All Purpose Scales CFA TR
Levi Brackman
27 July 2015
##load packages
library(psych)
library(GPArotation)
library(plyr)
library(dplyr)##
## Attaching package: 'dplyr'
##
## The following objects are masked from 'package:plyr':
##
## arrange, count, desc, failwith, id, mutate, rename, summarise,
## summarize
##
## The following objects are masked from 'package:stats':
##
## filter, lag
##
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# data preparation
data <- read.csv("~/Psychometric_study_data/allsurveysT1.csv")
purposescales<-select(data, PWB_1, PWB_2, PWB_3, PWB_4, PWB_5, PWB_6, PWB_7, PWB_8, PWB_9, APSI_1, APSI_2, APSI_3, APSI_4, APSI_5, APSI_6, APSI_7, APSI_8, LET_1, LET_2, LET_3, LET_4, LET_5, LET_6, MLQ_1, MLQ_2, MLQ_3, MLQ_4, MLQ_5, MLQ_6,MLQ_7, MLQ_8, MLQ_9, MLQ_10)
purposescales$PWB_1 <- 7- purposescales$PWB_1
purposescales$PWB_2 <- 7- purposescales$PWB_2
purposescales$PWB_3 <- 7- purposescales$PWB_3
purposescales$PWB_4 <- 7- purposescales$PWB_4
purposescales$PWB_9 <- 7- purposescales$PWB_9
purposescales$MLQ_9 <- 8- purposescales$MLQ_9
purposescales$LET_1 <- 6- purposescales$LET_1
purposescales$LET_3 <- 6- purposescales$LET_3
purposescales$LET_5 <- 6- purposescales$LET_5
purposescales<- data.frame(apply(purposescales,2, as.numeric))
purposescales<-tbl_df(purposescales)
purposescales## Source: local data frame [757 x 33]
##
## PWB_1 PWB_2 PWB_3 PWB_4 PWB_5 PWB_6 PWB_7 PWB_8 PWB_9 APSI_1 APSI_2
## 1 4 3 5 2 4 5 4 3 6 2 4
## 2 4 5 5 2 2 5 3 2 5 4 3
## 3 5 6 5 6 1 4 6 3 6 3 4
## 4 2 2 4 4 3 4 5 4 4 4 4
## 5 2 2 3 3 4 3 2 3 4 3 3
## 6 5 4 6 5 3 4 3 4 6 3 4
## 7 2 2 5 2 1 4 3 3 3 2 2
## 8 6 6 5 1 2 4 4 4 6 3 3
## 9 5 5 5 5 1 5 5 5 6 4 5
## 10 6 6 3 3 2 6 6 3 6 2 2
## .. ... ... ... ... ... ... ... ... ... ... ...
## Variables not shown: APSI_3 (dbl), APSI_4 (dbl), APSI_5 (dbl), APSI_6
## (dbl), APSI_7 (dbl), APSI_8 (dbl), LET_1 (dbl), LET_2 (dbl), LET_3
## (dbl), LET_4 (dbl), LET_5 (dbl), LET_6 (dbl), MLQ_1 (dbl), MLQ_2 (dbl),
## MLQ_3 (dbl), MLQ_4 (dbl), MLQ_5 (dbl), MLQ_6 (dbl), MLQ_7 (dbl), MLQ_8
## (dbl), MLQ_9 (dbl), MLQ_10 (dbl)str(purposescales)## Classes 'tbl_df', 'tbl' and 'data.frame': 757 obs. of 33 variables:
## $ PWB_1 : num 4 4 5 2 2 5 2 6 5 6 ...
## $ PWB_2 : num 3 5 6 2 2 4 2 6 5 6 ...
## $ PWB_3 : num 5 5 5 4 3 6 5 5 5 3 ...
## $ PWB_4 : num 2 2 6 4 3 5 2 1 5 3 ...
## $ PWB_5 : num 4 2 1 3 4 3 1 2 1 2 ...
## $ PWB_6 : num 5 5 4 4 3 4 4 4 5 6 ...
## $ PWB_7 : num 4 3 6 5 2 3 3 4 5 6 ...
## $ PWB_8 : num 3 2 3 4 3 4 3 4 5 3 ...
## $ PWB_9 : num 6 5 6 4 4 6 3 6 6 6 ...
## $ APSI_1: num 2 4 3 4 3 3 2 3 4 2 ...
## $ APSI_2: num 4 3 4 4 3 4 2 3 5 2 ...
## $ APSI_3: num 4 4 4 5 4 4 4 4 5 2 ...
## $ APSI_4: num 4 5 3 4 3 4 3 3 4 3 ...
## $ APSI_5: num 4 4 3 5 4 4 4 5 4 5 ...
## $ APSI_6: num 4 3 3 4 3 2 4 3 2 3 ...
## $ APSI_7: num 4 4 4 4 2 5 2 3 4 3 ...
## $ APSI_8: num 4 4 3 3 3 3 2 1 5 4 ...
## $ LET_1 : num 4 3 3 1 3 5 3 3 5 3 ...
## $ LET_2 : num 4 3 4 4 2 5 4 4 4 3 ...
## $ LET_3 : num 4 4 3 4 3 5 2 3 5 5 ...
## $ LET_4 : num 5 4 4 4 4 5 3 4 5 5 ...
## $ LET_5 : num 5 4 4 4 2 5 3 4 5 5 ...
## $ LET_6 : num 5 5 5 4 4 4 5 5 5 5 ...
## $ MLQ_1 : num 4 3 4 5 4 5 6 3 6 1 ...
## $ MLQ_2 : num 7 5 7 6 6 5 2 7 5 7 ...
## $ MLQ_3 : num 7 5 5 7 5 3 2 7 2 1 ...
## $ MLQ_4 : num 5 5 4 3 4 4 3 5 7 3 ...
## $ MLQ_5 : num 6 4 4 5 4 5 6 5 6 5 ...
## $ MLQ_6 : num 4 3 4 5 4 5 3 4 6 1 ...
## $ MLQ_7 : num 5 5 4 5 5 3 5 5 5 5 ...
## $ MLQ_8 : num 7 4 5 5 5 4 4 7 7 5 ...
## $ MLQ_9 : num 3 3 4 3 5 7 5 4 7 6 ...
## $ MLQ_10: num 7 5 4 6 5 3 4 5 2 1 ...colnames(purposescales) <- c("1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20","21","22","23","24","25","26","27","28","29","30","31","32","33")
#purposescales<- purposescales[complete.cases(purposescales[,]),]
##EFA
##number of factors
##parallal analysis and scree plot
parallel<-fa.parallel(purposescales, fm="ml",fa="fa")
## Parallel analysis suggests that the number of factors = 5 and the number of components = NA#two factors are greater than one Eigenvalue scree plot says there are two factors. Paralel analysis suggests 4 factors
#eigenvalues (kaiser)
parallel$fa.values## [1] 7.86492483 6.11092669 2.15452487 0.67489536 0.47121242
## [6] 0.22914309 0.17898852 0.12511231 0.01864097 -0.02040029
## [11] -0.08284879 -0.09406141 -0.13655348 -0.15699714 -0.16493689
## [16] -0.22067990 -0.24666433 -0.32352263 -0.34405605 -0.39602304
## [21] -0.44555951 -0.48643807 -0.50761022 -0.54271424 -0.59219248
## [26] -0.59872898 -0.62150523 -0.62816232 -0.65326968 -0.70223466
## [31] -0.73574460 -0.74417600 -0.78119902#over 1=2, over .7=2
#doign aprincipal components analysis to see how many factors there might be using that method
#Deal with NA doing principle componant analysis
princomp(na.omit(purposescales), cor = TRUE)## Call:
## princomp(x = na.omit(purposescales), cor = TRUE)
##
## Standard deviations:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7
## 2.9123873 2.6344008 1.7625717 1.2284666 1.1162543 0.9615061 0.8959260
## Comp.8 Comp.9 Comp.10 Comp.11 Comp.12 Comp.13 Comp.14
## 0.8575081 0.8423550 0.7797400 0.7509777 0.7333973 0.7113940 0.6911814
## Comp.15 Comp.16 Comp.17 Comp.18 Comp.19 Comp.20 Comp.21
## 0.6717013 0.6529565 0.6386146 0.6227516 0.6102691 0.6086141 0.5933355
## Comp.22 Comp.23 Comp.24 Comp.25 Comp.26 Comp.27 Comp.28
## 0.5858159 0.5703668 0.5557393 0.5464648 0.5247000 0.5022309 0.4988762
## Comp.29 Comp.30 Comp.31 Comp.32 Comp.33
## 0.4852249 0.4573967 0.4529373 0.4432153 0.4286089
##
## 33 variables and 470 observations.parallel2<-princomp(na.omit(purposescales), cor = TRUE)
summary(parallel2)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 2.9123873 2.6344008 1.76257166 1.22846658
## Proportion of Variance 0.2570303 0.2103051 0.09414118 0.04573122
## Cumulative Proportion 0.2570303 0.4673354 0.56147655 0.60720777
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 1.11625426 0.96150614 0.89592600 0.85750805
## Proportion of Variance 0.03775829 0.02801497 0.02432374 0.02228243
## Cumulative Proportion 0.64496606 0.67298103 0.69730477 0.71958719
## Comp.9 Comp.10 Comp.11 Comp.12
## Standard deviation 0.84235502 0.77974004 0.75097766 0.73339727
## Proportion of Variance 0.02150188 0.01842408 0.01708992 0.01629914
## Cumulative Proportion 0.74108907 0.75951315 0.77660307 0.79290221
## Comp.13 Comp.14 Comp.15 Comp.16
## Standard deviation 0.7113940 0.69118137 0.6717013 0.65295652
## Proportion of Variance 0.0153358 0.01447672 0.0136722 0.01291976
## Cumulative Proportion 0.8082380 0.82271473 0.8363869 0.84930669
## Comp.17 Comp.18 Comp.19 Comp.20
## Standard deviation 0.63861463 0.62275155 0.61026912 0.60861414
## Proportion of Variance 0.01235844 0.01175211 0.01128571 0.01122458
## Cumulative Proportion 0.86166514 0.87341724 0.88470295 0.89592753
## Comp.21 Comp.22 Comp.23 Comp.24
## Standard deviation 0.59333548 0.5858159 0.570366778 0.555739320
## Proportion of Variance 0.01066809 0.0103994 0.009858129 0.009358976
## Cumulative Proportion 0.90659562 0.9169950 0.926853154 0.936212129
## Comp.25 Comp.26 Comp.27 Comp.28
## Standard deviation 0.546464760 0.52470002 0.502230900 0.498876228
## Proportion of Variance 0.009049204 0.00834273 0.007643511 0.007541742
## Cumulative Proportion 0.945261333 0.95360406 0.961247575 0.968789317
## Comp.29 Comp.30 Comp.31 Comp.32
## Standard deviation 0.485224883 0.45739670 0.452937343 0.443215287
## Proportion of Variance 0.007134642 0.00633975 0.006216734 0.005952721
## Cumulative Proportion 0.975923960 0.98226371 0.988480444 0.994433165
## Comp.33
## Standard deviation 0.428608872
## Proportion of Variance 0.005566835
## Cumulative Proportion 1.000000000plot(parallel2)##results show at least two factors
#simple structure
twofactor<-fa(purposescales, nfactors=2, rotate="oblimin", fm="ml")
twofactor## Factor Analysis using method = ml
## Call: fa(r = purposescales, nfactors = 2, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 h2 u2 com
## 1 -0.29 0.57 0.396 0.60 1.5
## 2 0.06 0.36 0.132 0.87 1.1
## 3 -0.02 0.83 0.682 0.32 1.0
## 4 0.41 0.53 0.466 0.53 1.9
## 5 -0.02 -0.76 0.579 0.42 1.0
## 6 0.07 0.62 0.388 0.61 1.0
## 7 0.72 0.01 0.525 0.47 1.0
## 8 0.70 0.16 0.526 0.47 1.1
## 9 0.11 0.28 0.096 0.90 1.3
## 10 0.87 -0.10 0.760 0.24 1.0
## 11 0.77 -0.10 0.596 0.40 1.0
## 12 0.07 0.43 0.189 0.81 1.1
## 13 0.79 -0.11 0.631 0.37 1.0
## 14 0.64 -0.24 0.453 0.55 1.3
## 15 0.11 -0.84 0.709 0.29 1.0
## 16 0.78 -0.07 0.605 0.39 1.0
## 17 0.83 -0.10 0.691 0.31 1.0
## 18 0.15 0.69 0.500 0.50 1.1
## 19 0.68 -0.05 0.467 0.53 1.0
## 20 -0.12 0.83 0.701 0.30 1.0
## 21 0.60 -0.03 0.355 0.64 1.0
## 22 -0.20 0.81 0.686 0.31 1.1
## 23 0.36 0.46 0.349 0.65 1.9
## 24 0.47 0.41 0.404 0.60 2.0
## 25 -0.01 -0.34 0.119 0.88 1.0
## 26 0.14 -0.30 0.106 0.89 1.4
## 27 0.72 0.22 0.577 0.42 1.2
## 28 0.47 0.45 0.440 0.56 2.0
## 29 0.70 0.23 0.564 0.44 1.2
## 30 0.03 -0.18 0.034 0.97 1.0
## 31 0.04 -0.23 0.053 0.95 1.0
## 32 0.16 0.71 0.541 0.46 1.1
## 33 -0.13 -0.30 0.108 0.89 1.4
##
## ML1 ML2
## SS loadings 7.53 6.90
## Proportion Var 0.23 0.21
## Cumulative Var 0.23 0.44
## Proportion Explained 0.52 0.48
## Cumulative Proportion 0.52 1.00
##
## With factor correlations of
## ML1 ML2
## ML1 1.00 0.04
## ML2 0.04 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 528 and the objective function was 21.35 with Chi Square of 15888.56
## The degrees of freedom for the model are 463 and the objective function was 5.77
##
## 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 472 with the empirical chi square 4082.05 with prob < 0
## The total number of observations was 757 with MLE Chi Square = 4284.8 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.716
## RMSEA index = 0.106 and the 90 % confidence intervals are 0.102 0.107
## BIC = 1215.41
## Fit based upon off diagonal values = 0.92
## Measures of factor score adequacy
## ML1 ML2
## Correlation of scores with factors 0.97 0.97
## Multiple R square of scores with factors 0.95 0.94
## Minimum correlation of possible factor scores 0.90 0.89threefactor<-fa(purposescales, nfactors=3, rotate="oblimin", fm="ml")
threefactor## Factor Analysis using method = ml
## Call: fa(r = purposescales, nfactors = 3, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 ML3 h2 u2 com
## 1 -0.29 0.58 0.00 0.402 0.60 1.5
## 2 0.06 0.33 -0.07 0.131 0.87 1.2
## 3 -0.02 0.82 -0.02 0.685 0.32 1.0
## 4 0.41 0.49 -0.11 0.465 0.53 2.0
## 5 -0.01 -0.76 0.00 0.587 0.41 1.0
## 6 0.06 0.67 0.13 0.433 0.57 1.1
## 7 0.72 0.03 0.06 0.528 0.47 1.0
## 8 0.70 0.16 -0.02 0.525 0.48 1.1
## 9 0.11 0.29 0.03 0.098 0.90 1.3
## 10 0.87 -0.12 -0.05 0.767 0.23 1.0
## 11 0.77 -0.11 -0.03 0.598 0.40 1.0
## 12 0.07 0.47 0.10 0.214 0.79 1.1
## 13 0.79 -0.13 -0.04 0.633 0.37 1.1
## 14 0.64 -0.21 0.08 0.456 0.54 1.2
## 15 0.11 -0.82 0.08 0.710 0.29 1.1
## 16 0.78 -0.06 0.03 0.604 0.40 1.0
## 17 0.83 -0.11 -0.04 0.691 0.31 1.0
## 18 0.15 0.62 -0.20 0.514 0.49 1.3
## 19 0.69 -0.05 -0.01 0.469 0.53 1.0
## 20 -0.13 0.81 -0.08 0.697 0.30 1.1
## 21 0.60 -0.02 0.02 0.355 0.65 1.0
## 22 -0.21 0.81 0.00 0.693 0.31 1.1
## 23 0.35 0.50 0.10 0.373 0.63 1.9
## 24 0.46 0.44 0.05 0.417 0.58 2.0
## 25 -0.02 -0.09 0.77 0.634 0.37 1.0
## 26 0.13 -0.06 0.73 0.578 0.42 1.1
## 27 0.72 0.24 0.03 0.581 0.42 1.2
## 28 0.46 0.50 0.12 0.474 0.53 2.1
## 29 0.70 0.24 0.00 0.567 0.43 1.2
## 30 0.02 0.07 0.75 0.546 0.45 1.0
## 31 0.03 0.03 0.77 0.583 0.42 1.0
## 32 0.15 0.66 -0.16 0.545 0.46 1.2
## 33 -0.14 -0.03 0.81 0.692 0.31 1.1
##
## ML1 ML2 ML3
## SS loadings 7.53 6.54 3.17
## Proportion Var 0.23 0.20 0.10
## Cumulative Var 0.23 0.43 0.52
## Proportion Explained 0.44 0.38 0.18
## Cumulative Proportion 0.44 0.82 1.00
##
## With factor correlations of
## ML1 ML2 ML3
## ML1 1.00 0.04 0.00
## ML2 0.04 1.00 -0.24
## ML3 0.00 -0.24 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 528 and the objective function was 21.35 with Chi Square of 15888.56
## The degrees of freedom for the model are 432 and the objective function was 3.26
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 472 with the empirical chi square 1000.77 with prob < 4.1e-47
## The total number of observations was 757 with MLE Chi Square = 2418.39 with prob < 1e-272
##
## Tucker Lewis Index of factoring reliability = 0.842
## RMSEA index = 0.079 and the 90 % confidence intervals are 0.075 0.081
## BIC = -445.5
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## ML1 ML2 ML3
## Correlation of scores with factors 0.97 0.97 0.94
## Multiple R square of scores with factors 0.95 0.94 0.89
## Minimum correlation of possible factor scores 0.90 0.88 0.78fourfactor<-fa(purposescales, nfactors=4, rotate="oblimin", fm="ml")
fourfactor## Factor Analysis using method = ml
## Call: fa(r = purposescales, nfactors = 4, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 ML3 ML4 h2 u2 com
## 1 -0.13 0.67 0.02 -0.21 0.45 0.55 1.3
## 2 0.21 0.44 -0.06 -0.21 0.19 0.81 2.0
## 3 -0.01 0.81 -0.02 0.04 0.69 0.31 1.0
## 4 0.39 0.49 -0.11 0.08 0.47 0.53 2.1
## 5 -0.08 -0.80 0.00 0.04 0.62 0.38 1.0
## 6 0.05 0.65 0.13 0.08 0.44 0.56 1.1
## 7 0.69 0.06 0.06 0.08 0.53 0.47 1.1
## 8 0.70 0.20 -0.01 0.04 0.54 0.46 1.2
## 9 0.34 0.47 0.05 -0.31 0.21 0.79 2.7
## 10 0.78 -0.13 -0.06 0.15 0.76 0.24 1.1
## 11 0.74 -0.07 -0.03 0.05 0.60 0.40 1.0
## 12 0.03 0.44 0.10 0.09 0.22 0.78 1.2
## 13 0.75 -0.09 -0.04 0.07 0.64 0.36 1.1
## 14 0.73 -0.09 0.09 -0.13 0.50 0.50 1.1
## 15 0.18 -0.74 0.08 -0.17 0.71 0.29 1.3
## 16 0.78 0.00 0.03 0.02 0.62 0.38 1.0
## 17 0.85 -0.04 -0.03 -0.01 0.72 0.28 1.0
## 18 0.06 0.55 -0.21 0.18 0.51 0.49 1.5
## 19 0.60 -0.07 -0.01 0.15 0.47 0.53 1.2
## 20 -0.12 0.78 -0.09 0.05 0.69 0.31 1.1
## 21 0.59 0.02 0.03 0.02 0.36 0.64 1.0
## 22 -0.18 0.80 0.00 0.02 0.70 0.30 1.1
## 23 0.30 0.48 0.09 0.12 0.37 0.63 2.0
## 24 0.02 0.13 0.01 0.74 0.64 0.36 1.1
## 25 0.02 -0.05 0.78 -0.06 0.64 0.36 1.0
## 26 0.10 -0.07 0.73 0.06 0.58 0.42 1.1
## 27 0.38 0.03 0.00 0.56 0.68 0.32 1.8
## 28 0.13 0.28 0.10 0.56 0.57 0.43 1.7
## 29 0.34 0.01 -0.03 0.61 0.69 0.31 1.6
## 30 -0.08 0.00 0.75 0.18 0.56 0.44 1.1
## 31 0.07 0.06 0.78 -0.04 0.59 0.41 1.0
## 32 0.04 0.57 -0.17 0.23 0.55 0.45 1.5
## 33 -0.11 -0.01 0.82 -0.03 0.69 0.31 1.0
##
## ML1 ML2 ML3 ML4
## SS loadings 6.42 6.05 3.20 2.52
## Proportion Var 0.19 0.18 0.10 0.08
## Cumulative Var 0.19 0.38 0.47 0.55
## Proportion Explained 0.35 0.33 0.18 0.14
## Cumulative Proportion 0.35 0.69 0.86 1.00
##
## With factor correlations of
## ML1 ML2 ML3 ML4
## ML1 1.00 -0.06 0.00 0.48
## ML2 -0.06 1.00 -0.25 0.32
## ML3 0.00 -0.25 1.00 -0.08
## ML4 0.48 0.32 -0.08 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 528 and the objective function was 21.35 with Chi Square of 15888.56
## The degrees of freedom for the model are 402 and the objective function was 2.5
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic number of observations is 472 with the empirical chi square 655.09 with prob < 2e-14
## The total number of observations was 757 with MLE Chi Square = 1856.01 with prob < 4.9e-185
##
## Tucker Lewis Index of factoring reliability = 0.875
## RMSEA index = 0.07 and the 90 % confidence intervals are 0.066 0.072
## BIC = -808.99
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## ML1 ML2 ML3 ML4
## Correlation of scores with factors 0.97 0.97 0.94 0.92
## Multiple R square of scores with factors 0.94 0.94 0.89 0.85
## Minimum correlation of possible factor scores 0.88 0.87 0.78 0.70fivefactor<-fa(purposescales, nfactors=5, rotate="oblimin", fm="ml")
fivefactor## Factor Analysis using method = ml
## Call: fa(r = purposescales, nfactors = 5, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 ML3 ML4 ML5 h2 u2 com
## 1 -0.13 0.62 -0.01 -0.19 0.18 0.46 0.54 1.5
## 2 0.17 0.51 -0.02 -0.21 -0.15 0.23 0.77 1.8
## 3 -0.03 0.78 -0.03 0.06 0.07 0.69 0.31 1.0
## 4 0.33 0.57 -0.06 0.08 -0.23 0.54 0.46 2.0
## 5 -0.06 -0.76 0.01 0.02 -0.12 0.61 0.39 1.1
## 6 0.05 0.56 0.09 0.11 0.24 0.46 0.54 1.5
## 7 0.68 0.07 0.06 0.09 -0.03 0.53 0.47 1.1
## 8 0.68 0.19 -0.02 0.06 0.01 0.54 0.46 1.2
## 9 0.29 0.53 0.09 -0.31 -0.16 0.25 0.75 2.6
## 10 0.76 -0.09 -0.04 0.16 -0.13 0.77 0.23 1.2
## 11 0.76 -0.09 -0.04 0.06 0.05 0.62 0.38 1.1
## 12 0.13 0.26 -0.01 0.11 0.60 0.52 0.48 1.6
## 13 0.76 -0.12 -0.06 0.09 0.05 0.65 0.35 1.1
## 14 0.78 -0.14 0.05 -0.13 0.20 0.56 0.44 1.3
## 15 0.19 -0.69 0.10 -0.18 -0.14 0.72 0.28 1.4
## 16 0.76 0.00 0.03 0.04 -0.01 0.62 0.38 1.0
## 17 0.82 -0.02 -0.03 0.01 -0.07 0.71 0.29 1.0
## 18 0.01 0.60 -0.17 0.18 -0.17 0.56 0.44 1.5
## 19 0.56 -0.01 0.03 0.15 -0.20 0.49 0.51 1.4
## 20 -0.16 0.80 -0.06 0.05 -0.05 0.72 0.28 1.1
## 21 0.60 -0.01 0.00 0.04 0.09 0.38 0.62 1.1
## 22 -0.20 0.79 0.00 0.02 0.04 0.70 0.30 1.1
## 23 0.34 0.38 0.04 0.15 0.30 0.45 0.55 3.3
## 24 0.02 0.06 -0.01 0.78 0.13 0.68 0.32 1.1
## 25 0.00 -0.03 0.79 -0.06 -0.06 0.65 0.35 1.0
## 26 0.08 -0.04 0.75 0.06 -0.08 0.59 0.41 1.1
## 27 0.35 0.07 0.04 0.57 -0.17 0.70 0.30 1.9
## 28 0.14 0.23 0.08 0.58 0.12 0.59 0.41 1.6
## 29 0.31 0.04 0.00 0.62 -0.15 0.70 0.30 1.6
## 30 -0.09 0.00 0.75 0.18 -0.02 0.56 0.44 1.1
## 31 0.06 0.06 0.78 -0.04 0.01 0.59 0.41 1.0
## 32 0.01 0.58 -0.15 0.23 -0.05 0.55 0.45 1.5
## 33 -0.10 -0.04 0.80 -0.03 0.10 0.69 0.31 1.1
##
## ML1 ML2 ML3 ML4 ML5
## SS loadings 6.33 5.85 3.18 2.69 1.02
## Proportion Var 0.19 0.18 0.10 0.08 0.03
## Cumulative Var 0.19 0.37 0.47 0.55 0.58
## Proportion Explained 0.33 0.31 0.17 0.14 0.05
## Cumulative Proportion 0.33 0.64 0.81 0.95 1.00
##
## With factor correlations of
## ML1 ML2 ML3 ML4 ML5
## ML1 1.00 -0.04 0.02 0.46 -0.17
## ML2 -0.04 1.00 -0.26 0.35 0.18
## ML3 0.02 -0.26 1.00 -0.08 0.07
## ML4 0.46 0.35 -0.08 1.00 0.01
## ML5 -0.17 0.18 0.07 0.01 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 5 factors are sufficient.
##
## The degrees of freedom for the null model are 528 and the objective function was 21.35 with Chi Square of 15888.56
## The degrees of freedom for the model are 373 and the objective function was 1.95
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 472 with the empirical chi square 397.38 with prob < 0.18
## The total number of observations was 757 with MLE Chi Square = 1447.91 with prob < 2.8e-126
##
## Tucker Lewis Index of factoring reliability = 0.9
## RMSEA index = 0.063 and the 90 % confidence intervals are 0.058 0.065
## BIC = -1024.84
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## ML1 ML2 ML3 ML4 ML5
## Correlation of scores with factors 0.97 0.97 0.94 0.93 0.82
## Multiple R square of scores with factors 0.94 0.94 0.89 0.86 0.68
## Minimum correlation of possible factor scores 0.88 0.87 0.79 0.73 0.36#1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33
#Create dataset for Target rotationall_surveys<-read.csv("allsurveysT1.csv")
purposescales<-select(all_surveys, PWB_7, PWB_8, APSI_1, APSI_2, APSI_4, APSI_5, APSI_7, APSI_8, LET_2, LET_4, PWB_1, PWB_2, PWB_3, PWB_4, PWB_5, PWB_6, PWB_9, APSI_3, APSI_6, LET_1, LET_3, LET_5, LET_6, MLQ_9, MLQ_2, MLQ_3, MLQ_7, MLQ_8,MLQ_10, MLQ_1, MLQ_4, MLQ_5, MLQ_6)
purposescales$PWB_1 <- 7- purposescales$PWB_1
purposescales$PWB_2 <- 7- purposescales$PWB_2
purposescales$PWB_3 <- 7- purposescales$PWB_3
purposescales$PWB_4 <- 7- purposescales$PWB_4
purposescales$PWB_9 <- 7- purposescales$PWB_9
purposescales$MLQ_9 <- 8- purposescales$MLQ_9
purposescales$LET_1 <- 6- purposescales$LET_1
purposescales$LET_3 <- 6- purposescales$LET_3
purposescales$LET_5 <- 6- purposescales$LET_5
purposescales<- data.frame(apply(purposescales,2, as.numeric))library(GPArotation)
library(psych)
library(dplyr)
purposescales<-tbl_df(purposescales)
purposescales## Source: local data frame [757 x 33]
##
## PWB_7 PWB_8 APSI_1 APSI_2 APSI_4 APSI_5 APSI_7 APSI_8 LET_2 LET_4 PWB_1
## 1 4 3 2 4 4 4 4 4 4 5 4
## 2 3 2 4 3 5 4 4 4 3 4 4
## 3 6 3 3 4 3 3 4 3 4 4 5
## 4 5 4 4 4 4 5 4 3 4 4 2
## 5 2 3 3 3 3 4 2 3 2 4 2
## 6 3 4 3 4 4 4 5 3 5 5 5
## 7 3 3 2 2 3 4 2 2 4 3 2
## 8 4 4 3 3 3 5 3 1 4 4 6
## 9 5 5 4 5 4 4 4 5 4 5 5
## 10 6 3 2 2 3 5 3 4 3 5 6
## .. ... ... ... ... ... ... ... ... ... ... ...
## Variables not shown: PWB_2 (dbl), PWB_3 (dbl), PWB_4 (dbl), PWB_5 (dbl),
## PWB_6 (dbl), PWB_9 (dbl), APSI_3 (dbl), APSI_6 (dbl), LET_1 (dbl), LET_3
## (dbl), LET_5 (dbl), LET_6 (dbl), MLQ_9 (dbl), MLQ_2 (dbl), MLQ_3 (dbl),
## MLQ_7 (dbl), MLQ_8 (dbl), MLQ_10 (dbl), MLQ_1 (dbl), MLQ_4 (dbl), MLQ_5
## (dbl), MLQ_6 (dbl)str(purposescales)## Classes 'tbl_df', 'tbl' and 'data.frame': 757 obs. of 33 variables:
## $ PWB_7 : num 4 3 6 5 2 3 3 4 5 6 ...
## $ PWB_8 : num 3 2 3 4 3 4 3 4 5 3 ...
## $ APSI_1: num 2 4 3 4 3 3 2 3 4 2 ...
## $ APSI_2: num 4 3 4 4 3 4 2 3 5 2 ...
## $ APSI_4: num 4 5 3 4 3 4 3 3 4 3 ...
## $ APSI_5: num 4 4 3 5 4 4 4 5 4 5 ...
## $ APSI_7: num 4 4 4 4 2 5 2 3 4 3 ...
## $ APSI_8: num 4 4 3 3 3 3 2 1 5 4 ...
## $ LET_2 : num 4 3 4 4 2 5 4 4 4 3 ...
## $ LET_4 : num 5 4 4 4 4 5 3 4 5 5 ...
## $ PWB_1 : num 4 4 5 2 2 5 2 6 5 6 ...
## $ PWB_2 : num 3 5 6 2 2 4 2 6 5 6 ...
## $ PWB_3 : num 5 5 5 4 3 6 5 5 5 3 ...
## $ PWB_4 : num 2 2 6 4 3 5 2 1 5 3 ...
## $ PWB_5 : num 4 2 1 3 4 3 1 2 1 2 ...
## $ PWB_6 : num 5 5 4 4 3 4 4 4 5 6 ...
## $ PWB_9 : num 6 5 6 4 4 6 3 6 6 6 ...
## $ APSI_3: num 4 4 4 5 4 4 4 4 5 2 ...
## $ APSI_6: num 4 3 3 4 3 2 4 3 2 3 ...
## $ LET_1 : num 4 3 3 1 3 5 3 3 5 3 ...
## $ LET_3 : num 4 4 3 4 3 5 2 3 5 5 ...
## $ LET_5 : num 5 4 4 4 2 5 3 4 5 5 ...
## $ LET_6 : num 5 5 5 4 4 4 5 5 5 5 ...
## $ MLQ_9 : num 3 3 4 3 5 7 5 4 7 6 ...
## $ MLQ_2 : num 7 5 7 6 6 5 2 7 5 7 ...
## $ MLQ_3 : num 7 5 5 7 5 3 2 7 2 1 ...
## $ MLQ_7 : num 5 5 4 5 5 3 5 5 5 5 ...
## $ MLQ_8 : num 7 4 5 5 5 4 4 7 7 5 ...
## $ MLQ_10: num 7 5 4 6 5 3 4 5 2 1 ...
## $ MLQ_1 : num 4 3 4 5 4 5 6 3 6 1 ...
## $ MLQ_4 : num 5 5 4 3 4 4 3 5 7 3 ...
## $ MLQ_5 : num 6 4 4 5 4 5 6 5 6 5 ...
## $ MLQ_6 : num 4 3 4 5 4 5 3 4 6 1 ...colnames(purposescales) <- c("1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20","21","22","23","24","25","26","27","28","29","30","31","32","33")
#Target rotation: choose "simple structure" a priori and can be applied to oblique and orthogonal rotation based on
#what paper says facotrs should be purposescales
Targ_key <- make.keys(33,list(f1=1:10,f2=11:24, f3=25:29,f4=30:33))
Targ_key <- scrub(Targ_key,isvalue=1) #fix the 0s, allow the NAs to be estimated
Targ_key <- list(Targ_key)
out_targetQ <- fa(purposescales,4,rotate="TargetQ",Target=Targ_key) #TargetT for orthogonal rotation
out_targetQ[c("loadings", "score.cor", "TLI", "RMSEA")]## $loadings
##
## Loadings:
## MR2 MR1 MR3 MR4
## 1 0.671 0.102
## 2 0.221 0.668
## 3 -0.113 0.761 0.192
## 4 0.732
## 5 0.740 0.103
## 6 0.736 -0.114
## 7 0.762
## 8 0.838
## 9 0.578 0.180
## 10 0.576
## 11 0.690 -0.140 -0.252
## 12 0.480 0.217 -0.243
## 13 0.814
## 14 0.507 0.350 -0.102
## 15 -0.813
## 16 0.649 0.148
## 17 0.504 0.339 -0.343
## 18 0.442 0.114
## 19 -0.732 0.234 -0.156
## 20 0.547 -0.201 0.178
## 21 0.776 -0.171
## 22 0.796 -0.228
## 23 0.482 0.260 0.106 0.134
## 24 0.563 -0.156 0.234
## 25 0.772
## 26 0.727
## 27 0.745 0.183
## 28 0.774
## 29 -0.112 0.817
## 30 0.102 0.774
## 31 0.338 0.595
## 32 0.264 0.106 0.590
## 33 0.288 0.654
##
## MR2 MR1 MR3 MR4
## SS loadings 5.958 5.801 3.120 2.289
## Proportion Var 0.181 0.176 0.095 0.069
## Cumulative Var 0.181 0.356 0.451 0.520
##
## $score.cor
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.04012196 -0.26146080 0.41687774
## [2,] 0.04012196 1.00000000 0.02146049 0.60399438
## [3,] -0.26146080 0.02146049 1.00000000 -0.04316592
## [4,] 0.41687774 0.60399438 -0.04316592 1.00000000
##
## $TLI
## [1] 0.8751593
##
## $RMSEA
## RMSEA lower upper confidence
## 0.07004073 0.06597274 0.07233424 0.10000000out_targetQ## Factor Analysis using method = minres
## Call: fa(r = purposescales, nfactors = 4, rotate = "TargetQ", Target = Targ_key)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR2 MR1 MR3 MR4 h2 u2 com
## 1 0.07 0.67 0.06 0.10 0.54 0.46 1.1
## 2 0.22 0.67 -0.01 0.06 0.54 0.46 1.2
## 3 -0.11 0.76 -0.06 0.19 0.76 0.24 1.2
## 4 -0.05 0.73 -0.03 0.08 0.61 0.39 1.0
## 5 -0.08 0.74 -0.04 0.10 0.64 0.36 1.1
## 6 -0.06 0.74 0.09 -0.11 0.50 0.50 1.1
## 7 0.02 0.76 0.03 0.05 0.62 0.38 1.0
## 8 -0.01 0.84 -0.04 0.02 0.72 0.28 1.0
## 9 -0.06 0.58 -0.02 0.18 0.47 0.53 1.2
## 10 0.04 0.58 0.03 0.05 0.36 0.64 1.0
## 11 0.69 -0.14 0.04 -0.25 0.46 0.54 1.4
## 12 0.48 0.22 -0.05 -0.24 0.20 0.80 2.0
## 13 0.81 -0.06 0.00 0.03 0.69 0.31 1.0
## 14 0.51 0.35 -0.10 0.08 0.47 0.53 1.9
## 15 -0.81 -0.04 -0.02 0.06 0.62 0.38 1.0
## 16 0.65 0.00 0.15 0.08 0.44 0.56 1.1
## 17 0.50 0.34 0.06 -0.34 0.22 0.78 2.6
## 18 0.44 0.00 0.11 0.09 0.22 0.78 1.2
## 19 -0.73 0.23 0.07 -0.16 0.71 0.29 1.3
## 20 0.55 0.02 -0.20 0.18 0.51 0.49 1.5
## 21 0.78 -0.17 -0.07 0.04 0.69 0.31 1.1
## 22 0.80 -0.23 0.02 0.00 0.69 0.31 1.2
## 23 0.48 0.26 0.11 0.13 0.38 0.62 1.8
## 24 0.56 -0.01 -0.16 0.23 0.55 0.45 1.5
## 25 -0.06 0.03 0.77 -0.06 0.64 0.36 1.0
## 26 -0.08 0.10 0.73 0.08 0.58 0.42 1.1
## 27 -0.02 -0.09 0.74 0.18 0.56 0.44 1.2
## 28 0.06 0.06 0.77 -0.04 0.59 0.41 1.0
## 29 -0.02 -0.11 0.82 -0.03 0.70 0.30 1.0
## 30 0.10 -0.04 0.02 0.77 0.64 0.36 1.0
## 31 0.02 0.34 0.00 0.59 0.67 0.33 1.6
## 32 0.26 0.07 0.11 0.59 0.57 0.43 1.5
## 33 -0.01 0.29 -0.03 0.65 0.69 0.31 1.4
##
## MR2 MR1 MR3 MR4
## SS loadings 6.11 6.18 3.15 2.78
## Proportion Var 0.19 0.19 0.10 0.08
## Cumulative Var 0.19 0.37 0.47 0.55
## Proportion Explained 0.34 0.34 0.17 0.15
## Cumulative Proportion 0.34 0.67 0.85 1.00
##
## With factor correlations of
## MR2 MR1 MR3 MR4
## MR2 1.00 -0.04 -0.26 0.38
## MR1 -0.04 1.00 0.02 0.49
## MR3 -0.26 0.02 1.00 -0.08
## MR4 0.38 0.49 -0.08 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 528 and the objective function was 21.35 with Chi Square of 15888.56
## The degrees of freedom for the model are 402 and the objective function was 2.5
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic number of observations is 472 with the empirical chi square 650.24 with prob < 5.3e-14
## The total number of observations was 757 with MLE Chi Square = 1856.6 with prob < 3.9e-185
##
## Tucker Lewis Index of factoring reliability = 0.875
## RMSEA index = 0.07 and the 90 % confidence intervals are 0.066 0.072
## BIC = -808.41
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## MR2 MR1 MR3 MR4
## Correlation of scores with factors 0.97 0.97 0.94 0.93
## Multiple R square of scores with factors 0.94 0.94 0.89 0.87
## Minimum correlation of possible factor scores 0.88 0.88 0.78 0.74#The best fit to the data seems to be three factors. F1: questions 1,3,5,6. f2: 8,7,4. f3: 2,9CFI
1-((out_targetQ$STATISTIC - out_targetQ$dof)/(out_targetQ$null.chisq- out_targetQ$null.dof))## [1] 0.9053032