
## 60.000 2230.852 265.000 0.000 0.784
## rmsea rmsea.ci.lower rmsea.ci.upper srmr
## 0.077 0.075 0.080 0.077
# model comparison using anova()
anova(fit.5f.o, fit.5f.c)
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit.5f.c 265 101653 101960 2230.9
## fit.5f.o 275 102423 102679 3021.4 790.6 10 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1