EFA CFA & TR PWB Youth
Levi Brackman
28 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")
PWB<-select(data, PWB_1, PWB_2, PWB_3, PWB_4, PWB_5, PWB_6, PWB_7, PWB_8, PWB_9)
PWB$PWB_1 <- 7- PWB$PWB_1
PWB$PWB_2 <- 7- PWB$PWB_2
PWB$PWB_3 <- 7- PWB$PWB_3
PWB$PWB_4 <- 7- PWB$PWB_4
PWB$PWB_9 <- 7- PWB$PWB_9
PWB<- data.frame(apply(PWB,2, as.numeric))
PWB<-tbl_df(PWB)
PWB## Source: local data frame [757 x 9]
##
## PWB_1 PWB_2 PWB_3 PWB_4 PWB_5 PWB_6 PWB_7 PWB_8 PWB_9
## 1 4 3 5 2 4 5 4 3 6
## 2 4 5 5 2 2 5 3 2 5
## 3 5 6 5 6 1 4 6 3 6
## 4 2 2 4 4 3 4 5 4 4
## 5 2 2 3 3 4 3 2 3 4
## 6 5 4 6 5 3 4 3 4 6
## 7 2 2 5 2 1 4 3 3 3
## 8 6 6 5 1 2 4 4 4 6
## 9 5 5 5 5 1 5 5 5 6
## 10 6 6 3 3 2 6 6 3 6
## .. ... ... ... ... ... ... ... ... ...str(PWB)## Classes 'tbl_df', 'tbl' and 'data.frame': 757 obs. of 9 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 ...colnames(PWB) <- c("1","2", "3", "4", "5", "6", "7", "8", "9")
PWB<- PWB[complete.cases(PWB[,]),]
##EFA
##number of factors
##parallal analysis and scree plot
parallel<-fa.parallel(PWB, fm="ml",fa="fa")
## Parallel analysis suggests that the number of factors = 3 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] 2.764589905 0.925824683 0.367705915 0.031000693 -0.006112395
## [6] -0.150861796 -0.275610741 -0.317569437 -0.606030196#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(PWB), cor = TRUE)## Call:
## princomp(x = na.omit(PWB), cor = TRUE)
##
## Standard deviations:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7
## 1.8258502 1.3343875 1.0554192 0.8256147 0.7860937 0.6451339 0.6328747
## Comp.8 Comp.9
## 0.5906555 0.5537025
##
## 9 variables and 471 observations.parallel2<-princomp(na.omit(PWB), cor = TRUE)
summary(parallel2)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.8258502 1.3343875 1.0554192 0.82561467 0.78609375
## Proportion of Variance 0.3704143 0.1978433 0.1237677 0.07573773 0.06866038
## Cumulative Proportion 0.3704143 0.5682577 0.6920254 0.76776312 0.83642349
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 0.6451339 0.63287472 0.59065550 0.55370250
## Proportion of Variance 0.0462442 0.04450338 0.03876377 0.03406516
## Cumulative Proportion 0.8826677 0.92717107 0.96593484 1.00000000plot(parallel2)##results show at least two factors
#simple structure
twofactor<-fa(PWB, nfactors=2, rotate="oblimin", fm="ml")
twofactor## Factor Analysis using method = ml
## Call: fa(r = PWB, nfactors = 2, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 h2 u2 com
## 1 0.68 -0.25 0.48 0.52 1.3
## 2 0.40 0.13 0.18 0.82 1.2
## 3 0.80 -0.02 0.64 0.36 1.0
## 4 0.46 0.41 0.42 0.58 2.0
## 5 -0.81 -0.04 0.67 0.33 1.0
## 6 0.60 0.11 0.39 0.61 1.1
## 7 -0.07 0.87 0.74 0.26 1.0
## 8 0.10 0.72 0.54 0.46 1.0
## 9 0.36 0.10 0.15 0.85 1.1
##
## ML1 ML2
## SS loadings 2.66 1.55
## Proportion Var 0.30 0.17
## Cumulative Var 0.30 0.47
## Proportion Explained 0.63 0.37
## Cumulative Proportion 0.63 1.00
##
## With factor correlations of
## ML1 ML2
## ML1 1.00 0.12
## ML2 0.12 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 36 and the objective function was 3 with Chi Square of 1399.69
## The degrees of freedom for the model are 19 and the objective function was 0.32
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.09
##
## The harmonic number of observations is 471 with the empirical chi square 138.64 with prob < 3.3e-20
## The total number of observations was 471 with MLE Chi Square = 147.52 with prob < 6.6e-22
##
## Tucker Lewis Index of factoring reliability = 0.821
## RMSEA index = 0.121 and the 90 % confidence intervals are 0.102 0.138
## BIC = 30.58
## Fit based upon off diagonal values = 0.96
## Measures of factor score adequacy
## ML1 ML2
## Correlation of scores with factors 0.93 0.90
## Multiple R square of scores with factors 0.86 0.82
## Minimum correlation of possible factor scores 0.72 0.63threefactor<-fa(PWB, nfactors=3, rotate="oblimin", fm="ml")
threefactor## Factor Analysis using method = ml
## Call: fa(r = PWB, nfactors = 3, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML2 ML3 ML1 h2 u2 com
## 1 0.58 -0.28 0.21 0.50 0.500 1.7
## 2 -0.01 0.02 1.00 1.00 0.005 1.0
## 3 0.83 -0.02 -0.03 0.67 0.331 1.0
## 4 0.38 0.38 0.19 0.43 0.572 2.5
## 5 -0.80 -0.03 -0.04 0.67 0.331 1.0
## 6 0.68 0.13 -0.13 0.45 0.553 1.1
## 7 -0.08 0.85 0.05 0.72 0.278 1.0
## 8 0.12 0.73 -0.02 0.56 0.442 1.1
## 9 0.22 0.06 0.30 0.20 0.803 1.9
##
## ML2 ML3 ML1
## SS loadings 2.41 1.52 1.26
## Proportion Var 0.27 0.17 0.14
## Cumulative Var 0.27 0.44 0.58
## Proportion Explained 0.46 0.29 0.24
## Cumulative Proportion 0.46 0.76 1.00
##
## With factor correlations of
## ML2 ML3 ML1
## ML2 1.00 0.11 0.35
## ML3 0.11 1.00 0.12
## ML1 0.35 0.12 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 36 and the objective function was 3 with Chi Square of 1399.69
## The degrees of freedom for the model are 12 and the objective function was 0.09
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 471 with the empirical chi square 24.05 with prob < 0.02
## The total number of observations was 471 with MLE Chi Square = 42.44 with prob < 2.8e-05
##
## Tucker Lewis Index of factoring reliability = 0.933
## RMSEA index = 0.074 and the 90 % confidence intervals are 0.05 0.098
## BIC = -31.42
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## ML2 ML3 ML1
## Correlation of scores with factors 0.93 0.90 1.00
## Multiple R square of scores with factors 0.86 0.81 0.99
## Minimum correlation of possible factor scores 0.72 0.62 0.99fourfactor<-fa(PWB, nfactors=4, rotate="oblimin", fm="ml")
fourfactor## Factor Analysis using method = ml
## Call: fa(r = PWB, nfactors = 4, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 ML3 ML4 h2 u2 com
## 1 0.12 -0.20 0.37 0.51 0.61 0.39 2.3
## 2 -0.01 0.03 0.83 -0.01 0.68 0.32 1.0
## 3 0.85 -0.10 -0.03 0.08 0.75 0.25 1.0
## 4 0.57 0.29 0.20 -0.22 0.53 0.47 2.1
## 5 -0.56 -0.03 -0.12 -0.26 0.64 0.36 1.5
## 6 0.26 0.24 -0.09 0.57 0.56 0.44 1.9
## 7 -0.08 0.86 0.04 -0.01 0.72 0.28 1.0
## 8 0.07 0.73 -0.02 0.06 0.56 0.44 1.0
## 9 0.13 0.04 0.40 0.02 0.24 0.76 1.2
##
## ML1 ML2 ML3 ML4
## SS loadings 1.75 1.49 1.16 0.89
## Proportion Var 0.19 0.17 0.13 0.10
## Cumulative Var 0.19 0.36 0.49 0.59
## Proportion Explained 0.33 0.28 0.22 0.17
## Cumulative Proportion 0.33 0.61 0.83 1.00
##
## With factor correlations of
## ML1 ML2 ML3 ML4
## ML1 1.00 0.21 0.43 0.55
## ML2 0.21 1.00 0.14 -0.12
## ML3 0.43 0.14 1.00 0.17
## ML4 0.55 -0.12 0.17 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 36 and the objective function was 3 with Chi Square of 1399.69
## The degrees of freedom for the model are 6 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 471 with the empirical chi square 4.69 with prob < 0.58
## The total number of observations was 471 with MLE Chi Square = 8.85 with prob < 0.18
##
## Tucker Lewis Index of factoring reliability = 0.987
## RMSEA index = 0.032 and the 90 % confidence intervals are NA 0.073
## BIC = -28.08
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML1 ML2 ML3 ML4
## Correlation of scores with factors 0.92 0.90 0.87 0.83
## Multiple R square of scores with factors 0.85 0.81 0.75 0.69
## Minimum correlation of possible factor scores 0.69 0.63 0.51 0.38#question 1,3,5,6,9 seems to be one factor and all talk about plans or lack of plans
PWBWO15<-select(PWB, 1,3,4,5,6,9)
PWBWO15<-tbl_df(PWBWO15)
PWBWO15## Source: local data frame [471 x 6]
##
## 1 3 4 5 6 9
## 1 4 5 2 4 5 6
## 2 4 5 2 2 5 5
## 3 5 5 6 1 4 6
## 4 2 4 4 3 4 4
## 5 2 3 3 4 3 4
## 6 5 6 5 3 4 6
## 7 2 5 2 1 4 3
## 8 6 5 1 2 4 6
## 9 5 5 5 1 5 6
## 10 6 3 3 2 6 6
## .. . . . . . .twofactorWO15<-fa(PWBWO15, nfactors=1, rotate="oblimin", fm="ml")
twofactorWO15## Factor Analysis using method = ml
## Call: fa(r = PWBWO15, nfactors = 1, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 h2 u2 com
## 1 0.61 0.37 0.63 1
## 3 0.81 0.66 0.34 1
## 4 0.49 0.24 0.76 1
## 5 -0.83 0.69 0.31 1
## 6 0.63 0.40 0.60 1
## 9 0.35 0.12 0.88 1
##
## ML1
## SS loadings 2.48
## Proportion Var 0.41
##
## 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 1.78 with Chi Square of 833.12
## The degrees of freedom for the model are 9 and the objective function was 0.09
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.07
##
## The harmonic number of observations is 471 with the empirical chi square 36.77 with prob < 2.9e-05
## The total number of observations was 471 with MLE Chi Square = 40.05 with prob < 7.4e-06
##
## Tucker Lewis Index of factoring reliability = 0.937
## RMSEA index = 0.086 and the 90 % confidence intervals are 0.06 0.113
## BIC = -15.34
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## ML1
## Correlation of scores with factors 0.92
## Multiple R square of scores with factors 0.85
## Minimum correlation of possible factor scores 0.71#CFI, should be slightly higher than the TLI
1-((twofactorWO15$STATISTIC - twofactor$dof)/(twofactor$null.chisq- twofactor$null.dof))## [1] 0.984563#question 7,8 seems to be one factor and all talk about being active or wondering aimlessly
PWB78<-select(PWB, 7,8)
PWB78<-tbl_df(PWB78)
PWB78## Source: local data frame [471 x 2]
##
## 7 8
## 1 4 3
## 2 3 2
## 3 6 3
## 4 5 4
## 5 2 3
## 6 3 4
## 7 3 3
## 8 4 4
## 9 5 5
## 10 6 3
## .. . .twofactor78<-fa(PWB78, nfactors=1, rotate="oblimin", fm="ml")
twofactor78## Factor Analysis using method = ml
## Call: fa(r = PWB78, nfactors = 1, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 h2 u2 com
## 7 0.79 0.62 0.38 1
## 8 0.79 0.62 0.38 1
##
## ML1
## SS loadings 1.23
## Proportion Var 0.62
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 1 and the objective function was 0.48 with Chi Square of 224.1
## The degrees of freedom for the model are -1 and the objective function was 0
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is NA
##
## The harmonic number of observations is 471 with the empirical chi square 0 with prob < NA
## The total number of observations was 471 with MLE Chi Square = 0 with prob < NA
##
## Tucker Lewis Index of factoring reliability = 1.004
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML1
## Correlation of scores with factors 0.87
## Multiple R square of scores with factors 0.76
## Minimum correlation of possible factor scores 0.53#CFI, should be slightly higher than the TLI
1-((twofactorWO15$STATISTIC - twofactor$dof)/(twofactor$null.chisq- twofactor$null.dof))## [1] 0.984563#question 2,8 seems to be one factor
PWB29<-select(PWB, 2,8)
PWB29<-tbl_df(PWB29)
PWB29## Source: local data frame [471 x 2]
##
## 2 8
## 1 3 3
## 2 5 2
## 3 6 3
## 4 2 4
## 5 2 3
## 6 4 4
## 7 2 3
## 8 6 4
## 9 5 5
## 10 6 3
## .. . .twofactor29<-fa(PWB29, nfactors=1, rotate="oblimin", fm="ml")
twofactor29## Factor Analysis using method = ml
## Call: fa(r = PWB29, nfactors = 1, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 h2 u2 com
## 2 0.34 0.12 0.88 1
## 8 0.34 0.12 0.88 1
##
## ML1
## SS loadings 0.24
## Proportion Var 0.12
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 1 and the objective function was 0.01 with Chi Square of 6.65
## The degrees of freedom for the model are -1 and the objective function was 0
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is NA
##
## The harmonic number of observations is 471 with the empirical chi square 0 with prob < NA
## The total number of observations was 471 with MLE Chi Square = 0 with prob < NA
##
## Tucker Lewis Index of factoring reliability = 1.177
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML1
## Correlation of scores with factors 0.46
## Multiple R square of scores with factors 0.21
## Minimum correlation of possible factor scores -0.58#CFI, should be slightly higher than the TLI
1-((twofactor29$STATISTIC - twofactor$dof)/(twofactor$null.chisq- twofactor$null.dof))## [1] 1.013933##reliability
#alpha(PWB[,c(1,2,3,4,5,6,7,8,9)])
#alpha(PWB[,c(5,9,10,14)])
#What are the factors
#Factor 1 is positive emotions
#Factor 2 is negative emotions
#Create dataset for Target rotationall_surveys<-read.csv("allsurveysT1.csv")
PWB<-select(all_surveys, PWB_1, PWB_3, PWB_5,PWB_6, PWB_8,PWB_7, PWB_4, PWB_2, PWB_9)
PWB<- data.frame(apply(PWB,2, as.numeric))library(GPArotation)
library(psych)
library(dplyr)
PWB<-tbl_df(PWB)
PWB## Source: local data frame [757 x 9]
##
## PWB_1 PWB_3 PWB_5 PWB_6 PWB_8 PWB_7 PWB_4 PWB_2 PWB_9
## 1 3 2 4 5 3 4 5 4 1
## 2 3 2 2 5 2 3 5 2 2
## 3 2 2 1 4 3 6 1 1 1
## 4 5 3 3 4 4 5 3 5 3
## 5 5 4 4 3 3 2 4 5 3
## 6 2 1 3 4 4 3 2 3 1
## 7 5 2 1 4 3 3 5 5 4
## 8 1 2 2 4 4 4 6 1 1
## 9 2 2 1 5 5 5 2 2 1
## 10 1 4 2 6 3 6 4 1 1
## .. ... ... ... ... ... ... ... ... ...str(PWB)## Classes 'tbl_df', 'tbl' and 'data.frame': 757 obs. of 9 variables:
## $ PWB_1: num 3 3 2 5 5 2 5 1 2 1 ...
## $ PWB_3: num 2 2 2 3 4 1 2 2 2 4 ...
## $ 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_8: num 3 2 3 4 3 4 3 4 5 3 ...
## $ PWB_7: num 4 3 6 5 2 3 3 4 5 6 ...
## $ PWB_4: num 5 5 1 3 4 2 5 6 2 4 ...
## $ PWB_2: num 4 2 1 5 5 3 5 1 2 1 ...
## $ PWB_9: num 1 2 1 3 3 1 4 1 1 1 ...colnames(PWB) <- c("1","2", "3", "4", "5", "6", "7", "8", "9")
#Target rotation: choose "simple structure" a priori and can be applied to oblique and orthogonal rotation based on
#what paper says facotrs should be PWB
Targ_key <- make.keys(9,list(f1=1:4,f2=5:7, f3=8:9))
Targ_key <- scrub(Targ_key,isvalue=1) #fix the 0s, allow the NAs to be estimated
Targ_key <- list(Targ_key)
PWB_cor <- corFiml(PWB) # convert the raw data to correlation matrix uisng FIML
out_targetQ <- fa(PWB_cor,3,rotate="TargetQ",n.obs = 816,Target=Targ_key) #TargetT for orthogonal rotation
out_targetQ[c("loadings", "score.cor", "TLI", "RMSEA")]## $loadings
##
## Loadings:
## MR1 MR2 MR3
## 1 0.584 0.250 0.232
## 2 0.833
## 3 0.784
## 4 -0.692 0.153 0.173
## 5 0.739
## 6 0.173 0.864
## 7 0.304 -0.414 0.210
## 8 0.903
## 9 0.159 0.358
##
## MR1 MR2 MR3
## SS loadings 2.284 1.567 1.077
## Proportion Var 0.254 0.174 0.120
## Cumulative Var 0.254 0.428 0.547
##
## $score.cor
## [,1] [,2] [,3]
## [1,] 1.0000000 -0.2363435 0.3815248
## [2,] -0.2363435 1.0000000 -0.2859293
## [3,] 0.3815248 -0.2859293 1.0000000
##
## $TLI
## [1] 0.9200451
##
## $RMSEA
## RMSEA lower upper confidence
## 0.08110859 0.06388654 0.09855956 0.10000000out_targetQ## Factor Analysis using method = minres
## Call: fa(r = PWB_cor, nfactors = 3, n.obs = 816, rotate = "TargetQ",
## Target = Targ_key)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 h2 u2 com
## 1 0.58 0.25 0.23 0.51 0.49 1.7
## 2 0.83 -0.01 -0.04 0.67 0.33 1.0
## 3 0.78 -0.07 0.04 0.67 0.33 1.0
## 4 -0.69 0.15 0.17 0.46 0.54 1.2
## 5 -0.05 0.74 0.03 0.55 0.45 1.0
## 6 0.17 0.86 -0.04 0.73 0.27 1.1
## 7 0.30 -0.41 0.21 0.43 0.57 2.4
## 8 -0.06 -0.08 0.90 0.79 0.21 1.0
## 9 0.16 -0.08 0.36 0.22 0.78 1.5
##
## MR1 MR2 MR3
## SS loadings 2.32 1.59 1.12
## Proportion Var 0.26 0.18 0.12
## Cumulative Var 0.26 0.43 0.56
## Proportion Explained 0.46 0.32 0.22
## Cumulative Proportion 0.46 0.78 1.00
##
## With factor correlations of
## MR1 MR2 MR3
## MR1 1.00 -0.18 0.44
## MR2 -0.18 1.00 -0.13
## MR3 0.44 -0.13 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 36 and the objective function was 3 with Chi Square of 2435.57
## The degrees of freedom for the model are 12 and the objective function was 0.09
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 816 with the empirical chi square 40.13 with prob < 6.9e-05
## The total number of observations was 816 with MLE Chi Square = 75.79 with prob < 2.6e-11
##
## Tucker Lewis Index of factoring reliability = 0.92
## RMSEA index = 0.081 and the 90 % confidence intervals are 0.064 0.099
## BIC = -4.66
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## MR1 MR2 MR3
## Correlation of scores with factors 0.93 0.90 0.91
## Multiple R square of scores with factors 0.86 0.82 0.82
## Minimum correlation of possible factor scores 0.72 0.63 0.64#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] 0.9734151Droping question 4 because it loads on all of the factors. Much better fit to the data
all_surveys<-read.csv("allsurveysT1.csv")
PWB<-select(all_surveys, PWB_1, PWB_3, PWB_5,PWB_6, PWB_8,PWB_7, PWB_2, PWB_9)
PWB<- data.frame(apply(PWB,2, as.numeric))
PWB<-tbl_df(PWB)
PWB## Source: local data frame [757 x 8]
##
## PWB_1 PWB_3 PWB_5 PWB_6 PWB_8 PWB_7 PWB_2 PWB_9
## 1 3 2 4 5 3 4 4 1
## 2 3 2 2 5 2 3 2 2
## 3 2 2 1 4 3 6 1 1
## 4 5 3 3 4 4 5 5 3
## 5 5 4 4 3 3 2 5 3
## 6 2 1 3 4 4 3 3 1
## 7 5 2 1 4 3 3 5 4
## 8 1 2 2 4 4 4 1 1
## 9 2 2 1 5 5 5 2 1
## 10 1 4 2 6 3 6 1 1
## .. ... ... ... ... ... ... ... ...colnames(PWB) <- c("1","2", "3", "4", "5", "6", "7", "8")
#Target rotation: choose "simple structure" a priori and can be applied to oblique and orthogonal rotation based on
#what paper says facotrs should be PWB
Targ_key <- make.keys(8,list(f1=1:4,f2=5:6, f3=7:8))
Targ_key <- scrub(Targ_key,isvalue=1) #fix the 0s, allow the NAs to be estimated
Targ_key <- list(Targ_key)
PWB_cor <- corFiml(PWB) # convert the raw data to correlation matrix uisng FIML
out_targetQ <- fa(PWB_cor,3,rotate="TargetQ",n.obs = 816,Target=Targ_key) #TargetT for orthogonal rotation
out_targetQ[c("loadings", "score.cor", "TLI", "RMSEA")]## $loadings
##
## Loadings:
## MR1 MR2 MR3
## 1 0.569 0.251 0.235
## 2 0.808
## 3 0.788
## 4 -0.728 0.150 0.174
## 5 -0.113 0.713
## 6 0.864
## 7 0.832
## 8 0.153 0.397
##
## MR1 MR2 MR3
## SS loadings 2.175 1.353 0.947
## Proportion Var 0.272 0.169 0.118
## Cumulative Var 0.272 0.441 0.559
##
## $score.cor
## [,1] [,2] [,3]
## [1,] 1.00000000 -0.08530808 0.3815220
## [2,] -0.08530808 1.00000000 -0.1663979
## [3,] 0.38152199 -0.16639785 1.0000000
##
## $TLI
## [1] 0.9417259
##
## $RMSEA
## RMSEA lower upper confidence
## 0.07150314 0.04917574 0.09499976 0.10000000out_targetQ## Factor Analysis using method = minres
## Call: fa(r = PWB_cor, nfactors = 3, n.obs = 816, rotate = "TargetQ",
## Target = Targ_key)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 h2 u2 com
## 1 0.57 0.25 0.23 0.53 0.47 1.7
## 2 0.81 0.02 -0.03 0.63 0.37 1.0
## 3 0.79 -0.05 0.05 0.67 0.33 1.0
## 4 -0.73 0.15 0.17 0.49 0.51 1.2
## 5 -0.11 0.71 -0.01 0.54 0.46 1.1
## 6 0.09 0.86 -0.09 0.75 0.25 1.0
## 7 -0.01 -0.07 0.83 0.69 0.31 1.0
## 8 0.15 -0.07 0.40 0.24 0.76 1.4
##
## MR1 MR2 MR3
## SS loadings 2.20 1.36 0.98
## Proportion Var 0.28 0.17 0.12
## Cumulative Var 0.28 0.45 0.57
## Proportion Explained 0.49 0.30 0.22
## Cumulative Proportion 0.49 0.78 1.00
##
## With factor correlations of
## MR1 MR2 MR3
## MR1 1.00 -0.09 0.43
## MR2 -0.09 1.00 -0.04
## MR3 0.43 -0.04 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 28 and the objective function was 2.49 with Chi Square of 2018.34
## The degrees of freedom for the model are 7 and the objective function was 0.04
##
## 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 816 with the empirical chi square 17.53 with prob < 0.014
## The total number of observations was 816 with MLE Chi Square = 35.92 with prob < 7.5e-06
##
## Tucker Lewis Index of factoring reliability = 0.942
## RMSEA index = 0.072 and the 90 % confidence intervals are 0.049 0.095
## BIC = -11.01
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR3
## Correlation of scores with factors 0.92 0.90 0.86
## Multiple R square of scores with factors 0.85 0.81 0.74
## Minimum correlation of possible factor scores 0.70 0.62 0.48#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] 0.9854679Droping question 1 as well because it also loads on all of the factors. Much better fit to the data
all_surveys<-read.csv("allsurveysT1.csv")
PWB<-select(all_surveys, PWB_3, PWB_5,PWB_6, PWB_8,PWB_7, PWB_2, PWB_9)
PWB<- data.frame(apply(PWB,2, as.numeric))
PWB<-tbl_df(PWB)
PWB## Source: local data frame [757 x 7]
##
## PWB_3 PWB_5 PWB_6 PWB_8 PWB_7 PWB_2 PWB_9
## 1 2 4 5 3 4 4 1
## 2 2 2 5 2 3 2 2
## 3 2 1 4 3 6 1 1
## 4 3 3 4 4 5 5 3
## 5 4 4 3 3 2 5 3
## 6 1 3 4 4 3 3 1
## 7 2 1 4 3 3 5 4
## 8 2 2 4 4 4 1 1
## 9 2 1 5 5 5 2 1
## 10 4 2 6 3 6 1 1
## .. ... ... ... ... ... ... ...colnames(PWB) <- c("1","2", "3", "4", "5", "6", "7")
#Target rotation: choose "simple structure" a priori and can be applied to oblique and orthogonal rotation based on
#what paper says facotrs should be PWB
Targ_key <- make.keys(7,list(f1=1:3,f2=4:5, f3=6:7))
Targ_key <- scrub(Targ_key,isvalue=1) #fix the 0s, allow the NAs to be estimated
Targ_key <- list(Targ_key)
PWB_cor <- corFiml(PWB) # convert the raw data to correlation matrix uisng FIML
out_targetQ <- fa(PWB_cor,3,rotate="TargetQ",n.obs = 816,Target=Targ_key) #TargetT for orthogonal rotation
out_targetQ[c("loadings", "score.cor", "TLI", "RMSEA")]## $loadings
##
## Loadings:
## MR1 MR2 MR3
## 1 0.802
## 2 0.766 0.136
## 3 -0.717 0.126 0.169
## 4 0.759
## 5 0.811
## 6 0.698
## 7 0.514
##
## MR1 MR2 MR3
## SS loadings 1.766 1.259 0.802
## Proportion Var 0.252 0.180 0.115
## Cumulative Var 0.252 0.432 0.547
##
## $score.cor
## [,1] [,2] [,3]
## [1,] 1.0000000 -0.1618757 0.3299602
## [2,] -0.1618757 1.0000000 -0.1663915
## [3,] 0.3299602 -0.1663915 1.0000000
##
## $TLI
## [1] 0.9511193
##
## $RMSEA
## RMSEA lower upper confidence
## 0.06616171 0.03316035 0.10314114 0.10000000out_targetQ## Factor Analysis using method = minres
## Call: fa(r = PWB_cor, nfactors = 3, n.obs = 816, rotate = "TargetQ",
## Target = Targ_key)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 h2 u2 com
## 1 0.80 0.08 0.04 0.65 0.35 1.0
## 2 0.77 0.03 0.14 0.69 0.31 1.1
## 3 -0.72 0.13 0.17 0.48 0.52 1.2
## 4 -0.10 0.76 0.00 0.61 0.39 1.0
## 5 0.09 0.81 -0.04 0.65 0.35 1.0
## 6 -0.01 -0.03 0.70 0.49 0.51 1.0
## 7 0.07 -0.03 0.51 0.31 0.69 1.0
##
## MR1 MR2 MR3
## SS loadings 1.78 1.27 0.83
## Proportion Var 0.25 0.18 0.12
## Cumulative Var 0.25 0.44 0.55
## Proportion Explained 0.46 0.33 0.21
## Cumulative Proportion 0.46 0.79 1.00
##
## With factor correlations of
## MR1 MR2 MR3
## MR1 1.00 -0.18 0.44
## MR2 -0.18 1.00 -0.17
## MR3 0.44 -0.17 1.00
##
## Mean item complexity = 1.1
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 21 and the objective function was 1.9 with Chi Square of 1545.05
## The degrees of freedom for the model are 3 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 816 with the empirical chi square 5.86 with prob < 0.12
## The total number of observations was 816 with MLE Chi Square = 13.62 with prob < 0.0035
##
## Tucker Lewis Index of factoring reliability = 0.951
## RMSEA index = 0.066 and the 90 % confidence intervals are 0.033 0.103
## BIC = -6.5
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR3
## Correlation of scores with factors 0.91 0.88 0.79
## Multiple R square of scores with factors 0.83 0.78 0.63
## Minimum correlation of possible factor scores 0.67 0.55 0.26#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] 0.9930345Adding a 4th factor with questions 1 and 4
all_surveys<-read.csv("allsurveysT1.csv")
PWB<-select(all_surveys, PWB_3, PWB_5,PWB_6, PWB_8,PWB_7, PWB_2, PWB_9, PWB_1, PWB_4)
PWB<- data.frame(apply(PWB,2, as.numeric))
PWB<-tbl_df(PWB)
PWB## Source: local data frame [757 x 9]
##
## PWB_3 PWB_5 PWB_6 PWB_8 PWB_7 PWB_2 PWB_9 PWB_1 PWB_4
## 1 2 4 5 3 4 4 1 3 5
## 2 2 2 5 2 3 2 2 3 5
## 3 2 1 4 3 6 1 1 2 1
## 4 3 3 4 4 5 5 3 5 3
## 5 4 4 3 3 2 5 3 5 4
## 6 1 3 4 4 3 3 1 2 2
## 7 2 1 4 3 3 5 4 5 5
## 8 2 2 4 4 4 1 1 1 6
## 9 2 1 5 5 5 2 1 2 2
## 10 4 2 6 3 6 1 1 1 4
## .. ... ... ... ... ... ... ... ... ...colnames(PWB) <- c("1","2", "3", "4", "5", "6", "7", "8", "9")
#Target rotation: choose "simple structure" a priori and can be applied to oblique and orthogonal rotation based on
#what paper says facotrs should be PWB
Targ_key <- make.keys(9,list(f1=1:3,f2=4:5, f3=6:7, f4=8:9))
Targ_key <- scrub(Targ_key,isvalue=1) #fix the 0s, allow the NAs to be estimated
Targ_key <- list(Targ_key)
PWB_cor <- corFiml(PWB) # convert the raw data to correlation matrix uisng FIML
out_targetQ <- fa(PWB_cor,4,rotate="TargetQ",n.obs = 816,Target=Targ_key) #TargetT for orthogonal rotation
out_targetQ[c("loadings", "score.cor", "TLI", "RMSEA")]## $loadings
##
## Loadings:
## MR1 MR2 MR3 MR4
## 1 0.906 0.144 0.164
## 2 0.724 0.115
## 3 -0.676 0.247 0.152 0.273
## 4 -0.121 0.692
## 5 0.814 -0.102
## 6 -0.163 0.890
## 7 0.443
## 8 0.410 0.155 0.339 -0.361
## 9 0.375 -0.219 0.262 0.331
##
## MR1 MR2 MR3 MR4
## SS loadings 2.164 1.298 1.212 0.360
## Proportion Var 0.240 0.144 0.135 0.040
## Cumulative Var 0.240 0.385 0.519 0.559
##
## $score.cor
## [,1] [,2] [,3]
## [1,] 1.0000000 -0.1829474 0.4307783
## [2,] -0.1829474 1.0000000 -0.1663943
## [3,] 0.4307783 -0.1663943 1.0000000
##
## $TLI
## [1] 0.976284
##
## $RMSEA
## RMSEA lower upper confidence
## 0.04425545 0.01720263 0.07158094 0.10000000out_targetQ## Factor Analysis using method = minres
## Call: fa(r = PWB_cor, nfactors = 4, n.obs = 816, rotate = "TargetQ",
## Target = Targ_key)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 MR4 h2 u2 com
## 1 0.91 0.14 -0.02 0.16 0.75 0.25 1.1
## 2 0.72 -0.01 0.12 -0.03 0.64 0.36 1.1
## 3 -0.68 0.25 0.15 0.27 0.56 0.44 1.7
## 4 -0.12 0.69 0.00 -0.08 0.56 0.44 1.1
## 5 0.09 0.81 -0.06 -0.10 0.72 0.28 1.1
## 6 -0.16 -0.05 0.89 -0.04 0.67 0.33 1.1
## 7 0.07 -0.04 0.44 0.01 0.24 0.76 1.1
## 8 0.41 0.15 0.34 -0.36 0.61 0.39 3.2
## 9 0.37 -0.22 0.26 0.33 0.53 0.47 3.5
##
## MR1 MR2 MR3 MR4
## SS loadings 2.23 1.37 1.26 0.42
## Proportion Var 0.25 0.15 0.14 0.05
## Cumulative Var 0.25 0.40 0.54 0.59
## Proportion Explained 0.42 0.26 0.24 0.08
## Cumulative Proportion 0.42 0.68 0.92 1.00
##
## With factor correlations of
## MR1 MR2 MR3 MR4
## MR1 1.00 -0.16 0.53 -0.13
## MR2 -0.16 1.00 -0.14 -0.29
## MR3 0.53 -0.14 1.00 0.04
## MR4 -0.13 -0.29 0.04 1.00
##
## Mean item complexity = 1.7
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 36 and the objective function was 3 with Chi Square of 2435.57
## The degrees of freedom for the model are 6 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 816 with the empirical chi square 8.07 with prob < 0.23
## The total number of observations was 816 with MLE Chi Square = 15.45 with prob < 0.017
##
## Tucker Lewis Index of factoring reliability = 0.976
## RMSEA index = 0.044 and the 90 % confidence intervals are 0.017 0.072
## BIC = -24.77
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR3 MR4
## Correlation of scores with factors 0.94 0.89 0.88 0.71
## Multiple R square of scores with factors 0.87 0.80 0.78 0.51
## Minimum correlation of possible factor scores 0.75 0.60 0.56 0.01#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] 0.9960605