Perman_CFA
Levi Brackman
22 July 2015
From Julie Butler and Peggy Kerns PERMA & EPOCH
Items
How much of the time do you feel you are making progress towards accomplishing your goals? (Acomplishment)
How often do you become absorbed in what you are doing? (Engagement)
In general, how often do you feel joyful? (Positive Emotion)
To what extent do you receive help and support from others when you need it? (Relationship)
In general, how often do you feel anxious? (Negative Emotion)
How often do you achieve the important goals you have set for yourself? (Acomplishment)
In general, how often do you feel positive? (Positive Emotion)
In general, to what extent do you feel excited and interested in things? (Enagagement)
How lonely do you feel in your daily life? (Lonely -single item)
In general, how often do you feel angry? (Negative Emotion)
To what extent have you been feeling loved? (Relationship)
How often are you able to handle your responsibilities? (Acomplishment)
How satisfied are you with your personal relationships? (Relationship)
In general, how often do you feel sad? (Nagative Emotion)
How often do you lose track of time while doing something you enjoy? (Engagement)
In general, to what extent do you feel contented? (Positive Emotion)
Taking all things together, how happy would you say you are? (Happiness -single item)
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)loadthedata
data <- read.csv("~/Psychometric_study_data/allsurveysT1.csv")
View(data)create the models
seven.model= 'Acomplishment =~ PERMA_1 + PERMA_6 + PERMA_12
Engagement =~ PERMA_2 + PERMA_8 + PERMA_15
Positive Emotion =~ PERMA_3 + PERMA_7 + PERMA_16
Relationship =~ PERMA_4 + PERMA_11 + PERMA_13
Negative Emotion =~ PERMA_5 + PERMA_10 + PERMA_14
Lonely =~ PERMA_9
Happy =~ PERMA_17'
one.model= 'One =~ PERMA_1 + PERMA_2 + PERMA_3 + PERMA_4 + PERMA_5 + PERMA_6 + PERMA_7 + PERMA_8 + PERMA_9 +
PERMA_10 + PERMA_11 + PERMA_12 + PERMA_13 + PERMA_14 + PERMA_15 + PERMA_16 + PERMA_17'run the models
seven.fit=cfa(seven.model, data=data)
one.fit=cfa(one.model, data=data)create pictures
semPaths(seven.fit, whatLabels = "std", layout = "tree")
semPaths(one.fit, whatLabels = "std", layout = "tree")
#summaries
summary(seven.fit, standardized = TRUE, rsquare=TRUE)## lavaan (0.5-18) converged normally after 190 iterations
##
## Used Total
## Number of observations 324 757
##
## Estimator ML
## Minimum Function Test Statistic 156.407
## Degrees of freedom 100
## P-value (Chi-square) 0.000
##
## Parameter estimates:
##
## Information Expected
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## Acomplishment =~
## PERMA_1 1.000 1.925 0.783
## PERMA_6 0.800 0.075 10.728 0.000 1.539 0.631
## PERMA_12 0.739 0.072 10.324 0.000 1.423 0.609
## Engagement =~
## PERMA_2 1.000 1.576 0.675
## PERMA_8 1.007 0.096 10.463 0.000 1.588 0.696
## PERMA_15 0.813 0.110 7.364 0.000 1.281 0.466
## PositiveEmotion =~
## PERMA_3 1.000 1.733 0.743
## PERMA_7 1.073 0.076 14.158 0.000 1.859 0.775
## PERMA_16 0.966 0.076 12.664 0.000 1.675 0.700
## Relationship =~
## PERMA_4 1.000 1.482 0.540
## PERMA_11 1.226 0.155 7.911 0.000 1.817 0.656
## PERMA_13 1.214 0.155 7.817 0.000 1.800 0.642
## NegativeEmotion =~
## PERMA_5 1.000 1.768 0.559
## PERMA_10 0.829 0.178 4.652 0.000 1.466 0.446
## PERMA_14 0.928 0.190 4.883 0.000 1.640 0.510
## Lonely =~
## PERMA_9 1.000 3.564 1.000
## Happy =~
## PERMA_17 1.000 2.423 1.000
##
## Covariances:
## Acomplishment ~~
## Engagement 2.528 0.320 7.905 0.000 0.833 0.833
## PositiveEmotn 2.926 0.333 8.787 0.000 0.877 0.877
## Relationship 2.275 0.340 6.697 0.000 0.798 0.798
## NegativeEmotn -0.341 0.309 -1.102 0.270 -0.100 -0.100
## Lonely -1.393 0.452 -3.079 0.002 -0.203 -0.203
## Happy 2.773 0.351 7.896 0.000 0.595 0.595
## Engagement ~~
## PositiveEmotn 2.422 0.298 8.122 0.000 0.887 0.887
## Relationship 1.778 0.287 6.194 0.000 0.761 0.761
## NegativeEmotn 0.036 0.263 0.138 0.890 0.013 0.013
## Lonely -0.164 0.381 -0.431 0.666 -0.029 -0.029
## Happy 2.360 0.316 7.468 0.000 0.618 0.618
## PositiveEmotion ~~
## Relationship 2.026 0.304 6.656 0.000 0.789 0.789
## NegativeEmotn -0.965 0.293 -3.291 0.001 -0.315 -0.315
## Lonely -1.710 0.405 -4.222 0.000 -0.277 -0.277
## Happy 3.526 0.361 9.770 0.000 0.840 0.840
## Relationship ~~
## NegativeEmotn -0.375 0.258 -1.456 0.145 -0.143 -0.143
## Lonely -1.152 0.383 -3.006 0.003 -0.218 -0.218
## Happy 2.451 0.357 6.860 0.000 0.683 0.683
## NegativeEmotion ~~
## Lonely 2.567 0.572 4.485 0.000 0.407 0.407
## Happy -1.173 0.359 -3.267 0.001 -0.274 -0.274
## Lonely ~~
## Happy -1.998 0.493 -4.056 0.000 -0.231 -0.231
##
## Variances:
## PERMA_1 2.331 0.282 2.331 0.386
## PERMA_6 3.570 0.323 3.570 0.601
## PERMA_12 3.442 0.306 3.442 0.630
## PERMA_2 2.961 0.292 2.961 0.544
## PERMA_8 2.690 0.276 2.690 0.516
## PERMA_15 5.920 0.494 5.920 0.783
## PERMA_3 2.440 0.220 2.440 0.448
## PERMA_7 2.298 0.217 2.298 0.399
## PERMA_16 2.921 0.253 2.921 0.510
## PERMA_4 5.348 0.475 5.348 0.709
## PERMA_11 4.359 0.444 4.359 0.569
## PERMA_13 4.626 0.459 4.626 0.588
## PERMA_5 6.870 0.824 6.870 0.687
## PERMA_10 8.641 0.833 8.641 0.801
## PERMA_14 7.639 0.818 7.639 0.740
## PERMA_9 0.000 0.000 0.000
## PERMA_17 0.000 0.000 0.000
## Acomplishment 3.704 0.487 1.000 1.000
## Engagement 2.484 0.400 1.000 1.000
## PositiveEmotn 3.003 0.397 1.000 1.000
## Relationship 2.196 0.474 1.000 1.000
## NegativeEmotn 3.125 0.844 1.000 1.000
## Lonely 12.705 0.998 1.000 1.000
## Happy 5.873 0.461 1.000 1.000
##
## R-Square:
##
## PERMA_1 0.614
## PERMA_6 0.399
## PERMA_12 0.370
## PERMA_2 0.456
## PERMA_8 0.484
## PERMA_15 0.217
## PERMA_3 0.552
## PERMA_7 0.601
## PERMA_16 0.490
## PERMA_4 0.291
## PERMA_11 0.431
## PERMA_13 0.412
## PERMA_5 0.313
## PERMA_10 0.199
## PERMA_14 0.260
## PERMA_9 1.000
## PERMA_17 1.000summary(one.fit, standardized = TRUE, rsquare=TRUE)## lavaan (0.5-18) converged normally after 39 iterations
##
## Used Total
## Number of observations 324 757
##
## Estimator ML
## Minimum Function Test Statistic 354.086
## Degrees of freedom 119
## P-value (Chi-square) 0.000
##
## Parameter estimates:
##
## Information Expected
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## One =~
## PERMA_1 1.000 1.744 0.710
## PERMA_2 0.772 0.078 9.839 0.000 1.345 0.577
## PERMA_3 0.986 0.079 12.525 0.000 1.720 0.737
## PERMA_4 0.759 0.092 8.231 0.000 1.323 0.482
## PERMA_5 -0.243 0.106 -2.294 0.022 -0.423 -0.134
## PERMA_6 0.769 0.082 9.391 0.000 1.341 0.550
## PERMA_7 1.058 0.081 13.052 0.000 1.845 0.769
## PERMA_8 0.887 0.077 11.530 0.000 1.546 0.677
## PERMA_9 -0.493 0.119 -4.130 0.000 -0.859 -0.241
## PERMA_10 -0.166 0.110 -1.512 0.130 -0.290 -0.088
## PERMA_11 0.887 0.093 9.538 0.000 1.547 0.559
## PERMA_12 0.763 0.079 9.708 0.000 1.330 0.569
## PERMA_13 0.887 0.094 9.411 0.000 1.546 0.551
## PERMA_14 -0.253 0.108 -2.354 0.019 -0.441 -0.137
## PERMA_15 0.550 0.092 5.971 0.000 0.959 0.349
## PERMA_16 0.975 0.081 12.083 0.000 1.700 0.710
## PERMA_17 1.068 0.082 13.041 0.000 1.862 0.768
##
## Variances:
## PERMA_1 2.995 0.263 2.995 0.496
## PERMA_2 3.635 0.301 3.635 0.668
## PERMA_3 2.486 0.222 2.486 0.457
## PERMA_4 5.794 0.470 5.794 0.768
## PERMA_5 9.816 0.773 9.816 0.982
## PERMA_6 4.141 0.340 4.141 0.697
## PERMA_7 2.351 0.217 2.351 0.408
## PERMA_8 2.820 0.243 2.820 0.541
## PERMA_9 11.967 0.946 11.967 0.942
## PERMA_10 10.706 0.842 10.706 0.992
## PERMA_11 5.267 0.434 5.267 0.688
## PERMA_12 3.698 0.305 3.698 0.676
## PERMA_13 5.475 0.450 5.475 0.696
## PERMA_14 10.135 0.798 10.135 0.981
## PERMA_15 6.641 0.529 6.641 0.878
## PERMA_16 2.836 0.249 2.836 0.495
## PERMA_17 2.405 0.222 2.405 0.410
## One 3.041 0.428 1.000 1.000
##
## R-Square:
##
## PERMA_1 0.504
## PERMA_2 0.332
## PERMA_3 0.543
## PERMA_4 0.232
## PERMA_5 0.018
## PERMA_6 0.303
## PERMA_7 0.592
## PERMA_8 0.459
## PERMA_9 0.058
## PERMA_10 0.008
## PERMA_11 0.312
## PERMA_12 0.324
## PERMA_13 0.304
## PERMA_14 0.019
## PERMA_15 0.122
## PERMA_16 0.505
## PERMA_17 0.590Residual correlations
correl = residuals(seven.fit, type="cor")
correl## $type
## [1] "cor.bollen"
##
## $cor
## PERMA_1 PERMA_6 PERMA_12 PERMA_2 PERMA_8 PERMA_15 PERMA_3 PERMA_7
## PERMA_1 0.000
## PERMA_6 0.013 0.000
## PERMA_12 -0.017 0.006 0.000
## PERMA_2 -0.003 -0.028 0.031 0.000
## PERMA_8 0.038 0.009 0.030 -0.050 0.000
## PERMA_15 -0.074 -0.053 -0.044 0.143 -0.028 0.000
## PERMA_3 -0.028 -0.046 -0.014 -0.047 0.058 -0.057 0.000
## PERMA_7 -0.008 -0.011 0.020 -0.036 0.070 -0.055 0.049 0.000
## PERMA_16 0.058 0.034 0.004 0.000 0.018 -0.051 -0.011 -0.051
## PERMA_4 0.053 -0.002 0.041 0.026 0.023 -0.011 -0.068 0.041
## PERMA_11 -0.021 -0.055 -0.022 -0.041 0.016 -0.112 -0.014 -0.039
## PERMA_13 -0.002 0.014 0.016 0.046 0.001 0.006 0.019 -0.061
## PERMA_5 0.007 0.037 -0.048 0.004 -0.103 0.140 0.027 0.000
## PERMA_10 -0.015 0.068 -0.063 0.026 -0.029 0.155 -0.012 0.046
## PERMA_14 -0.010 0.079 -0.057 0.057 -0.113 0.120 -0.035 -0.011
## PERMA_9 0.034 -0.009 -0.061 0.068 -0.096 0.076 0.032 0.006
## PERMA_17 0.016 -0.052 0.022 -0.039 0.071 -0.079 0.015 0.001
## PERMA_16 PERMA_4 PERMA_11 PERMA_13 PERMA_5 PERMA_10 PERMA_14
## PERMA_1
## PERMA_6
## PERMA_12
## PERMA_2
## PERMA_8
## PERMA_15
## PERMA_3
## PERMA_7
## PERMA_16 0.000
## PERMA_4 0.047 0.000
## PERMA_11 0.065 -0.031 0.000
## PERMA_13 0.055 -0.020 0.035 0.000
## PERMA_5 -0.033 0.036 -0.041 0.014 0.000
## PERMA_10 -0.018 0.001 0.015 -0.028 0.043 0.000
## PERMA_14 0.032 0.078 -0.033 -0.006 -0.010 -0.036 0.000
## PERMA_9 -0.047 0.027 -0.028 0.011 -0.019 -0.009 0.030
## PERMA_17 -0.020 0.004 0.041 -0.046 0.016 0.056 -0.065
## PERMA_9 PERMA_17
## PERMA_1
## PERMA_6
## PERMA_12
## PERMA_2
## PERMA_8
## PERMA_15
## PERMA_3
## PERMA_7
## PERMA_16
## PERMA_4
## PERMA_11
## PERMA_13
## PERMA_5
## PERMA_10
## PERMA_14
## PERMA_9 0.000
## PERMA_17 0.000 0.000
##
## $mean
## PERMA_1 PERMA_6 PERMA_12 PERMA_2 PERMA_8 PERMA_15 PERMA_3 PERMA_7
## 0 0 0 0 0 0 0 0
## PERMA_16 PERMA_4 PERMA_11 PERMA_13 PERMA_5 PERMA_10 PERMA_14 PERMA_9
## 0 0 0 0 0 0 0 0
## PERMA_17
## 0View(correl$cor)
correl1 = residuals(one.fit, type="cor")
correl1## $type
## [1] "cor.bollen"
##
## $cor
## PERMA_1 PERMA_2 PERMA_3 PERMA_4 PERMA_5 PERMA_6 PERMA_7 PERMA_8
## PERMA_1 0.000
## PERMA_2 0.028 0.000
## PERMA_3 -0.041 -0.027 0.000
## PERMA_4 0.049 0.026 -0.107 0.000
## PERMA_5 0.059 0.086 -0.005 0.058 0.000
## PERMA_6 0.117 0.011 -0.040 0.004 0.075 0.000
## PERMA_7 -0.021 -0.016 0.058 0.001 -0.034 -0.005 0.000
## PERMA_8 0.011 0.029 0.017 -0.017 -0.007 0.003 0.027 0.000
## PERMA_9 0.046 0.187 0.004 0.025 0.176 -0.004 -0.023 0.047
## PERMA_10 0.012 0.080 -0.051 0.009 0.281 0.088 0.005 0.035
## PERMA_11 -0.007 -0.026 -0.041 0.054 -0.019 -0.032 -0.067 -0.015
## PERMA_12 0.056 0.046 -0.037 0.029 -0.006 0.077 -0.004 -0.003
## PERMA_13 0.008 0.058 -0.012 0.060 0.037 0.034 -0.092 -0.033
## PERMA_14 0.047 0.141 -0.053 0.104 0.257 0.122 -0.030 -0.015
## PERMA_15 -0.018 0.257 -0.007 0.012 0.190 0.000 -0.003 0.060
## PERMA_16 0.034 0.009 -0.014 0.003 -0.061 0.031 -0.055 -0.032
## PERMA_17 -0.063 -0.064 0.072 0.002 -0.034 -0.099 0.061 -0.020
## PERMA_9 PERMA_10 PERMA_11 PERMA_12 PERMA_13 PERMA_14 PERMA_15
## PERMA_1
## PERMA_2
## PERMA_3
## PERMA_4
## PERMA_5
## PERMA_6
## PERMA_7
## PERMA_8
## PERMA_9 0.000
## PERMA_10 0.151 0.000
## PERMA_11 -0.036 0.022 0.000
## PERMA_12 -0.048 -0.040 -0.022 0.000
## PERMA_13 0.004 -0.021 0.148 0.014 0.000
## PERMA_14 0.205 0.180 -0.004 -0.010 0.023 0.000
## PERMA_15 0.146 0.188 -0.075 -0.007 0.042 0.171 0.000
## PERMA_16 -0.069 -0.054 0.030 -0.027 0.018 0.017 -0.009
## PERMA_17 -0.046 0.002 0.059 -0.053 -0.032 -0.099 -0.059
## PERMA_16 PERMA_17
## PERMA_1
## PERMA_2
## PERMA_3
## PERMA_4
## PERMA_5
## PERMA_6
## PERMA_7
## PERMA_8
## PERMA_9
## PERMA_10
## PERMA_11
## PERMA_12
## PERMA_13
## PERMA_14
## PERMA_15
## PERMA_16 0.000
## PERMA_17 0.022 0.000
##
## $mean
## PERMA_1 PERMA_2 PERMA_3 PERMA_4 PERMA_5 PERMA_6 PERMA_7 PERMA_8
## 0 0 0 0 0 0 0 0
## PERMA_9 PERMA_10 PERMA_11 PERMA_12 PERMA_13 PERMA_14 PERMA_15 PERMA_16
## 0 0 0 0 0 0 0 0
## PERMA_17
## 0View(correl1$cor)zscore correlation anything over 1.96 is going to be statistically significant at the .05 level
zcorrels = residuals(seven.fit, type = "standardized")
View(zcorrels$cov)
zcorrels1 = residuals(one.fit, type = "standardized")
View(zcorrels1$cov)Modification indicies
modindices(seven.fit, sort. = TRUE, minimum.value = 3.84)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 PositiveEmotion =~ PERMA_8 27.491 0.992 1.719 0.753 0.753
## 2 NegativeEmotion =~ PERMA_8 24.289 -0.455 -0.805 -0.353 -0.353
## 3 PERMA_2 ~~ PERMA_15 22.586 1.331 1.331 0.207 0.207
## 4 NegativeEmotion =~ PERMA_15 18.917 0.470 0.832 0.302 0.302
## 5 PositiveEmotion =~ PERMA_15 15.865 -0.858 -1.487 -0.541 -0.541
## 6 Acomplishment =~ PERMA_15 12.532 -0.829 -1.596 -0.580 -0.580
## 7 Acomplishment =~ PERMA_8 12.434 0.766 1.474 0.646 0.646
## 8 Happy =~ PERMA_8 11.485 0.244 0.591 0.259 0.259
## 9 PERMA_2 ~~ PERMA_8 10.698 -0.988 -0.988 -0.185 -0.185
## 10 Lonely =~ PERMA_8 10.586 -0.113 -0.402 -0.176 -0.176
## 11 Relationship =~ PERMA_16 10.548 0.654 0.969 0.405 0.405
## 12 PERMA_3 ~~ PERMA_7 8.711 0.546 0.546 0.098 0.098
## 13 Relationship =~ PERMA_15 8.653 -0.692 -1.026 -0.373 -0.373
## 14 Relationship =~ PERMA_8 6.913 0.549 0.814 0.356 0.356
## 15 PERMA_7 ~~ PERMA_16 6.801 -0.485 -0.485 -0.084 -0.084
## 16 PERMA_3 ~~ PERMA_4 6.095 -0.553 -0.553 -0.086 -0.086
## 17 PositiveEmotion =~ PERMA_2 5.994 -0.465 -0.806 -0.345 -0.345
## 18 Acomplishment =~ PERMA_11 5.861 -0.573 -1.103 -0.399 -0.399
## 19 PERMA_14 ~~ PERMA_17 5.852 -0.716 -0.716 -0.092 -0.092
## 20 Happy =~ PERMA_15 5.702 -0.197 -0.478 -0.174 -0.174
## 21 Happy =~ PERMA_13 5.475 -0.251 -0.607 -0.217 -0.217
## 22 Acomplishment =~ PERMA_16 5.280 0.360 0.692 0.289 0.289
## 23 PositiveEmotion =~ PERMA_6 5.092 -0.437 -0.757 -0.311 -0.311
## 24 PERMA_13 ~~ PERMA_17 4.989 -0.550 -0.550 -0.081 -0.081
## 25 Happy =~ PERMA_11 4.764 0.234 0.566 0.205 0.205
## 26 Engagement =~ PERMA_11 4.657 -0.536 -0.844 -0.305 -0.305
## 27 Lonely =~ PERMA_2 4.596 0.075 0.267 0.114 0.114
## 28 NegativeEmotion =~ PERMA_12 4.021 -0.175 -0.310 -0.133 -0.133
## 29 PERMA_15 ~~ PERMA_10 3.867 0.853 0.853 0.094 0.094
## 30 PERMA_8 ~~ PERMA_14 3.859 -0.613 -0.613 -0.084 -0.084modindices(one.fit, sort. = TRUE, minimum.value = 3.84)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 PERMA_2 ~~ PERMA_15 38.971 1.764 1.764 0.275 0.275
## 2 PERMA_5 ~~ PERMA_10 26.289 2.924 2.924 0.282 0.282
## 3 PERMA_5 ~~ PERMA_14 22.248 2.619 2.619 0.258 0.258
## 4 PERMA_2 ~~ PERMA_9 19.072 1.648 1.648 0.198 0.198
## 5 PERMA_11 ~~ PERMA_13 16.480 1.273 1.273 0.164 0.164
## 6 PERMA_1 ~~ PERMA_6 15.210 0.832 0.832 0.139 0.139
## 7 PERMA_9 ~~ PERMA_14 14.848 2.367 2.367 0.207 0.207
## 8 PERMA_6 ~~ PERMA_17 14.060 -0.738 -0.738 -0.125 -0.125
## 9 PERMA_5 ~~ PERMA_15 13.821 1.681 1.681 0.193 0.193
## 10 PERMA_10 ~~ PERMA_15 13.379 1.726 1.726 0.191 0.191
## 11 PERMA_3 ~~ PERMA_17 13.073 0.590 0.590 0.104 0.104
## 12 PERMA_3 ~~ PERMA_4 12.641 -0.818 -0.818 -0.128 -0.128
## 13 PERMA_7 ~~ PERMA_13 12.245 -0.783 -0.783 -0.116 -0.116
## 14 PERMA_14 ~~ PERMA_15 11.160 1.535 1.535 0.174 0.174
## 15 PERMA_5 ~~ PERMA_9 10.957 2.001 2.001 0.178 0.178
## 16 PERMA_7 ~~ PERMA_17 10.947 0.538 0.538 0.093 0.093
## 17 PERMA_10 ~~ PERMA_14 10.807 1.905 1.905 0.180 0.180
## 18 PERMA_2 ~~ PERMA_14 10.380 1.116 1.116 0.149 0.149
## 19 PERMA_14 ~~ PERMA_17 9.278 -0.906 -0.906 -0.116 -0.116
## 20 PERMA_1 ~~ PERMA_17 8.920 -0.526 -0.526 -0.088 -0.088
## 21 PERMA_9 ~~ PERMA_15 8.552 1.463 1.463 0.149 0.149
## 22 PERMA_3 ~~ PERMA_7 8.472 0.470 0.470 0.084 0.084
## 23 PERMA_9 ~~ PERMA_10 8.010 1.786 1.786 0.153 0.153
## 24 PERMA_6 ~~ PERMA_14 7.401 1.003 1.003 0.128 0.128
## 25 PERMA_7 ~~ PERMA_16 6.653 -0.438 -0.438 -0.076 -0.076
## 26 PERMA_7 ~~ PERMA_11 6.584 -0.564 -0.564 -0.085 -0.085
## 27 PERMA_2 ~~ PERMA_17 6.250 -0.463 -0.463 -0.082 -0.082
## 28 PERMA_11 ~~ PERMA_17 5.141 0.504 0.504 0.075 0.075
## 29 PERMA_4 ~~ PERMA_14 4.834 0.952 0.952 0.108 0.108
## 30 PERMA_6 ~~ PERMA_12 4.513 0.486 0.486 0.085 0.085
## 31 PERMA_12 ~~ PERMA_17 4.158 -0.381 -0.381 -0.067 -0.067
## 32 PERMA_2 ~~ PERMA_5 3.865 0.670 0.670 0.091 0.091Fit Measures
fitmeasures(seven.fit)## npar fmin chisq
## 53.000 0.241 156.407
## df pvalue baseline.chisq
## 100.000 0.000 1844.188
## baseline.df baseline.pvalue cfi
## 136.000 0.000 0.967
## tli nnfi rfi
## 0.955 0.955 0.885
## nfi pnfi ifi
## 0.915 0.673 0.968
## rni logl unrestricted.logl
## 0.967 -12363.383 -12285.179
## aic bic ntotal
## 24832.765 25033.145 324.000
## bic2 rmsea rmsea.ci.lower
## 24865.034 0.042 0.029
## rmsea.ci.upper rmsea.pvalue rmr
## 0.054 0.861 0.342
## rmr_nomean srmr srmr_bentler
## 0.342 0.045 0.045
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.045 0.045 0.045
## srmr_mplus srmr_mplus_nomean cn_05
## 0.045 0.045 258.577
## cn_01 gfi agfi
## 282.326 0.946 0.917
## pgfi mfi ecvi
## 0.618 0.917 0.810fitmeasures(one.fit)## npar fmin chisq
## 34.000 0.546 354.086
## df pvalue baseline.chisq
## 119.000 0.000 1844.188
## baseline.df baseline.pvalue cfi
## 136.000 0.000 0.862
## tli nnfi rfi
## 0.843 0.843 0.781
## nfi pnfi ifi
## 0.808 0.707 0.864
## rni logl unrestricted.logl
## 0.862 -12462.222 -12285.179
## aic bic ntotal
## 24992.444 25120.990 324.000
## bic2 rmsea rmsea.ci.lower
## 25013.145 0.078 0.069
## rmsea.ci.upper rmsea.pvalue rmr
## 0.088 0.000 0.635
## rmr_nomean srmr srmr_bentler
## 0.635 0.072 0.072
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.072 0.072 0.072
## srmr_mplus srmr_mplus_nomean cn_05
## 0.072 0.072 134.101
## cn_01 gfi agfi
## 145.392 0.865 0.827
## pgfi mfi ecvi
## 0.673 0.696 1.303Create dataset for Target rotation
PermaTR<-select(data, PERMA_1 , PERMA_6 , PERMA_12, PERMA_2 , PERMA_8 , PERMA_15 ,PERMA_3 , PERMA_7 , PERMA_16 , PERMA_4 , PERMA_11 , PERMA_13 , PERMA_5 , PERMA_10 , PERMA_14, PERMA_9 , PERMA_17)
colnames(PermaTR) <- c("1","2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17")
#Target RorationTarg_key <- make.keys(17,list(f1=1:3,f2=4:6, f3=7:9, f4=10:12, f5=13:15, f6=16, f7=17))
Targ_key <- scrub(Targ_key,isvalue=1) #fix the 0s, allow the NAs to be estimated
Targ_key <- list(Targ_key)
out_targetQ <- fa(PermaTR,7,rotate="TargetQ",Target=Targ_key) #TargetT for orthogonal rotation
out_targetQ[c("loadings", "score.cor", "TLI", "RMSEA","uniquenesses")]## $loadings
##
## Loadings:
## MR1 MR4 MR2 MR5 MR3 MR7 MR6
## 1 0.511 0.134 0.158
## 2 0.712 0.153 0.148 -0.129
## 3 0.432 0.141 0.157 -0.155
## 4 0.103 0.731
## 5 0.248 0.255 0.114 0.155
## 6 0.588 0.157 0.107
## 7 0.124 0.151 0.352 0.208 0.337
## 8 0.313 0.207 -0.113 0.124 0.404
## 9 0.751 -0.182
## 10 0.180 0.368 -0.108 0.195 -0.242
## 11 0.669 0.130
## 12 0.690 -0.164 0.134
## 13 0.600
## 14 0.522 0.153
## 15 0.440 -0.125
## 16 -0.140 0.261 0.252 -0.154
## 17 0.254 0.321 0.517
##
## MR1 MR4 MR2 MR5 MR3 MR7 MR6
## SS loadings 1.213 1.193 1.156 0.995 0.927 0.646 0.259
## Proportion Var 0.071 0.070 0.068 0.059 0.055 0.038 0.015
## Cumulative Var 0.071 0.142 0.210 0.268 0.323 0.361 0.376
##
## $score.cor
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1.0000000 0.5774848 0.4763781 -0.1397813 0.6699912 0.6553088
## [2,] 0.5774848 1.0000000 0.3873415 -0.1269681 0.5535138 0.5587356
## [3,] 0.4763781 0.3873415 1.0000000 0.1428735 0.4400615 0.4125253
## [4,] -0.1397813 -0.1269681 0.1428735 1.0000000 -0.2527211 -0.2502201
## [5,] 0.6699912 0.5535138 0.4400615 -0.2527211 1.0000000 0.7356230
## [6,] 0.6553088 0.5587356 0.4125253 -0.2502201 0.7356230 1.0000000
##
## $TLI
## [1] 0.9760554
##
## $RMSEA
## RMSEA lower upper confidence
## 0.03146148 0.01755932 0.04328689 0.10000000
##
## $uniquenesses
## 1 2 3 4 5 6 7
## 0.4259841 0.4853750 0.6108533 0.3735635 0.5353151 0.6088251 0.3153644
## 8 9 10 11 12 13 14
## 0.3045924 0.2643278 0.6368634 0.5233771 0.4764847 0.6572774 0.7395460
## 15 16 17
## 0.7362427 0.7751917 0.2439653out_targetQ## Factor Analysis using method = minres
## Call: fa(r = PermaTR, nfactors = 7, rotate = "TargetQ", Target = Targ_key)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR2 MR5 MR3 MR7 MR6 h2 u2 com
## 1 0.51 0.13 0.08 0.02 0.16 0.00 -0.04 0.57 0.43 1.4
## 2 0.71 0.03 -0.08 0.15 0.15 -0.13 0.03 0.51 0.49 1.3
## 3 0.43 0.14 0.16 -0.16 -0.06 -0.01 -0.01 0.39 0.61 1.8
## 4 0.01 0.10 0.73 -0.06 0.06 -0.08 -0.05 0.63 0.37 1.1
## 5 0.25 0.07 0.26 -0.08 0.11 0.15 0.07 0.46 0.54 3.6
## 6 -0.07 -0.02 0.59 0.16 0.11 -0.02 0.03 0.39 0.61 1.3
## 7 0.12 0.03 0.15 -0.08 0.35 0.21 0.34 0.68 0.32 3.4
## 8 0.31 -0.04 0.21 -0.11 0.12 0.40 0.07 0.70 0.30 3.0
## 9 0.08 0.04 0.08 -0.03 0.75 -0.03 -0.18 0.74 0.26 1.2
## 10 0.18 0.37 0.09 0.04 -0.11 0.19 -0.24 0.36 0.64 3.4
## 11 -0.04 0.67 -0.07 0.03 0.05 0.13 -0.02 0.48 0.52 1.1
## 12 0.06 0.69 0.08 -0.01 -0.03 -0.16 0.13 0.52 0.48 1.2
## 13 0.05 0.05 -0.03 0.60 -0.05 0.03 0.10 0.34 0.66 1.1
## 14 0.01 0.00 0.01 0.52 -0.03 0.15 0.00 0.26 0.74 1.2
## 15 0.08 -0.04 0.09 0.44 0.01 -0.12 -0.09 0.26 0.74 1.5
## 16 -0.14 -0.07 0.26 0.25 -0.15 -0.06 0.04 0.22 0.78 3.6
## 17 -0.08 0.25 0.05 -0.03 0.32 0.52 0.04 0.76 0.24 2.3
##
## MR1 MR4 MR2 MR5 MR3 MR7 MR6
## SS loadings 1.64 1.54 1.44 1.06 1.42 0.90 0.28
## Proportion Var 0.10 0.09 0.08 0.06 0.08 0.05 0.02
## Cumulative Var 0.10 0.19 0.27 0.33 0.42 0.47 0.49
## Proportion Explained 0.20 0.19 0.17 0.13 0.17 0.11 0.03
## Cumulative Proportion 0.20 0.38 0.56 0.69 0.86 0.97 1.00
##
## With factor correlations of
## MR1 MR4 MR2 MR5 MR3 MR7 MR6
## MR1 1.00 0.59 0.53 -0.20 0.59 0.44 0.07
## MR4 0.59 1.00 0.47 -0.24 0.67 0.35 0.05
## MR2 0.53 0.47 1.00 0.11 0.42 0.30 0.12
## MR5 -0.20 -0.24 0.11 1.00 -0.33 -0.28 -0.10
## MR3 0.59 0.67 0.42 -0.33 1.00 0.40 0.12
## MR7 0.44 0.35 0.30 -0.28 0.40 1.00 0.20
## MR6 0.07 0.05 0.12 -0.10 0.12 0.20 1.00
##
## Mean item complexity = 2
## Test of the hypothesis that 7 factors are sufficient.
##
## The degrees of freedom for the null model are 136 and the objective function was 5.69 with Chi Square of 4266.11
## The degrees of freedom for the model are 38 and the objective function was 0.09
##
## 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 324 with the empirical chi square 19.64 with prob < 0.99
## The total number of observations was 757 with MLE Chi Square = 65.45 with prob < 0.0037
##
## Tucker Lewis Index of factoring reliability = 0.976
## RMSEA index = 0.031 and the 90 % confidence intervals are 0.018 0.043
## BIC = -186.46
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR2 MR5 MR3
## Correlation of scores with factors 0.88 0.88 0.87 0.79 0.9
## Multiple R square of scores with factors 0.78 0.77 0.76 0.63 0.8
## Minimum correlation of possible factor scores 0.56 0.55 0.51 0.26 0.6
## MR7 MR6
## Correlation of scores with factors 0.83 0.65
## Multiple R square of scores with factors 0.69 0.42
## Minimum correlation of possible factor scores 0.38 -0.16