First, we will check that all variables are correctly coded. Second, we will check for non-identifiability. Third, we will run a confirmatory factor analysis. Fourth, we will, in iterations, check the predictive power of all exogeneous covariates (predictors), and remove any that have no or very little predictive power (need to do that due to many being ordered). Fifth, we’ll check SEM diagnostics to see that the model can be trusted.
Let’s start by loading lavaan, for developing our structural equation model (SEM), data.table, for loading our data, semPlot in case we want to plot our SEM, and devtools to print our computing environment.
library(lavaan)
library(data.table)
library(semPlot)
library(devtools)
d <- fread("../data/export_2020-05-29.csv", stringsAsFactors=TRUE,
na.strings=c("", "null", "NA", -99))Gender has way too few data points outside male/female so keep only those. Remove 33 cases (15 NAs, 16 non-binary, and 2 Other).
sort(table(d$Gender, useNA="always"), decreasing=TRUE)##
## Male Female NB <NA> Other
## 1978 435 16 15 2d <- d[d$Gender == "Female" | d$Gender == "Male", ]
nrow(d)## [1] 2413The data we will use will be stored in a new data frame df, so that we keep the original data (\(n=2194\)) untouched. All predictors will be in small letters and the suffixes on the variable names (always good practice to do this) will be:
_n nominal_o ordered_s scaled_b binaryUnder the hood we now format data correctly, and in the end we have a new data frame df, which only contains complete cases.
Let’s examine our df,
str(df)## 'data.frame': 1511 obs. of 38 variables:
## $ gender_b : num 0 0 0 0 1 0 0 0 0 0 ...
## $ covidstatus_o: num 2 2 4 2 4 2 2 2 3 2 ...
## $ isolation_o : int 3 3 3 3 3 4 3 3 3 2 ...
## $ exp_s : num -0.1855 -0.999 0.3569 -0.0499 0.0857 ...
## $ homeexp_s : num 0.558 0.219 1.573 1.235 -0.457 ...
## $ fulltime_b : int 1 1 1 1 1 0 1 1 1 1 ...
## $ edu_o : num 6 6 4 6 4 3 5 4 4 4 ...
## $ orgsize_o : int 3 5 2 6 3 6 6 2 5 4 ...
## $ disab_o : num 2 2 2 2 2 2 2 2 2 2 ...
## $ adultcohab_o : num 2 2 2 2 2 3 1 3 1 2 ...
## $ childcohab_o : num 1 1 3 1 3 1 1 2 1 3 ...
## $ dev_b : int 0 1 1 1 0 1 1 1 1 0 ...
## $ fear : num -3.8 -3.9 -0.9 -4 1 -1.6 -2.3 -4.1 -3.1 -3 ...
## $ age_s : num 0.453 -0.161 1.068 1.068 0.453 ...
## $ DeltaW1 : Ord.factor w/ 11 levels "1"<"2"<"3"<"4"<..: 3 5 4 5 4 7 1 6 4 6 ...
## $ DeltaW2 : Ord.factor w/ 11 levels "1"<"2"<"3"<"4"<..: 6 5 4 5 4 6 2 6 7 6 ...
## $ DeltaW3 : Ord.factor w/ 11 levels "1"<"2"<"3"<"4"<..: 3 6 3 5 4 7 2 6 4 6 ...
## $ DeltaW4 : Ord.factor w/ 11 levels "0"<"1"<"2"<"3"<..: 3 6 4 5 4 7 2 7 6 6 ...
## $ DeltaW5 : Ord.factor w/ 11 levels "1"<"2"<"3"<"4"<..: 6 5 5 6 4 7 2 6 5 6 ...
## $ DeltaP1 : Ord.factor w/ 8 levels "1"<"2"<"3"<"4"<..: 5 5 4 5 3 5 2 4 4 5 ...
## $ DeltaP2 : Ord.factor w/ 9 levels "1"<"2"<"3"<"4"<..: 5 8 6 6 6 5 7 5 5 5 ...
## $ DeltaP3 : Ord.factor w/ 9 levels "1"<"2"<"3"<"4"<..: 7 6 6 4 5 5 8 6 5 5 ...
## $ DeltaP4 : Ord.factor w/ 9 levels "1"<"2"<"3"<"4"<..: 7 6 7 4 6 5 9 4 5 5 ...
## $ DeltaP5 : Ord.factor w/ 9 levels "1"<"2"<"3"<"4"<..: 7 7 5 5 8 5 7 4 5 5 ...
## $ DeltaP6 : Ord.factor w/ 9 levels "1"<"2"<"3"<"4"<..: 7 7 6 6 6 5 8 5 5 5 ...
## $ DeltaP7 : Ord.factor w/ 9 levels "1"<"2"<"3"<"4"<..: 6 5 6 5 7 7 8 6 5 5 ...
## $ DeltaP8 : Ord.factor w/ 11 levels "1"<"2"<"3"<"4"<..: 6 4 3 6 6 7 1 5 6 7 ...
## $ DP1 : Ord.factor w/ 5 levels "1"<"2"<"3"<"4"<..: 5 5 3 5 5 3 5 4 4 5 ...
## $ DP2 : Ord.factor w/ 5 levels "1"<"2"<"3"<"4"<..: 5 2 4 3 5 2 4 5 1 2 ...
## $ DP3 : Ord.factor w/ 5 levels "1"<"2"<"3"<"4"<..: 2 4 4 4 5 4 1 5 4 3 ...
## $ DP4 : Ord.factor w/ 5 levels "1"<"2"<"3"<"4"<..: 5 5 4 5 5 5 5 5 5 5 ...
## $ DP5 : Ord.factor w/ 5 levels "1"<"2"<"3"<"4"<..: 3 3 4 5 5 5 2 5 5 5 ...
## $ ERG1 : Ord.factor w/ 6 levels "1"<"2"<"3"<"4"<..: 2 2 2 5 1 2 5 2 4 2 ...
## $ ERG2 : Ord.factor w/ 6 levels "1"<"2"<"3"<"4"<..: 6 6 3 6 2 6 5 5 5 5 ...
## $ ERG3 : Ord.factor w/ 6 levels "1"<"2"<"3"<"4"<..: 6 6 6 5 6 6 6 6 5 6 ...
## $ ERG4 : Ord.factor w/ 6 levels "1"<"2"<"3"<"4"<..: 6 4 4 6 6 6 5 6 5 6 ...
## $ ERG5 : Ord.factor w/ 6 levels "1"<"2"<"3"<"4"<..: 6 5 5 4 2 4 5 6 5 3 ...
## $ ERG6 : Ord.factor w/ 6 levels "1"<"2"<"3"<"4"<..: 4 5 4 5 1 3 4 6 4 3 ...So we have \(n=1511\), a number of predictors and outcomes, and they should now be correctly formatted.
For all our predictors, and the corresponding outcomes, we analyzed non-identifiability. It would take too much space to show all these steps but, in short, for each outcome check the corresponding covariates by creating a model matrix (without the intercept). The model matrix is then QR decomposed and we check for non-identifiability on the decomposed matrix. This can be done qualitatively, by examining pair plots.1 However, one can also do this quantitatively.2
Below we list our measurement model for the SEM,
m_cfa <- '
DWell =~ DeltaW1 + DeltaW2 + DeltaW3 + DeltaW4 +
DeltaW5
DPerf =~ DeltaP1 + DeltaP2 + DeltaP3 + DeltaP4 +
DeltaP5 + DeltaP6 + DeltaP8
DP =~ DP1 + DP2 + DP3 + DP4 + DP5
ERG =~ ERG1 + ERG2 + ERG3 + ERG4 + ERG5 + ERG6
'After \(= \sim\) we list the exogenous variables that models the latent variable on the left-hand side. DWell, is our latent variable of wellbeing (before/after the pandemic), DPerf, is our latent variable of performance (before/after), DPis our latent variable for disaster preparedness, and ERG, latent variable for ergonomics. The exogenous variables (predictors) are all ordered categorical in nature, i.e., Likert scale.
Let’s conduct confirmatory factor analysis,
res_cfa <- cfa(m_cfa, data = df)
summary(res_cfa, fit.measures=TRUE)## lavaan 0.6-5 ended normally after 53 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 185
##
## Number of observations 1377
##
## Model Test User Model:
## Standard Robust
## Test Statistic 1134.078 1176.437
## Degrees of freedom 224 224
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.032
## Shift parameter 77.040
## for the simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 46918.147 21831.773
## Degrees of freedom 253 253
## P-value 0.000 0.000
## Scaling correction factor 2.163
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.980 0.956
## Tucker-Lewis Index (TLI) 0.978 0.950
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.054 0.056
## 90 Percent confidence interval - lower 0.051 0.052
## 90 Percent confidence interval - upper 0.057 0.059
## P-value RMSEA <= 0.05 0.011 0.002
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.048 0.048
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Unstructured
## Standard errors Robust.sem
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## DWell =~
## DeltaW1 1.000
## DeltaW2 0.897 0.016 56.020 0.000
## DeltaW3 0.957 0.016 60.951 0.000
## DeltaW4 0.794 0.018 43.437 0.000
## DeltaW5 0.854 0.016 51.815 0.000
## DPerf =~
## DeltaP1 1.000
## DeltaP2 -1.251 0.050 -24.854 0.000
## DeltaP3 -1.114 0.052 -21.285 0.000
## DeltaP4 -1.226 0.052 -23.657 0.000
## DeltaP5 -1.220 0.054 -22.639 0.000
## DeltaP6 -1.288 0.056 -23.168 0.000
## DeltaP8 1.436 0.055 25.980 0.000
## DP =~
## DP1 1.000
## DP2 0.711 0.084 8.502 0.000
## DP3 1.143 0.106 10.799 0.000
## DP4 0.883 0.099 8.954 0.000
## DP5 1.086 0.108 10.071 0.000
## ERG =~
## ERG1 1.000
## ERG2 0.924 0.033 27.983 0.000
## ERG3 0.812 0.036 22.312 0.000
## ERG4 0.928 0.034 27.122 0.000
## ERG5 1.045 0.033 31.703 0.000
## ERG6 1.240 0.034 36.887 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## DWell ~~
## DPerf 0.265 0.016 16.508 0.000
## DP 0.020 0.016 1.240 0.215
## ERG 0.162 0.017 9.500 0.000
## DPerf ~~
## DP 0.032 0.011 3.049 0.002
## ERG 0.118 0.012 9.618 0.000
## DP ~~
## ERG 0.132 0.016 8.381 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .DeltaW1 0.000
## .DeltaW2 0.000
## .DeltaW3 0.000
## .DeltaW4 0.000
## .DeltaW5 0.000
## .DeltaP1 0.000
## .DeltaP2 0.000
## .DeltaP3 0.000
## .DeltaP4 0.000
## .DeltaP5 0.000
## .DeltaP6 0.000
## .DeltaP8 0.000
## .DP1 0.000
## .DP2 0.000
## .DP3 0.000
## .DP4 0.000
## .DP5 0.000
## .ERG1 0.000
## .ERG2 0.000
## .ERG3 0.000
## .ERG4 0.000
## .ERG5 0.000
## .ERG6 0.000
## DWell 0.000
## DPerf 0.000
## DP 0.000
## ERG 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|)
## DeltaW1|t1 -2.978 0.217 -13.743 0.000
## DeltaW1|t2 -2.183 0.088 -24.930 0.000
## DeltaW1|t3 -1.603 0.055 -28.924 0.000
## DeltaW1|t4 -1.004 0.041 -24.634 0.000
## DeltaW1|t5 -0.219 0.034 -6.433 0.000
## DeltaW1|t6 0.809 0.038 21.225 0.000
## DeltaW1|t7 1.546 0.053 28.924 0.000
## DeltaW1|t8 1.991 0.074 26.945 0.000
## DeltaW1|t9 2.482 0.118 20.954 0.000
## DeltaW1|t10 2.978 0.217 13.743 0.000
## DeltaW2|t1 -2.851 0.183 -15.542 0.000
## DeltaW2|t2 -2.203 0.089 -24.689 0.000
## DeltaW2|t3 -1.623 0.056 -28.905 0.000
## DeltaW2|t4 -1.083 0.042 -25.739 0.000
## DeltaW2|t5 -0.415 0.035 -11.897 0.000
## DeltaW2|t6 0.565 0.036 15.766 0.000
## DeltaW2|t7 1.221 0.045 27.287 0.000
## DeltaW2|t8 1.751 0.061 28.555 0.000
## DeltaW2|t9 2.320 0.100 23.198 0.000
## DeltaW2|t10 2.978 0.217 13.743 0.000
## DeltaW3|t1 -2.409 0.110 -21.979 0.000
## DeltaW3|t2 -1.895 0.068 -27.727 0.000
## DeltaW3|t3 -1.382 0.049 -28.451 0.000
## DeltaW3|t4 -0.753 0.038 -20.066 0.000
## DeltaW3|t5 -0.125 0.034 -3.690 0.000
## DeltaW3|t6 0.804 0.038 21.125 0.000
## DeltaW3|t7 1.494 0.052 28.851 0.000
## DeltaW3|t8 1.953 0.072 27.276 0.000
## DeltaW3|t9 2.482 0.118 20.954 0.000
## DeltaW3|t10 3.184 0.289 11.000 0.000
## DeltaW4|t1 -2.320 0.100 -23.198 0.000
## DeltaW4|t2 -1.651 0.057 -28.863 0.000
## DeltaW4|t3 -1.198 0.044 -27.067 0.000
## DeltaW4|t4 -0.675 0.037 -18.374 0.000
## DeltaW4|t5 0.210 0.034 6.165 0.000
## DeltaW4|t6 0.820 0.038 21.424 0.000
## DeltaW4|t7 1.368 0.048 28.378 0.000
## DeltaW4|t8 1.814 0.064 28.249 0.000
## DeltaW4|t9 2.444 0.114 21.493 0.000
## DeltaW5|t1 -2.570 0.131 -19.672 0.000
## DeltaW5|t2 -1.965 0.072 -27.171 0.000
## DeltaW5|t3 -1.345 0.048 -28.247 0.000
## DeltaW5|t4 -0.743 0.037 -19.862 0.000
## DeltaW5|t5 -0.147 0.034 -4.336 0.000
## DeltaW5|t6 0.872 0.039 22.411 0.000
## DeltaW5|t7 1.559 0.054 28.931 0.000
## DeltaW5|t8 2.077 0.080 26.105 0.000
## DeltaW5|t9 2.523 0.124 20.352 0.000
## DeltaW5|t10 2.978 0.217 13.743 0.000
## DeltaP1|t1 -2.978 0.217 -13.743 0.000
## DeltaP1|t2 -2.183 0.088 -24.930 0.000
## DeltaP1|t3 -1.368 0.048 -28.378 0.000
## DeltaP1|t4 -0.419 0.035 -12.004 0.000
## DeltaP1|t5 1.051 0.042 25.305 0.000
## DeltaP1|t6 2.110 0.082 25.758 0.000
## DeltaP1|t7 2.978 0.217 13.743 0.000
## DeltaP2|t1 -2.978 0.217 -13.743 0.000
## DeltaP2|t2 -2.685 0.149 -17.984 0.000
## DeltaP2|t3 -1.843 0.066 -28.078 0.000
## DeltaP2|t4 -0.975 0.040 -24.175 0.000
## DeltaP2|t5 0.516 0.035 14.553 0.000
## DeltaP2|t6 1.323 0.047 28.106 0.000
## DeltaP2|t7 2.203 0.089 24.689 0.000
## DeltaP2|t8 3.184 0.289 11.000 0.000
## DeltaP3|t1 -3.184 0.289 -11.000 0.000
## DeltaP3|t2 -2.482 0.118 -20.954 0.000
## DeltaP3|t3 -1.814 0.064 -28.249 0.000
## DeltaP3|t4 -0.986 0.040 -24.360 0.000
## DeltaP3|t5 0.291 0.034 8.474 0.000
## DeltaP3|t6 1.382 0.049 28.451 0.000
## DeltaP3|t7 2.294 0.097 23.541 0.000
## DeltaP3|t8 2.978 0.217 13.743 0.000
## DeltaP4|t1 -2.685 0.149 -17.984 0.000
## DeltaP4|t2 -2.183 0.088 -24.930 0.000
## DeltaP4|t3 -1.462 0.051 -28.770 0.000
## DeltaP4|t4 -0.606 0.036 -16.762 0.000
## DeltaP4|t5 0.541 0.036 15.187 0.000
## DeltaP4|t6 1.436 0.050 28.685 0.000
## DeltaP4|t7 2.482 0.118 20.954 0.000
## DeltaP4|t8 2.758 0.163 16.896 0.000
## DeltaP5|t1 -2.978 0.217 -13.743 0.000
## DeltaP5|t2 -2.378 0.106 -22.422 0.000
## DeltaP5|t3 -1.616 0.056 -28.913 0.000
## DeltaP5|t4 -0.772 0.038 -20.471 0.000
## DeltaP5|t5 0.571 0.036 15.923 0.000
## DeltaP5|t6 1.372 0.048 28.403 0.000
## DeltaP5|t7 2.164 0.086 25.156 0.000
## DeltaP5|t8 2.851 0.183 15.542 0.000
## DeltaP6|t1 -2.851 0.183 -15.542 0.000
## DeltaP6|t2 -2.164 0.086 -25.156 0.000
## DeltaP6|t3 -1.489 0.052 -28.839 0.000
## DeltaP6|t4 -0.652 0.037 -17.856 0.000
## DeltaP6|t5 0.508 0.035 14.341 0.000
## DeltaP6|t6 1.368 0.048 28.378 0.000
## DeltaP6|t7 2.378 0.106 22.422 0.000
## DeltaP6|t8 3.184 0.289 11.000 0.000
## DeltaP8|t1 -2.851 0.183 -15.542 0.000
## DeltaP8|t2 -2.570 0.131 -19.672 0.000
## DeltaP8|t3 -2.203 0.089 -24.689 0.000
## DeltaP8|t4 -1.688 0.059 -28.778 0.000
## DeltaP8|t5 -1.080 0.042 -25.696 0.000
## DeltaP8|t6 -0.447 0.035 -12.750 0.000
## DeltaP8|t7 1.086 0.042 25.782 0.000
## DeltaP8|t8 1.884 0.068 27.805 0.000
## DeltaP8|t9 2.409 0.110 21.979 0.000
## DeltaP8|t10 2.978 0.217 13.743 0.000
## DP1|t1 -1.906 0.069 -27.646 0.000
## DP1|t2 -1.180 0.044 -26.878 0.000
## DP1|t3 -0.646 0.036 -17.701 0.000
## DP1|t4 0.061 0.034 1.805 0.071
## DP2|t1 -0.650 0.037 -17.804 0.000
## DP2|t2 -0.120 0.034 -3.528 0.000
## DP2|t3 0.415 0.035 11.897 0.000
## DP2|t4 1.010 0.041 24.725 0.000
## DP3|t1 -0.960 0.040 -23.942 0.000
## DP3|t2 -0.443 0.035 -12.643 0.000
## DP3|t3 0.138 0.034 4.067 0.000
## DP3|t4 0.817 0.038 21.374 0.000
## DP4|t1 -2.409 0.110 -21.979 0.000
## DP4|t2 -1.853 0.066 -28.015 0.000
## DP4|t3 -1.306 0.047 -27.988 0.000
## DP4|t4 -0.337 0.034 -9.760 0.000
## DP5|t1 -1.658 0.057 -28.849 0.000
## DP5|t2 -1.154 0.043 -26.605 0.000
## DP5|t3 -0.700 0.037 -18.941 0.000
## DP5|t4 -0.050 0.034 -1.482 0.138
## ERG1|t1 -1.472 0.051 -28.800 0.000
## ERG1|t2 -0.845 0.039 -21.920 0.000
## ERG1|t3 -0.298 0.034 -8.688 0.000
## ERG1|t4 0.348 0.035 10.081 0.000
## ERG1|t5 1.063 0.042 25.480 0.000
## ERG2|t1 -2.145 0.085 -25.369 0.000
## ERG2|t2 -1.571 0.054 -28.934 0.000
## ERG2|t3 -1.120 0.043 -26.201 0.000
## ERG2|t4 -0.560 0.036 -15.661 0.000
## ERG2|t5 0.223 0.034 6.541 0.000
## ERG3|t1 -2.378 0.106 -22.422 0.000
## ERG3|t2 -1.814 0.064 -28.249 0.000
## ERG3|t3 -1.421 0.050 -28.627 0.000
## ERG3|t4 -0.832 0.038 -21.673 0.000
## ERG3|t5 0.030 0.034 0.889 0.374
## ERG4|t1 -2.409 0.110 -21.979 0.000
## ERG4|t2 -1.917 0.070 -27.560 0.000
## ERG4|t3 -1.363 0.048 -28.352 0.000
## ERG4|t4 -0.738 0.037 -19.761 0.000
## ERG4|t5 0.178 0.034 5.250 0.000
## ERG5|t1 -1.610 0.056 -28.919 0.000
## ERG5|t2 -1.001 0.041 -24.589 0.000
## ERG5|t3 -0.569 0.036 -15.871 0.000
## ERG5|t4 -0.030 0.034 -0.889 0.374
## ERG5|t5 0.639 0.036 17.545 0.000
## ERG6|t1 -1.665 0.058 -28.833 0.000
## ERG6|t2 -1.048 0.041 -25.261 0.000
## ERG6|t3 -0.487 0.035 -13.812 0.000
## ERG6|t4 0.208 0.034 6.111 0.000
## ERG6|t5 0.874 0.039 22.459 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .DeltaW1 0.263
## .DeltaW2 0.408
## .DeltaW3 0.325
## .DeltaW4 0.535
## .DeltaW5 0.463
## .DeltaP1 0.697
## .DeltaP2 0.526
## .DeltaP3 0.624
## .DeltaP4 0.545
## .DeltaP5 0.549
## .DeltaP6 0.498
## .DeltaP8 0.375
## .DP1 0.717
## .DP2 0.857
## .DP3 0.631
## .DP4 0.780
## .DP5 0.667
## .ERG1 0.511
## .ERG2 0.582
## .ERG3 0.678
## .ERG4 0.578
## .ERG5 0.466
## .ERG6 0.248
## DWell 0.737 0.016 47.195 0.000
## DPerf 0.303 0.023 13.321 0.000
## DP 0.283 0.038 7.413 0.000
## ERG 0.489 0.024 20.356 0.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|)
## DeltaW1 1.000
## DeltaW2 1.000
## DeltaW3 1.000
## DeltaW4 1.000
## DeltaW5 1.000
## DeltaP1 1.000
## DeltaP2 1.000
## DeltaP3 1.000
## DeltaP4 1.000
## DeltaP5 1.000
## DeltaP6 1.000
## DeltaP8 1.000
## DP1 1.000
## DP2 1.000
## DP3 1.000
## DP4 1.000
## DP5 1.000
## ERG1 1.000
## ERG2 1.000
## ERG3 1.000
## ERG4 1.000
## ERG5 1.000
## ERG6 1.000The summary shows that CFI/TLI and SRMR look ok. CFI/TLI should be \(\gt 0.95\) and SRMR and RMSEAshould be \(\lt 0.05\).3 In our case, the latter diagnostics are slightly higher than the threshold but that is to be expected considering our large sample size.
Next, let’s check our estimations,
estVals <- parameterEstimates(res_cfa, standardized = TRUE)
estVals[estVals$op == "=~", "est"]## [1] 1.0000000 0.8966882 0.9569860 0.7943853 0.8539630 1.0000000
## [7] -1.2511532 -1.1143185 -1.2258009 -1.2201362 -1.2878288 1.4364037
## [13] 1.0000000 0.7109824 1.1430215 0.8826622 1.0858519 1.0000000
## [19] 0.9242234 0.8115668 0.9283170 1.0449425 1.2395777and our factor loadings, which should be \(0\) or close to \(0\),
estVals[estVals$op == "=~", "pvalue"]## [1] NA 0 0 0 0 NA 0 0 0 0 0 0 NA 0 0 0 0 NA 0 0 0 0 0look good.4
Next, are the factor loadings signficant?
pValues <- na.omit(estVals[estVals$op == "=~", "pvalue"])
print(
paste0(
if(sum(pValues < .05) != length(pValues)){"NOT "},
"All factor loadings significant"))## [1] "All factor loadings significant"Finally, here are the intercorrelations from the confirmatory factor analysis,
inspect(res_cfa, "cor.lv")## DWell DPerf DP ERG
## DWell 1.000
## DPerf 0.560 1.000
## DP 0.044 0.110 1.000
## ERG 0.270 0.308 0.356 1.000Here is the full structural (regression) model (with all predictors),5
m_full <- '
DWell =~ DeltaW1 + DeltaW2 + DeltaW3 + DeltaW4 +DeltaW5
DPerf =~ DeltaP1 + DeltaP2 + DeltaP3 + DeltaP4 + DeltaP5 + DeltaP6 + DeltaP8
DP =~ DP1 + DP2 + DP3 + DP4 + DP5
ERG =~ ERG1 + ERG2 + ERG3 + ERG4 + ERG5 + ERG6
DP ~ gender_b + covidstatus_o + isolation_o + exp_s + homeexp_s +
fulltime_b + age_s + edu_o + orgsize_o + disab_o + adultcohab_o +
childcohab_o + dev_b
ERG ~ gender_b + covidstatus_o + isolation_o + exp_s + homeexp_s +
fulltime_b + age_s + edu_o + orgsize_o + disab_o + adultcohab_o +
childcohab_o + dev_b
fear ~ DP + gender_b + covidstatus_o + isolation_o + exp_s + homeexp_s +
fulltime_b + age_s + edu_o + orgsize_o + disab_o + adultcohab_o +
childcohab_o + dev_b
DWell ~ ERG + fear + DP +
gender_b + covidstatus_o + isolation_o + exp_s + homeexp_s +
fulltime_b + age_s + edu_o + orgsize_o + disab_o + adultcohab_o +
childcohab_o + dev_b
DPerf ~ ERG + fear + DP +
gender_b + covidstatus_o + isolation_o + exp_s + homeexp_s +
fulltime_b + age_s + edu_o + orgsize_o + disab_o + adultcohab_o +
childcohab_o + dev_b
DWell ~ DPerf
'Variables starting with a capital letter indicates a latent variable.
Run the equations and show summary,
res_full <- sem(m_full, data = df)
summary(res_full, fit.measures = TRUE) ## lavaan 0.6-5 ended normally after 116 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 254
##
## Number of observations 1377
##
## Model Test User Model:
## Standard Robust
## Test Statistic 2261.618 2404.643
## Degrees of freedom 492 492
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.011
## Shift parameter 167.901
## for the simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 46695.636 22310.239
## Degrees of freedom 276 276
## P-value 0.000 0.000
## Scaling correction factor 2.107
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.962 0.913
## Tucker-Lewis Index (TLI) 0.979 0.951
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.051 0.053
## 90 Percent confidence interval - lower 0.049 0.051
## 90 Percent confidence interval - upper 0.053 0.055
## P-value RMSEA <= 0.05 0.190 0.007
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.067 0.067
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Unstructured
## Standard errors Robust.sem
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## DWell =~
## DeltaW1 1.000
## DeltaW2 0.895 0.016 54.572 0.000
## DeltaW3 0.955 0.016 59.610 0.000
## DeltaW4 0.805 0.018 45.198 0.000
## DeltaW5 0.851 0.016 51.729 0.000
## DPerf =~
## DeltaP1 1.000
## DeltaP2 -1.256 0.051 -24.527 0.000
## DeltaP3 -1.115 0.052 -21.605 0.000
## DeltaP4 -1.230 0.052 -23.684 0.000
## DeltaP5 -1.222 0.054 -22.652 0.000
## DeltaP6 -1.289 0.056 -23.081 0.000
## DeltaP8 1.450 0.055 26.172 0.000
## DP =~
## DP1 1.000
## DP2 0.700 0.071 9.931 0.000
## DP3 1.104 0.087 12.706 0.000
## DP4 0.789 0.083 9.558 0.000
## DP5 1.030 0.088 11.704 0.000
## ERG =~
## ERG1 1.000
## ERG2 0.954 0.035 27.282 0.000
## ERG3 0.791 0.037 21.613 0.000
## ERG4 0.912 0.035 26.424 0.000
## ERG5 1.047 0.034 31.215 0.000
## ERG6 1.246 0.035 35.163 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## DP ~
## gender_b 0.008 0.055 0.151 0.880
## covidstatus_o 0.074 0.032 2.313 0.021
## isolation_o 0.047 0.045 1.058 0.290
## exp_s 0.023 0.037 0.631 0.528
## homeexp_s 0.030 0.023 1.279 0.201
## fulltime_b -0.035 0.084 -0.423 0.672
## age_s 0.026 0.036 0.711 0.477
## edu_o -0.048 0.026 -1.892 0.059
## orgsize_o 0.002 0.017 0.145 0.885
## disab_o -0.179 0.059 -3.029 0.002
## adultcohab_o 0.081 0.019 4.305 0.000
## childcohab_o 0.001 0.028 0.032 0.975
## dev_b -0.017 0.052 -0.334 0.739
## ERG ~
## gender_b -0.093 0.056 -1.674 0.094
## covidstatus_o -0.045 0.031 -1.429 0.153
## isolation_o 0.014 0.047 0.293 0.770
## exp_s 0.047 0.041 1.134 0.257
## homeexp_s 0.063 0.024 2.656 0.008
## fulltime_b -0.020 0.089 -0.230 0.818
## age_s 0.052 0.040 1.316 0.188
## edu_o -0.008 0.027 -0.304 0.761
## orgsize_o -0.006 0.017 -0.385 0.700
## disab_o -0.117 0.057 -2.039 0.041
## adultcohab_o -0.047 0.019 -2.456 0.014
## childcohab_o -0.162 0.028 -5.701 0.000
## dev_b 0.021 0.055 0.384 0.701
## fear ~
## DP -0.352 0.108 -3.248 0.001
## gender_b 0.278 0.121 2.306 0.021
## covidstatus_o 0.197 0.075 2.607 0.009
## isolation_o 0.535 0.104 5.136 0.000
## exp_s -0.057 0.094 -0.604 0.546
## homeexp_s 0.064 0.051 1.250 0.211
## fulltime_b -0.102 0.204 -0.501 0.616
## age_s 0.050 0.091 0.551 0.582
## edu_o -0.126 0.059 -2.134 0.033
## orgsize_o -0.064 0.037 -1.746 0.081
## disab_o 0.278 0.118 2.352 0.019
## adultcohab_o 0.065 0.042 1.567 0.117
## childcohab_o 0.109 0.062 1.753 0.080
## dev_b -0.350 0.112 -3.112 0.002
## DWell ~
## ERG 0.125 0.033 3.762 0.000
## fear -0.033 0.012 -2.628 0.009
## DP -0.017 0.050 -0.344 0.731
## gender_b -0.012 0.056 -0.209 0.834
## covidstatus_o -0.109 0.037 -2.986 0.003
## isolation_o 0.050 0.050 0.995 0.320
## exp_s -0.074 0.043 -1.712 0.087
## homeexp_s -0.014 0.023 -0.613 0.540
## fulltime_b 0.108 0.087 1.239 0.215
## age_s 0.092 0.044 2.100 0.036
## edu_o -0.017 0.028 -0.607 0.544
## orgsize_o -0.014 0.018 -0.785 0.433
## disab_o 0.080 0.053 1.517 0.129
## adultcohab_o 0.004 0.021 0.193 0.847
## childcohab_o -0.038 0.031 -1.226 0.220
## dev_b -0.005 0.057 -0.091 0.927
## DPerf ~
## ERG 0.244 0.024 10.239 0.000
## fear -0.002 0.009 -0.187 0.852
## DP 0.097 0.035 2.754 0.006
## gender_b 0.028 0.044 0.640 0.522
## covidstatus_o 0.005 0.023 0.222 0.825
## isolation_o -0.002 0.036 -0.043 0.966
## exp_s 0.002 0.031 0.066 0.947
## homeexp_s -0.031 0.020 -1.595 0.111
## fulltime_b -0.007 0.069 -0.109 0.914
## age_s 0.055 0.031 1.778 0.075
## edu_o 0.003 0.020 0.154 0.877
## orgsize_o -0.008 0.014 -0.622 0.534
## disab_o 0.107 0.047 2.307 0.021
## adultcohab_o 0.041 0.015 2.762 0.006
## childcohab_o 0.014 0.023 0.590 0.555
## dev_b 0.040 0.044 0.898 0.369
## DWell ~
## DPerf 0.820 0.045 18.258 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .DeltaW1 0.000
## .DeltaW2 0.000
## .DeltaW3 0.000
## .DeltaW4 0.000
## .DeltaW5 0.000
## .DeltaP1 0.000
## .DeltaP2 0.000
## .DeltaP3 0.000
## .DeltaP4 0.000
## .DeltaP5 0.000
## .DeltaP6 0.000
## .DeltaP8 0.000
## .DP1 0.000
## .DP2 0.000
## .DP3 0.000
## .DP4 0.000
## .DP5 0.000
## .ERG1 0.000
## .ERG2 0.000
## .ERG3 0.000
## .ERG4 0.000
## .ERG5 0.000
## .ERG6 0.000
## .fear -3.231 0.508 -6.360 0.000
## .DWell 0.000
## .DPerf 0.000
## .DP 0.000
## .ERG 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|)
## DeltaW1|t1 -2.786 0.381 -7.318 0.000
## DeltaW1|t2 -1.977 0.319 -6.198 0.000
## DeltaW1|t3 -1.391 0.314 -4.437 0.000
## DeltaW1|t4 -0.788 0.307 -2.564 0.010
## DeltaW1|t5 0.005 0.306 0.017 0.987
## DeltaW1|t6 1.044 0.307 3.402 0.001
## DeltaW1|t7 1.787 0.310 5.762 0.000
## DeltaW1|t8 2.234 0.310 7.196 0.000
## DeltaW1|t9 2.727 0.321 8.481 0.000
## DeltaW1|t10 3.223 0.364 8.867 0.000
## DeltaW2|t1 -2.688 0.375 -7.160 0.000
## DeltaW2|t2 -2.031 0.332 -6.112 0.000
## DeltaW2|t3 -1.444 0.332 -4.355 0.000
## DeltaW2|t4 -0.897 0.328 -2.738 0.006
## DeltaW2|t5 -0.220 0.326 -0.675 0.500
## DeltaW2|t6 0.770 0.326 2.363 0.018
## DeltaW2|t7 1.430 0.328 4.367 0.000
## DeltaW2|t8 1.964 0.331 5.928 0.000
## DeltaW2|t9 2.534 0.352 7.207 0.000
## DeltaW2|t10 3.191 0.413 7.724 0.000
## DeltaW3|t1 -2.561 0.339 -7.562 0.000
## DeltaW3|t2 -2.042 0.321 -6.351 0.000
## DeltaW3|t3 -1.520 0.323 -4.706 0.000
## DeltaW3|t4 -0.881 0.319 -2.757 0.006
## DeltaW3|t5 -0.243 0.318 -0.763 0.445
## DeltaW3|t6 0.699 0.319 2.191 0.028
## DeltaW3|t7 1.396 0.321 4.346 0.000
## DeltaW3|t8 1.858 0.328 5.661 0.000
## DeltaW3|t9 2.389 0.334 7.158 0.000
## DeltaW3|t10 3.092 0.437 7.067 0.000
## DeltaW4|t1 -2.430 0.319 -7.615 0.000
## DeltaW4|t2 -1.763 0.304 -5.801 0.000
## DeltaW4|t3 -1.306 0.301 -4.343 0.000
## DeltaW4|t4 -0.776 0.298 -2.606 0.009
## DeltaW4|t5 0.122 0.296 0.411 0.681
## DeltaW4|t6 0.739 0.297 2.489 0.013
## DeltaW4|t7 1.293 0.297 4.351 0.000
## DeltaW4|t8 1.744 0.301 5.801 0.000
## DeltaW4|t9 2.379 0.326 7.289 0.000
## DeltaW5|t1 -2.264 0.342 -6.616 0.000
## DeltaW5|t2 -1.647 0.314 -5.249 0.000
## DeltaW5|t3 -1.016 0.313 -3.244 0.001
## DeltaW5|t4 -0.406 0.310 -1.311 0.190
## DeltaW5|t5 0.200 0.309 0.649 0.517
## DeltaW5|t6 1.237 0.310 3.986 0.000
## DeltaW5|t7 1.932 0.309 6.258 0.000
## DeltaW5|t8 2.459 0.313 7.854 0.000
## DeltaW5|t9 2.907 0.326 8.916 0.000
## DeltaW5|t10 3.360 0.359 9.354 0.000
## DeltaP1|t1 -2.985 0.369 -8.095 0.000
## DeltaP1|t2 -2.175 0.321 -6.771 0.000
## DeltaP1|t3 -1.354 0.318 -4.255 0.000
## DeltaP1|t4 -0.398 0.314 -1.268 0.205
## DeltaP1|t5 1.080 0.314 3.439 0.001
## DeltaP1|t6 2.148 0.325 6.601 0.000
## DeltaP1|t7 3.024 0.376 8.042 0.000
## DeltaP2|t1 -3.135 0.427 -7.348 0.000
## DeltaP2|t2 -2.829 0.374 -7.566 0.000
## DeltaP2|t3 -1.973 0.346 -5.701 0.000
## DeltaP2|t4 -1.096 0.340 -3.229 0.001
## DeltaP2|t5 0.408 0.339 1.204 0.229
## DeltaP2|t6 1.222 0.340 3.596 0.000
## DeltaP2|t7 2.111 0.343 6.157 0.000
## DeltaP2|t8 3.105 0.466 6.666 0.000
## DeltaP3|t1 -3.676 0.407 -9.029 0.000
## DeltaP3|t2 -2.971 0.371 -8.008 0.000
## DeltaP3|t3 -2.291 0.353 -6.491 0.000
## DeltaP3|t4 -1.456 0.345 -4.217 0.000
## DeltaP3|t5 -0.161 0.344 -0.467 0.640
## DeltaP3|t6 0.951 0.345 2.759 0.006
## DeltaP3|t7 1.877 0.358 5.244 0.000
## DeltaP3|t8 2.559 0.400 6.394 0.000
## DeltaP4|t1 -2.831 0.352 -8.043 0.000
## DeltaP4|t2 -2.326 0.329 -7.076 0.000
## DeltaP4|t3 -1.600 0.322 -4.976 0.000
## DeltaP4|t4 -0.740 0.321 -2.302 0.021
## DeltaP4|t5 0.413 0.321 1.286 0.198
## DeltaP4|t6 1.314 0.322 4.076 0.000
## DeltaP4|t7 2.367 0.328 7.219 0.000
## DeltaP4|t8 2.642 0.352 7.508 0.000
## DeltaP5|t1 -3.189 0.370 -8.613 0.000
## DeltaP5|t2 -2.584 0.320 -8.070 0.000
## DeltaP5|t3 -1.818 0.308 -5.910 0.000
## DeltaP5|t4 -0.965 0.304 -3.178 0.001
## DeltaP5|t5 0.390 0.303 1.285 0.199
## DeltaP5|t6 1.196 0.303 3.942 0.000
## DeltaP5|t7 1.992 0.307 6.481 0.000
## DeltaP5|t8 2.678 0.339 7.908 0.000
## DeltaP6|t1 -3.043 0.362 -8.411 0.000
## DeltaP6|t2 -2.355 0.343 -6.868 0.000
## DeltaP6|t3 -1.680 0.334 -5.035 0.000
## DeltaP6|t4 -0.837 0.332 -2.522 0.012
## DeltaP6|t5 0.338 0.331 1.021 0.307
## DeltaP6|t6 1.208 0.332 3.636 0.000
## DeltaP6|t7 2.227 0.349 6.381 0.000
## DeltaP6|t8 3.039 0.433 7.027 0.000
## DeltaP8|t1 -2.938 0.416 -7.064 0.000
## DeltaP8|t2 -2.656 0.381 -6.963 0.000
## DeltaP8|t3 -2.288 0.358 -6.394 0.000
## DeltaP8|t4 -1.770 0.357 -4.954 0.000
## DeltaP8|t5 -1.158 0.353 -3.278 0.001
## DeltaP8|t6 -0.521 0.352 -1.479 0.139
## DeltaP8|t7 1.017 0.354 2.878 0.004
## DeltaP8|t8 1.816 0.357 5.082 0.000
## DeltaP8|t9 2.341 0.368 6.361 0.000
## DeltaP8|t10 2.915 0.418 6.967 0.000
## DP1|t1 -2.091 0.349 -5.991 0.000
## DP1|t2 -1.361 0.343 -3.964 0.000
## DP1|t3 -0.824 0.343 -2.406 0.016
## DP1|t4 -0.112 0.342 -0.328 0.743
## DP2|t1 -0.598 0.321 -1.867 0.062
## DP2|t2 -0.061 0.320 -0.191 0.848
## DP2|t3 0.479 0.320 1.494 0.135
## DP2|t4 1.082 0.321 3.371 0.001
## DP3|t1 -1.086 0.314 -3.456 0.001
## DP3|t2 -0.567 0.313 -1.811 0.070
## DP3|t3 0.017 0.313 0.056 0.956
## DP3|t4 0.702 0.313 2.245 0.025
## DP4|t1 -1.081 0.371 -2.912 0.004
## DP4|t2 -0.512 0.351 -1.458 0.145
## DP4|t3 0.049 0.348 0.141 0.888
## DP4|t4 1.059 0.349 3.037 0.002
## DP5|t1 -2.505 0.348 -7.194 0.000
## DP5|t2 -1.980 0.348 -5.684 0.000
## DP5|t3 -1.509 0.347 -4.350 0.000
## DP5|t4 -0.839 0.346 -2.427 0.015
## ERG1|t1 -2.432 0.301 -8.083 0.000
## ERG1|t2 -1.781 0.297 -5.989 0.000
## ERG1|t3 -1.215 0.296 -4.103 0.000
## ERG1|t4 -0.546 0.296 -1.846 0.065
## ERG1|t5 0.186 0.297 0.626 0.532
## ERG2|t1 -3.655 0.338 -10.816 0.000
## ERG2|t2 -3.044 0.332 -9.177 0.000
## ERG2|t3 -2.553 0.329 -7.765 0.000
## ERG2|t4 -1.949 0.327 -5.953 0.000
## ERG2|t5 -1.116 0.326 -3.429 0.001
## ERG3|t1 -2.661 0.373 -7.124 0.000
## ERG3|t2 -2.088 0.349 -5.990 0.000
## ERG3|t3 -1.687 0.346 -4.875 0.000
## ERG3|t4 -1.085 0.343 -3.164 0.002
## ERG3|t5 -0.204 0.341 -0.600 0.549
## ERG4|t1 -2.743 0.320 -8.584 0.000
## ERG4|t2 -2.245 0.313 -7.172 0.000
## ERG4|t3 -1.686 0.313 -5.391 0.000
## ERG4|t4 -1.055 0.313 -3.375 0.001
## ERG4|t5 -0.126 0.312 -0.405 0.686
## ERG5|t1 -1.672 0.334 -5.000 0.000
## ERG5|t2 -1.054 0.334 -3.160 0.002
## ERG5|t3 -0.613 0.333 -1.842 0.066
## ERG5|t4 -0.064 0.333 -0.194 0.846
## ERG5|t5 0.611 0.332 1.842 0.066
## ERG6|t1 -2.009 0.304 -6.607 0.000
## ERG6|t2 -1.384 0.303 -4.563 0.000
## ERG6|t3 -0.816 0.304 -2.686 0.007
## ERG6|t4 -0.109 0.304 -0.360 0.719
## ERG6|t5 0.567 0.304 1.867 0.062
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .DeltaW1 0.266
## .DeltaW2 0.413
## .DeltaW3 0.331
## .DeltaW4 0.524
## .DeltaW5 0.469
## .DeltaP1 0.701
## .DeltaP2 0.528
## .DeltaP3 0.629
## .DeltaP4 0.548
## .DeltaP5 0.554
## .DeltaP6 0.504
## .DeltaP8 0.372
## .DP1 0.696
## .DP2 0.851
## .DP3 0.630
## .DP4 0.811
## .DP5 0.678
## .ERG1 0.517
## .ERG2 0.560
## .ERG3 0.698
## .ERG4 0.598
## .ERG5 0.470
## .ERG6 0.250
## .fear 2.664 0.124 21.522 0.000
## .DWell 0.498 0.020 25.526 0.000
## .DPerf 0.267 0.021 12.913 0.000
## .DP 0.304 0.035 8.784 0.000
## .ERG 0.483 0.024 19.764 0.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|)
## DeltaW1 1.000
## DeltaW2 1.000
## DeltaW3 1.000
## DeltaW4 1.000
## DeltaW5 1.000
## DeltaP1 1.000
## DeltaP2 1.000
## DeltaP3 1.000
## DeltaP4 1.000
## DeltaP5 1.000
## DeltaP6 1.000
## DeltaP8 1.000
## DP1 1.000
## DP2 1.000
## DP3 1.000
## DP4 1.000
## DP5 1.000
## ERG1 1.000
## ERG2 1.000
## ERG3 1.000
## ERG4 1.000
## ERG5 1.000
## ERG6 1.000Let’s remove all covariates with \(p \gt 0.1\),
m_sem <- '
DWell =~ DeltaW1 + DeltaW2 + DeltaW3 + DeltaW4 + DeltaW5
DPerf =~ DeltaP1 + DeltaP2 + DeltaP3 + DeltaP4 + DeltaP5 + DeltaP6 +
DeltaP8
DP =~ DP1 + DP2 + DP3 + DP4 + DP5
ERG =~ ERG1 + ERG2 + ERG3 + ERG4 + ERG5 + ERG6
DP ~ covidstatus_o + edu_o + disab_o + adultcohab_o
ERG ~ gender_b + homeexp_s + disab_o + adultcohab_o + childcohab_o
fear ~ DP +
gender_b + covidstatus_o + isolation_o + edu_o + orgsize_o +
disab_o + childcohab_o + dev_b
DWell ~ ERG + fear + DP + covidstatus_o + exp_s + age_s
DPerf ~ ERG + fear + DP + age_s + disab_o + adultcohab_o
DWell ~ DPerf
'and then run the equations again,
res_sem <- sem(m_sem, data = df)
summary(res_sem, fit.measures = TRUE)## lavaan 0.6-5 ended normally after 100 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 212
##
## Number of observations 1377
##
## Model Test User Model:
## Standard Robust
## Test Statistic 2302.693 1962.688
## Degrees of freedom 510 510
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.305
## Shift parameter 197.904
## for the simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 46611.308 22269.086
## Degrees of freedom 276 276
## P-value 0.000 0.000
## Scaling correction factor 2.107
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.961 0.934
## Tucker-Lewis Index (TLI) 0.979 0.964
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.051 0.045
## 90 Percent confidence interval - lower 0.048 0.043
## 90 Percent confidence interval - upper 0.053 0.048
## P-value RMSEA <= 0.05 0.331 1.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.067 0.067
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Unstructured
## Standard errors Robust.sem
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## DWell =~
## DeltaW1 1.000
## DeltaW2 0.895 0.016 54.689 0.000
## DeltaW3 0.955 0.016 58.948 0.000
## DeltaW4 0.805 0.018 44.927 0.000
## DeltaW5 0.851 0.016 51.570 0.000
## DPerf =~
## DeltaP1 1.000
## DeltaP2 -1.258 0.051 -24.522 0.000
## DeltaP3 -1.116 0.052 -21.513 0.000
## DeltaP4 -1.231 0.052 -23.634 0.000
## DeltaP5 -1.223 0.054 -22.597 0.000
## DeltaP6 -1.290 0.056 -23.032 0.000
## DeltaP8 1.452 0.056 26.133 0.000
## DP =~
## DP1 1.000
## DP2 0.694 0.070 9.879 0.000
## DP3 1.096 0.087 12.643 0.000
## DP4 0.772 0.082 9.434 0.000
## DP5 1.028 0.087 11.747 0.000
## ERG =~
## ERG1 1.000
## ERG2 0.955 0.035 27.234 0.000
## ERG3 0.789 0.037 21.552 0.000
## ERG4 0.909 0.035 26.166 0.000
## ERG5 1.047 0.033 31.303 0.000
## ERG6 1.247 0.036 35.032 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## DP ~
## covidstatus_o 0.073 0.032 2.260 0.024
## edu_o -0.050 0.026 -1.882 0.060
## disab_o -0.179 0.059 -3.035 0.002
## adultcohab_o 0.080 0.019 4.234 0.000
## ERG ~
## gender_b -0.080 0.059 -1.354 0.176
## homeexp_s 0.044 0.026 1.709 0.087
## disab_o -0.110 0.057 -1.932 0.053
## adultcohab_o -0.047 0.019 -2.457 0.014
## childcohab_o -0.163 0.031 -5.184 0.000
## fear ~
## DP -0.336 0.106 -3.161 0.002
## gender_b 0.273 0.122 2.241 0.025
## covidstatus_o 0.196 0.075 2.607 0.009
## isolation_o 0.502 0.105 4.764 0.000
## edu_o -0.122 0.060 -2.047 0.041
## orgsize_o -0.060 0.037 -1.619 0.105
## disab_o 0.265 0.119 2.227 0.026
## childcohab_o 0.116 0.063 1.831 0.067
## dev_b -0.356 0.116 -3.056 0.002
## DWell ~
## ERG 0.125 0.033 3.813 0.000
## fear -0.031 0.012 -2.542 0.011
## DP -0.020 0.049 -0.416 0.678
## covidstatus_o -0.121 0.040 -3.041 0.002
## exp_s -0.052 0.051 -1.011 0.312
## age_s 0.097 0.044 2.204 0.028
## DPerf ~
## ERG 0.242 0.024 10.233 0.000
## fear -0.002 0.009 -0.204 0.838
## DP 0.097 0.035 2.788 0.005
## age_s 0.070 0.032 2.220 0.026
## disab_o 0.124 0.049 2.513 0.012
## adultcohab_o 0.041 0.015 2.752 0.006
## DWell ~
## DPerf 0.822 0.045 18.361 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .DeltaW1 0.000
## .DeltaW2 0.000
## .DeltaW3 0.000
## .DeltaW4 0.000
## .DeltaW5 0.000
## .DeltaP1 0.000
## .DeltaP2 0.000
## .DeltaP3 0.000
## .DeltaP4 0.000
## .DeltaP5 0.000
## .DeltaP6 0.000
## .DeltaP8 0.000
## .DP1 0.000
## .DP2 0.000
## .DP3 0.000
## .DP4 0.000
## .DP5 0.000
## .ERG1 0.000
## .ERG2 0.000
## .ERG3 0.000
## .ERG4 0.000
## .ERG5 0.000
## .ERG6 0.000
## .fear -3.313 0.477 -6.949 0.000
## .DWell 0.000
## .DPerf 0.000
## .DP 0.000
## .ERG 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|)
## DeltaW1|t1 -2.760 0.360 -7.667 0.000
## DeltaW1|t2 -1.952 0.293 -6.651 0.000
## DeltaW1|t3 -1.366 0.288 -4.746 0.000
## DeltaW1|t4 -0.764 0.284 -2.694 0.007
## DeltaW1|t5 0.030 0.283 0.105 0.917
## DeltaW1|t6 1.068 0.284 3.767 0.000
## DeltaW1|t7 1.811 0.287 6.310 0.000
## DeltaW1|t8 2.259 0.289 7.823 0.000
## DeltaW1|t9 2.751 0.308 8.924 0.000
## DeltaW1|t10 3.247 0.359 9.050 0.000
## DeltaW2|t1 -2.804 0.348 -8.055 0.000
## DeltaW2|t2 -2.146 0.306 -7.021 0.000
## DeltaW2|t3 -1.559 0.304 -5.122 0.000
## DeltaW2|t4 -1.011 0.301 -3.358 0.001
## DeltaW2|t5 -0.334 0.300 -1.116 0.265
## DeltaW2|t6 0.655 0.299 2.188 0.029
## DeltaW2|t7 1.315 0.301 4.362 0.000
## DeltaW2|t8 1.849 0.306 6.050 0.000
## DeltaW2|t9 2.418 0.325 7.447 0.000
## DeltaW2|t10 3.074 0.391 7.867 0.000
## DeltaW3|t1 -2.699 0.314 -8.586 0.000
## DeltaW3|t2 -2.180 0.299 -7.295 0.000
## DeltaW3|t3 -1.659 0.300 -5.539 0.000
## DeltaW3|t4 -1.020 0.296 -3.447 0.001
## DeltaW3|t5 -0.383 0.295 -1.299 0.194
## DeltaW3|t6 0.559 0.295 1.893 0.058
## DeltaW3|t7 1.256 0.298 4.218 0.000
## DeltaW3|t8 1.717 0.305 5.633 0.000
## DeltaW3|t9 2.249 0.314 7.160 0.000
## DeltaW3|t10 2.952 0.421 7.013 0.000
## DeltaW4|t1 -2.640 0.300 -8.794 0.000
## DeltaW4|t2 -1.972 0.285 -6.919 0.000
## DeltaW4|t3 -1.515 0.281 -5.384 0.000
## DeltaW4|t4 -0.985 0.279 -3.535 0.000
## DeltaW4|t5 -0.089 0.277 -0.323 0.747
## DeltaW4|t6 0.527 0.278 1.896 0.058
## DeltaW4|t7 1.080 0.279 3.875 0.000
## DeltaW4|t8 1.531 0.283 5.412 0.000
## DeltaW4|t9 2.167 0.311 6.973 0.000
## DeltaW5|t1 -2.206 0.323 -6.829 0.000
## DeltaW5|t2 -1.589 0.289 -5.493 0.000
## DeltaW5|t3 -0.959 0.289 -3.319 0.001
## DeltaW5|t4 -0.349 0.287 -1.219 0.223
## DeltaW5|t5 0.257 0.286 0.900 0.368
## DeltaW5|t6 1.293 0.288 4.498 0.000
## DeltaW5|t7 1.989 0.286 6.953 0.000
## DeltaW5|t8 2.516 0.290 8.687 0.000
## DeltaW5|t9 2.964 0.306 9.684 0.000
## DeltaW5|t10 3.415 0.354 9.657 0.000
## DeltaP1|t1 -2.825 0.349 -8.088 0.000
## DeltaP1|t2 -2.017 0.307 -6.569 0.000
## DeltaP1|t3 -1.196 0.304 -3.931 0.000
## DeltaP1|t4 -0.241 0.300 -0.803 0.422
## DeltaP1|t5 1.236 0.300 4.120 0.000
## DeltaP1|t6 2.303 0.312 7.391 0.000
## DeltaP1|t7 3.178 0.363 8.755 0.000
## DeltaP2|t1 -3.174 0.412 -7.698 0.000
## DeltaP2|t2 -2.868 0.356 -8.064 0.000
## DeltaP2|t3 -2.012 0.327 -6.157 0.000
## DeltaP2|t4 -1.135 0.319 -3.551 0.000
## DeltaP2|t5 0.370 0.319 1.160 0.246
## DeltaP2|t6 1.184 0.320 3.695 0.000
## DeltaP2|t7 2.073 0.327 6.349 0.000
## DeltaP2|t8 3.067 0.449 6.825 0.000
## DeltaP3|t1 -3.564 0.390 -9.146 0.000
## DeltaP3|t2 -2.859 0.344 -8.313 0.000
## DeltaP3|t3 -2.180 0.326 -6.686 0.000
## DeltaP3|t4 -1.346 0.319 -4.214 0.000
## DeltaP3|t5 -0.050 0.318 -0.158 0.874
## DeltaP3|t6 1.061 0.319 3.325 0.001
## DeltaP3|t7 1.985 0.338 5.871 0.000
## DeltaP3|t8 2.666 0.376 7.087 0.000
## DeltaP4|t1 -2.869 0.331 -8.662 0.000
## DeltaP4|t2 -2.364 0.307 -7.707 0.000
## DeltaP4|t3 -1.638 0.302 -5.424 0.000
## DeltaP4|t4 -0.778 0.301 -2.583 0.010
## DeltaP4|t5 0.375 0.301 1.247 0.212
## DeltaP4|t6 1.276 0.302 4.232 0.000
## DeltaP4|t7 2.328 0.306 7.600 0.000
## DeltaP4|t8 2.604 0.333 7.811 0.000
## DeltaP5|t1 -3.178 0.354 -8.983 0.000
## DeltaP5|t2 -2.573 0.304 -8.468 0.000
## DeltaP5|t3 -1.807 0.290 -6.231 0.000
## DeltaP5|t4 -0.954 0.286 -3.340 0.001
## DeltaP5|t5 0.401 0.285 1.406 0.160
## DeltaP5|t6 1.207 0.286 4.225 0.000
## DeltaP5|t7 2.003 0.290 6.903 0.000
## DeltaP5|t8 2.689 0.321 8.372 0.000
## DeltaP6|t1 -3.110 0.342 -9.095 0.000
## DeltaP6|t2 -2.423 0.321 -7.553 0.000
## DeltaP6|t3 -1.747 0.312 -5.608 0.000
## DeltaP6|t4 -0.904 0.310 -2.921 0.003
## DeltaP6|t5 0.270 0.309 0.875 0.382
## DeltaP6|t6 1.140 0.310 3.680 0.000
## DeltaP6|t7 2.159 0.325 6.634 0.000
## DeltaP6|t8 2.970 0.413 7.191 0.000
## DeltaP8|t1 -2.981 0.395 -7.542 0.000
## DeltaP8|t2 -2.699 0.358 -7.542 0.000
## DeltaP8|t3 -2.330 0.336 -6.930 0.000
## DeltaP8|t4 -1.813 0.334 -5.429 0.000
## DeltaP8|t5 -1.200 0.329 -3.649 0.000
## DeltaP8|t6 -0.563 0.328 -1.718 0.086
## DeltaP8|t7 0.975 0.329 2.962 0.003
## DeltaP8|t8 1.773 0.334 5.311 0.000
## DeltaP8|t9 2.298 0.347 6.622 0.000
## DeltaP8|t10 2.873 0.398 7.225 0.000
## DP1|t1 -2.019 0.329 -6.135 0.000
## DP1|t2 -1.288 0.324 -3.981 0.000
## DP1|t3 -0.751 0.322 -2.334 0.020
## DP1|t4 -0.039 0.321 -0.122 0.903
## DP2|t1 -0.622 0.296 -2.102 0.036
## DP2|t2 -0.084 0.295 -0.286 0.775
## DP2|t3 0.455 0.296 1.540 0.124
## DP2|t4 1.058 0.296 3.574 0.000
## DP3|t1 -1.213 0.293 -4.144 0.000
## DP3|t2 -0.694 0.291 -2.384 0.017
## DP3|t3 -0.110 0.291 -0.377 0.706
## DP3|t4 0.575 0.290 1.980 0.048
## DP4|t1 -0.928 0.342 -2.711 0.007
## DP4|t2 -0.360 0.323 -1.113 0.266
## DP4|t3 0.202 0.322 0.627 0.531
## DP4|t4 1.211 0.321 3.776 0.000
## DP5|t1 -2.328 0.324 -7.192 0.000
## DP5|t2 -1.804 0.324 -5.565 0.000
## DP5|t3 -1.333 0.323 -4.133 0.000
## DP5|t4 -0.664 0.322 -2.063 0.039
## ERG1|t1 -2.494 0.285 -8.743 0.000
## ERG1|t2 -1.844 0.281 -6.551 0.000
## ERG1|t3 -1.277 0.280 -4.563 0.000
## ERG1|t4 -0.609 0.280 -2.177 0.030
## ERG1|t5 0.123 0.280 0.438 0.661
## ERG2|t1 -3.638 0.324 -11.225 0.000
## ERG2|t2 -3.027 0.318 -9.529 0.000
## ERG2|t3 -2.537 0.316 -8.031 0.000
## ERG2|t4 -1.932 0.314 -6.155 0.000
## ERG2|t5 -1.100 0.312 -3.525 0.000
## ERG3|t1 -2.757 0.351 -7.853 0.000
## ERG3|t2 -2.184 0.328 -6.652 0.000
## ERG3|t3 -1.783 0.326 -5.473 0.000
## ERG3|t4 -1.182 0.323 -3.658 0.000
## ERG3|t5 -0.302 0.321 -0.940 0.347
## ERG4|t1 -2.563 0.299 -8.559 0.000
## ERG4|t2 -2.066 0.293 -7.046 0.000
## ERG4|t3 -1.507 0.295 -5.110 0.000
## ERG4|t4 -0.876 0.294 -2.979 0.003
## ERG4|t5 0.051 0.294 0.175 0.861
## ERG5|t1 -1.613 0.314 -5.137 0.000
## ERG5|t2 -0.995 0.313 -3.182 0.001
## ERG5|t3 -0.554 0.312 -1.778 0.075
## ERG5|t4 -0.006 0.311 -0.019 0.985
## ERG5|t5 0.670 0.311 2.157 0.031
## ERG6|t1 -1.992 0.288 -6.909 0.000
## ERG6|t2 -1.367 0.287 -4.758 0.000
## ERG6|t3 -0.798 0.287 -2.779 0.005
## ERG6|t4 -0.092 0.287 -0.320 0.749
## ERG6|t5 0.585 0.287 2.039 0.041
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .DeltaW1 0.267
## .DeltaW2 0.413
## .DeltaW3 0.332
## .DeltaW4 0.525
## .DeltaW5 0.470
## .DeltaP1 0.702
## .DeltaP2 0.528
## .DeltaP3 0.629
## .DeltaP4 0.548
## .DeltaP5 0.554
## .DeltaP6 0.504
## .DeltaP8 0.372
## .DP1 0.693
## .DP2 0.852
## .DP3 0.630
## .DP4 0.817
## .DP5 0.675
## .ERG1 0.516
## .ERG2 0.559
## .ERG3 0.699
## .ERG4 0.600
## .ERG5 0.469
## .ERG6 0.248
## .fear 2.674 0.124 21.537 0.000
## .DWell 0.498 0.019 25.583 0.000
## .DPerf 0.267 0.021 12.884 0.000
## .DP 0.307 0.035 8.819 0.000
## .ERG 0.484 0.024 19.745 0.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|)
## DeltaW1 1.000
## DeltaW2 1.000
## DeltaW3 1.000
## DeltaW4 1.000
## DeltaW5 1.000
## DeltaP1 1.000
## DeltaP2 1.000
## DeltaP3 1.000
## DeltaP4 1.000
## DeltaP5 1.000
## DeltaP6 1.000
## DeltaP8 1.000
## DP1 1.000
## DP2 1.000
## DP3 1.000
## DP4 1.000
## DP5 1.000
## ERG1 1.000
## ERG2 1.000
## ERG3 1.000
## ERG4 1.000
## ERG5 1.000
## ERG6 1.000To summarize, SRMR\(\lt 0.8\) and RMSEA\(= 0.06\), is generally considered a good fit given our sample size (Hu and Bentler 1999). TLI is above \(\gt 0.95\), while CFI\(>0.9\) (both ok considering the sample size).
Now one can conduct inferences on our SEM, which you can find in the manuscript.
devtools::session_info("lavaan")## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.0.0 (2020-04-24)
## os macOS Catalina 10.15.4
## system x86_64, darwin17.0
## ui X11
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz Europe/Stockholm
## date 2020-06-01
##
## ─ Packages ───────────────────────────────────────────────────────────────────
## package * version date lib source
## lavaan * 0.6-6 2020-05-13 [1] CRAN (R 4.0.0)
## MASS 7.3-51.6 2020-04-26 [2] CRAN (R 4.0.0)
## mnormt 1.5-7 2020-04-30 [1] CRAN (R 4.0.0)
## numDeriv 2016.8-1.1 2019-06-06 [1] CRAN (R 4.0.0)
## pbivnorm 0.6.0 2015-01-23 [1] CRAN (R 4.0.0)
##
## [1] /Users/torkarr/Library/R/4.0/library
## [2] /Library/Frameworks/R.framework/Versions/4.0/Resources/libraryHu, Li‐tze, and Peter M. Bentler. 1999. “Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria Versus New Alternatives.” Structural Equation Modeling: A Multidisciplinary Journal 6 (1): 1–55. https://doi.org/10.1080/10705519909540118.
https://www.martinmodrak.cz/2018/05/14/identifying-non-identifiability/↩︎
https://discourse.mc-stan.org/t/blog-post-identifying-non-identifiability/4201/3↩︎
https://paolotoffanin.wordpress.com/2018/05/19/beginning-with-sem-in-lavaan/↩︎
The NAs are for marker variables so nothing to worry about.↩︎
Detailed explanations of each variable can be found in the manuscript.↩︎