library(psych)
library(lavaan)
## This is lavaan 0.6-15
## lavaan is FREE software! Please report any bugs.
##
## Attaching package: 'lavaan'
## The following object is masked from 'package:psych':
##
## cor2cov
library(semTools)
##
## ###############################################################################
## This is semTools 0.5-6
## All users of R (or SEM) are invited to submit functions or ideas for functions.
## ###############################################################################
##
## Attaching package: 'semTools'
## The following objects are masked from 'package:psych':
##
## reliability, skew
library(semPlot)
library(naniar)
library(dplyr) #loading packages
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
PersonalIdentity<-read.csv("WLS_HW1_CFA_rev23.csv",header=T,sep=",") #reading in data file
PI1 <- dplyr::select(PersonalIdentity, idpub, sexrsp, byear, educ92, natfth, ge096fa, ge095ma, in501rer, in502rer, in503rer, in504rer, in505rer, in506rer, in507rer) #subsetting variables of interest
vis_miss(PI1) #viewing missingness. There does seem to be quite a bit of missingess; however, missing data will be excluded from analyses.
## Warning: `gather_()` was deprecated in tidyr 1.2.0.
## ℹ Please use `gather()` instead.
## ℹ The deprecated feature was likely used in the visdat package.
## Please report the issue at <]8;;https://github.com/ropensci/visdat/issueshttps://github.com/ropensci/visdat/issues]8;;>.
describe(PI1) #finding descriptives of variables of interest. Females make up about half of the sample. Participants' age is reaching emerging adulthood. Mean number of years of education based on highest degree earned was 13.61. Majority of participants' parental nationality were predominately white.Skewness and kurtosis do not seem to be an issue, they are all acceptable. Data seem to meet normality assumptions
## vars n mean sd median trimmed mad min max
## idpub 1 9688 916831.23 9803.71 916803.5 916798.82 12724.41 900021 933957
## sexrsp 2 9688 1.52 0.50 2.0 1.53 0.00 1 2
## byear 3 9688 38.84 0.51 39.0 38.90 0.00 37 40
## educ92 4 8452 13.61 2.26 12.0 13.21 0.00 12 21
## natfth 5 9410 11.61 6.35 14.0 11.58 1.48 1 41
## ge096fa 6 7200 11.50 6.33 14.0 11.50 1.48 1 42
## ge095ma 7 7012 11.85 7.15 14.0 11.51 1.48 1 47
## in501rer 8 6508 4.92 1.86 5.0 5.15 1.48 1 7
## in502rer 9 6628 4.69 2.09 5.0 4.86 2.97 1 7
## in503rer 10 6581 5.84 1.47 6.0 6.12 1.48 1 7
## in504rer 11 6574 3.83 1.73 4.0 3.83 1.48 1 7
## in505rer 12 6489 3.27 1.82 3.0 3.15 2.97 1 7
## in506rer 13 6569 3.17 1.81 3.0 3.04 1.48 1 7
## in507rer 14 6573 3.18 1.90 3.0 3.02 2.97 1 7
## range skew kurtosis se
## idpub 33936 0.02 -1.21 99.60
## sexrsp 1 -0.09 -1.99 0.01
## byear 3 -1.10 2.71 0.01
## educ92 9 1.14 0.04 0.02
## natfth 40 0.75 3.13 0.07
## ge096fa 41 0.72 3.13 0.07
## ge095ma 46 1.20 3.96 0.09
## in501rer 6 -0.82 -0.36 0.02
## in502rer 6 -0.50 -1.09 0.03
## in503rer 6 -1.55 2.04 0.02
## in504rer 6 -0.02 -0.87 0.02
## in505rer 6 0.33 -0.98 0.02
## in506rer 6 0.39 -0.93 0.02
## in507rer 6 0.43 -0.96 0.02
Sex <- factor(PI1$sexrsp, levels = 1:2, labels = c("Male", "Female")) #turning sex into a factor
summary(Sex) #getting summary/frequency of sex
## Male Female
## 4637 5051
var(PI1$sexrsp)
## [1] 0.2495692
var(PI1$byear)
## [1] 0.2566144
var(PI1$in501rer, na.rm=TRUE)
## [1] 3.463347
var(PI1$in502rer, na.rm=TRUE)
## [1] 4.349543
var(PI1$in503rer, na.rm=TRUE)
## [1] 2.14743
var(PI1$in504rer, na.rm=TRUE)
## [1] 2.989324
var(PI1$in505rer, na.rm=TRUE)
## [1] 3.323253
var(PI1$in506rer, na.rm=TRUE)
## [1] 3.280475
var(PI1$in507rer, na.rm=TRUE) #finding variances of participants' sex, birth year, and identity measures. All variances do not warrant concern.
## [1] 3.593664
cor_matrix <- cor(PI1[, c("sexrsp", "byear", "educ92", "ge096fa", "ge095ma", "in501rer", "in502rer", "in503rer", "in504rer", "in505rer", "in506rer", "in507rer")],use = "complete.obs")
print(cor_matrix) #correlation matrix. No identity item shared a coefficient large enough to warrant concern for multicollinearity. The relationships between demographic variables and identity variables are much weaker than the identity variables with themselves.
## sexrsp byear educ92 ge096fa ge095ma
## sexrsp 1.000000000 0.1138806444 -0.162533776 0.026662324 0.003370268
## byear 0.113880644 1.0000000000 0.128222962 -0.016097271 -0.004332427
## educ92 -0.162533776 0.1282229615 1.000000000 -0.050767992 -0.033842045
## ge096fa 0.026662324 -0.0160972708 -0.050767992 1.000000000 0.254314241
## ge095ma 0.003370268 -0.0043324272 -0.033842045 0.254314241 1.000000000
## in501rer -0.068227346 -0.0024026596 0.057349085 0.004723738 -0.009813353
## in502rer 0.190242593 -0.0026990695 -0.136521597 0.053316114 0.010900563
## in503rer 0.059791596 0.0002852176 -0.041904767 0.029809285 0.018775213
## in504rer 0.048198020 0.0072050635 0.001453911 0.008161050 -0.003042774
## in505rer -0.021504377 -0.0326697638 -0.031779412 0.012461162 -0.004688384
## in506rer -0.050525169 -0.0322035240 0.055836301 0.020349392 -0.011474062
## in507rer -0.017799725 -0.0521535454 -0.036304601 0.050904857 0.051532626
## in501rer in502rer in503rer in504rer in505rer
## sexrsp -0.068227346 0.19024259 0.0597915957 0.048198020 -0.021504377
## byear -0.002402660 -0.00269907 0.0002852176 0.007205063 -0.032669764
## educ92 0.057349085 -0.13652160 -0.0419047667 0.001453911 -0.031779412
## ge096fa 0.004723738 0.05331611 0.0298092850 0.008161050 0.012461162
## ge095ma -0.009813353 0.01090056 0.0187752133 -0.003042774 -0.004688384
## in501rer 1.000000000 0.26810466 0.3062585032 0.310688270 0.314206072
## in502rer 0.268104663 1.00000000 0.3944631997 0.405896025 0.314786385
## in503rer 0.306258503 0.39446320 1.0000000000 0.303159717 0.222182602
## in504rer 0.310688270 0.40589602 0.3031597167 1.000000000 0.644023379
## in505rer 0.314206072 0.31478638 0.2221826021 0.644023379 1.000000000
## in506rer 0.223421528 0.21119632 0.1504190754 0.334008047 0.435272824
## in507rer 0.255355382 0.27594593 0.1938785053 0.311975932 0.384454068
## in506rer in507rer
## sexrsp -0.05052517 -0.01779972
## byear -0.03220352 -0.05215355
## educ92 0.05583630 -0.03630460
## ge096fa 0.02034939 0.05090486
## ge095ma -0.01147406 0.05153263
## in501rer 0.22342153 0.25535538
## in502rer 0.21119632 0.27594593
## in503rer 0.15041908 0.19387851
## in504rer 0.33400805 0.31197593
## in505rer 0.43527282 0.38445407
## in506rer 1.00000000 0.49664345
## in507rer 0.49664345 1.00000000
cov_matrix <- cov(PI1[, c("sexrsp", "byear", "educ92", "ge096fa", "ge095ma","in501rer", "in502rer", "in503rer", "in504rer", "in505rer", "in506rer", "in507rer")],use = "complete.obs")
print(cov_matrix) #covariance matrix. Matrix appears normal, no causes of concern for identity items.
## sexrsp byear educ92 ge096fa ge095ma
## sexrsp 0.24910749 0.0276323242 -0.187901266 0.08318199 0.01197815
## byear 0.02763232 0.2363459807 0.144388500 -0.04891750 -0.01499814
## educ92 -0.18790127 0.1443885003 5.365193422 -0.73505631 -0.55818889
## ge096fa 0.08318199 -0.0489175041 -0.735056307 39.07291932 11.31984594
## ge095ma 0.01197815 -0.0149981361 -0.558188892 11.31984594 50.70652052
## in501rer -0.06271171 -0.0021511125 0.244633518 0.05437766 -0.12869038
## in502rer 0.19750059 -0.0027293262 -0.657750688 0.69320818 0.16145374
## in503rer 0.04326092 0.0002010077 -0.140707857 0.27011688 0.19381126
## in504rer 0.04125482 0.0060070883 0.005775405 0.08748550 -0.03715812
## in505rer -0.01949464 -0.0288479544 -0.133700635 0.14147881 -0.06063871
## in506rer -0.04532184 -0.0281373917 0.232442566 0.22861025 -0.14684374
## in507rer -0.01669194 -0.0476385041 -0.157999071 0.59785700 0.68946836
## in501rer in502rer in503rer in504rer in505rer
## sexrsp -0.062711710 0.197500594 0.0432609212 0.041254819 -0.01949464
## byear -0.002151113 -0.002729326 0.0002010077 0.006007088 -0.02884795
## educ92 0.244633518 -0.657750688 -0.1407078574 0.005775405 -0.13370063
## ge096fa 0.054377663 0.693208177 0.2701168768 0.087485500 0.14147881
## ge095ma -0.128690379 0.161453737 0.1938112643 -0.037158121 -0.06063871
## in501rer 3.391513443 1.026995164 0.8176118131 0.981236568 1.05100858
## in502rer 1.026995164 4.326478205 1.1894220460 1.447885284 1.18926357
## in503rer 0.817611813 1.189422046 2.1014761293 0.753677966 0.58501526
## in504rer 0.981236568 1.447885284 0.7536779665 2.941062081 2.00608184
## in505rer 1.051008580 1.189263573 0.5850152623 2.006081837 3.29905711
## in506rer 0.739482868 0.789514168 0.3918965786 1.029473928 1.42089765
## in507rer 0.883572020 1.078428678 0.5280706883 1.005248317 1.31201725
## in506rer in507rer
## sexrsp -0.04532184 -0.01669194
## byear -0.02813739 -0.04763850
## educ92 0.23244257 -0.15799907
## ge096fa 0.22861025 0.59785700
## ge095ma -0.14684374 0.68946836
## in501rer 0.73948287 0.88357202
## in502rer 0.78951417 1.07842868
## in503rer 0.39189658 0.52807069
## in504rer 1.02947393 1.00524832
## in505rer 1.42089765 1.31201725
## in506rer 3.23007535 1.67707006
## in507rer 1.67707006 3.53020834
PI1 <- mutate(PI1, Age = 103-(PI1$byear)) #turning birth year into age
psych::describe(PI1$Age) #getting summary of age. Participants' age is reaching emerging adulthood, this will be useful in highlighting in the intro/discussion sections.
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 9688 64.16 0.51 64 64.1 0 63 66 3 1.1 2.71 0.01
glimpse(PI1$ge096fa) #looking at fathers' nationality
## int [1:9688] NA 14 4 NA 2 14 14 NA 14 14 ...
PI1$ge096fa <- as.factor(PI1$ge096fa) #turning fathers' nationality into a factor
summary(PI1$ge096fa) #looking at summary/frequency of fathers' nationality. Predominately white, non-Hispanic Americans and consisted mainly of German, English, Irish, Scandinavian, Polish, and Czech ancestry.
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 633 108 52 463 549 166 128 182 6 82 81 231 4 3417 474 202
## 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33
## 43 21 47 4 20 10 91 3 8 21 55 2 1 1 1 1
## 34 35 36 37 38 39 40 41 42 NA's
## 1 5 16 11 20 9 16 11 4 2488
glimpse(PI1$ge095ma) #looking at mothers' nationality
## int [1:9688] NA 4 1 NA 41 14 4 NA 14 14 ...
PI1$ge095ma <- as.factor(PI1$ge095ma) #turning mothers' nationality into a factor
summary(PI1$ge095ma) #looking at summary/frequency of mothers' nationality. Predominately white, non-Hispanic Americans and consisted mainly of German, English, Irish, Scandinavian, Polish, and Czech ancestry
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 622 91 38 495 554 151 104 168 28 75 81 218 14 3106 527 192
## 17 18 19 20 22 23 24 25 26 27 28 30 32 33 35 36
## 48 31 59 3 50 7 80 5 8 32 36 1 1 1 2 16
## 37 38 39 40 41 42 43 44 46 47 NA's
## 8 58 26 27 32 11 3 1 1 1 2676
null_model <- "
in501rer ~~ in501rer
in502rer ~~ in502rer
in503rer ~~ in503rer
in504rer ~~ in504rer
in505rer ~~ in505rer
in506rer ~~ in506rer
in507rer ~~ in507rer"
null_model_fit <- cfa(null_model, data = PI1)
summary(null_model_fit, standard = TRUE, fit.measures = TRUE)
## lavaan 0.6.15 ended normally after 9 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Used Total
## Number of observations 6312 9688
##
## Model Test User Model:
##
## Test statistic 11105.204
## Degrees of freedom 21
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 11105.204
## Degrees of freedom 21
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.000
## Tucker-Lewis Index (TLI) -0.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -88628.385
## Loglikelihood unrestricted model (H1) -83075.783
##
## Akaike (AIC) 177270.770
## Bayesian (BIC) 177318.022
## Sample-size adjusted Bayesian (SABIC) 177295.778
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.289
## 90 Percent confidence interval - lower 0.285
## 90 Percent confidence interval - upper 0.294
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.300
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## in501rer 3.451 0.061 56.178 0.000 3.451 1.000
## in502rer 4.361 0.078 56.178 0.000 4.361 1.000
## in503rer 2.154 0.038 56.178 0.000 2.154 1.000
## in504rer 2.978 0.053 56.178 0.000 2.978 1.000
## in505rer 3.310 0.059 56.178 0.000 3.310 1.000
## in506rer 3.251 0.058 56.178 0.000 3.251 1.000
## in507rer 3.565 0.063 56.178 0.000 3.565 1.000
semPaths(null_model_fit)
anova(null_model_fit) #null/baseline model. Null model had a high χ2 value, thus was uninterpretable. In addition, the corresponding p-value was highly significant. All other fit indices (AIC, BIC, CFI, TLI, RMSEA) were not acceptable. This model is the worst fitting model.
## Chi-Squared Test Statistic (unscaled)
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## Saturated 0 0
## Model 21 177271 177318 11105 11105 21 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
inspect(cfa(null_model_fit, PI1), what = "std") #null model factor patterns and correlations
## $lambda
##
## in501rer
## in502rer
## in503rer
## in504rer
## in505rer
## in506rer
## in507rer
##
## $theta
## in501r in502r in503r in504r in505r in506r in507r
## in501rer 1
## in502rer 0 1
## in503rer 0 0 1
## in504rer 0 0 0 1
## in505rer 0 0 0 0 1
## in506rer 0 0 0 0 0 1
## in507rer 0 0 0 0 0 0 1
##
## $psi
## <0 x 0 matrix>
model_1f <- "
F1 = ~ in501rer + in502rer + in503rer + in504rer + in505rer + in506rer + in507rer"
model_1f_fit <- cfa(model_1f, data = PI1)
summary(model_1f_fit, standard = TRUE, fit.measures = TRUE)
## lavaan 0.6.15 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 6312 9688
##
## Model Test User Model:
##
## Test statistic 1858.735
## Degrees of freedom 14
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 11105.204
## Degrees of freedom 21
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.834
## Tucker-Lewis Index (TLI) 0.750
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -84005.150
## Loglikelihood unrestricted model (H1) -83075.783
##
## Akaike (AIC) 168038.301
## Bayesian (BIC) 168132.804
## Sample-size adjusted Bayesian (SABIC) 168088.315
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.144
## 90 Percent confidence interval - lower 0.139
## 90 Percent confidence interval - upper 0.150
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.072
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 =~
## in501rer 1.000 0.840 0.452
## in502rer 1.241 0.046 26.990 0.000 1.042 0.499
## in503rer 0.689 0.030 23.317 0.000 0.579 0.394
## in504rer 1.563 0.048 32.499 0.000 1.312 0.760
## in505rer 1.693 0.052 32.716 0.000 1.421 0.781
## in506rer 1.170 0.041 28.303 0.000 0.982 0.545
## in507rer 1.198 0.043 27.973 0.000 1.006 0.533
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .in501rer 2.746 0.052 52.954 0.000 2.746 0.796
## .in502rer 3.276 0.063 51.999 0.000 3.276 0.751
## .in503rer 1.820 0.034 53.875 0.000 1.820 0.845
## .in504rer 1.256 0.033 38.064 0.000 1.256 0.422
## .in505rer 1.291 0.036 35.663 0.000 1.291 0.390
## .in506rer 2.286 0.045 50.833 0.000 2.286 0.703
## .in507rer 2.554 0.050 51.167 0.000 2.554 0.716
## F1 0.705 0.041 17.178 0.000 1.000 1.000
semPaths(model_1f_fit)
anova(model_1f_fit) #one-factor model. One-factor model had a high χ2 value, thus was uninterpretable. In addition, the corresponding p-value was highly significant. All other fit indices (AIC, BIC, CFI, TLI, RMSEA) were not acceptable. This model did not fit the data well.
## Chi-Squared Test Statistic (unscaled)
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## Saturated 0 0.0
## Model 14 168038 168133 1858.7 1858.7 14 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
inspect(cfa(model_1f_fit, PI1), what = "std") #one-factor model factor patterns and correlations
## $lambda
## F1
## in501rer 0.452
## in502rer 0.499
## in503rer 0.394
## in504rer 0.760
## in505rer 0.781
## in506rer 0.545
## in507rer 0.533
##
## $theta
## in501r in502r in503r in504r in505r in506r in507r
## in501rer 0.796
## in502rer 0.000 0.751
## in503rer 0.000 0.000 0.845
## in504rer 0.000 0.000 0.000 0.422
## in505rer 0.000 0.000 0.000 0.000 0.390
## in506rer 0.000 0.000 0.000 0.000 0.000 0.703
## in507rer 0.000 0.000 0.000 0.000 0.000 0.000 0.716
##
## $psi
## F1
## F1 1
model_2f <- "
F1 = ~ in501rer + in502rer + in503rer
F2 = ~ in504rer + in505rer + in506rer + in507rer"
model_2f_fit <- cfa(model_2f, data = PI1)
summary(model_2f_fit, standard = TRUE, fit.measures = TRUE)
## lavaan 0.6.15 ended normally after 37 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 15
##
## Used Total
## Number of observations 6312 9688
##
## Model Test User Model:
##
## Test statistic 1283.951
## Degrees of freedom 13
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 11105.204
## Degrees of freedom 21
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.885
## Tucker-Lewis Index (TLI) 0.815
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -83717.758
## Loglikelihood unrestricted model (H1) -83075.783
##
## Akaike (AIC) 167465.517
## Bayesian (BIC) 167566.770
## Sample-size adjusted Bayesian (SABIC) 167519.104
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.124
## 90 Percent confidence interval - lower 0.119
## 90 Percent confidence interval - upper 0.130
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.058
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 =~
## in501rer 1.000 0.984 0.530
## in502rer 1.352 0.047 28.747 0.000 1.330 0.637
## in503rer 0.839 0.030 27.522 0.000 0.825 0.562
## F2 =~
## in504rer 1.000 1.315 0.762
## in505rer 1.122 0.021 52.958 0.000 1.475 0.811
## in506rer 0.754 0.019 39.452 0.000 0.991 0.550
## in507rer 0.755 0.020 37.750 0.000 0.992 0.526
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 ~~
## F2 0.896 0.035 25.726 0.000 0.693 0.693
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .in501rer 2.484 0.054 45.658 0.000 2.484 0.720
## .in502rer 2.594 0.069 37.437 0.000 2.594 0.595
## .in503rer 1.474 0.034 43.616 0.000 1.474 0.684
## .in504rer 1.249 0.034 36.875 0.000 1.249 0.419
## .in505rer 1.134 0.037 30.436 0.000 1.134 0.342
## .in506rer 2.269 0.045 50.640 0.000 2.269 0.698
## .in507rer 2.580 0.050 51.314 0.000 2.580 0.724
## F1 0.968 0.053 18.210 0.000 1.000 1.000
## F2 1.729 0.054 31.734 0.000 1.000 1.000
semPaths(model_2f_fit)
anova(model_2f_fit) #two-factor model. Two-factor model had a high χ2 value, thus was uninterpretable. In addition, the corresponding p-value was highly significant. All other fit indices (AIC, BIC, CFI, TLI, RMSEA) were not acceptable. This model did not fit the data well.
## Chi-Squared Test Statistic (unscaled)
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## Saturated 0 0
## Model 13 167466 167567 1284 1284 13 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
inspect(cfa(model_2f_fit, PI1), what = "std") #two-factor model factor patterns and correlations.Based on factor pattern, factor structure, and factor correlations, factor one and factor two had a moderate, positive association with one another, r = .69. In addition, volunteer identity and org/group identity contributed the most to factor two. Finally, the variances for volunteer identity and org/group identity were explained the most by the two factors.
## $lambda
## F1 F2
## in501rer 0.530 0.000
## in502rer 0.637 0.000
## in503rer 0.562 0.000
## in504rer 0.000 0.762
## in505rer 0.000 0.811
## in506rer 0.000 0.550
## in507rer 0.000 0.526
##
## $theta
## in501r in502r in503r in504r in505r in506r in507r
## in501rer 0.720
## in502rer 0.000 0.595
## in503rer 0.000 0.000 0.684
## in504rer 0.000 0.000 0.000 0.419
## in505rer 0.000 0.000 0.000 0.000 0.342
## in506rer 0.000 0.000 0.000 0.000 0.000 0.698
## in507rer 0.000 0.000 0.000 0.000 0.000 0.000 0.724
##
## $psi
## F1 F2
## F1 1.000
## F2 0.693 1.000
Model3_2F_UNCOR<-
'FamWorkRelEth = ~ in501rer + in502rer + in503rer + in507rer
Altru = ~ in504rer + in505rer + in506rer
Altru ~~ 0*FamWorkRelEth
' #alternative two-factor model
Model3_2F_UNCOR_fit <- cfa(Model3_2F_UNCOR, data = PI1)
summary(Model3_2F_UNCOR_fit, standard = TRUE, fit.measures = TRUE)
## lavaan 0.6.15 ended normally after 42 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 6312 9688
##
## Model Test User Model:
##
## Test statistic 3540.379
## Degrees of freedom 14
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 11105.204
## Degrees of freedom 21
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.682
## Tucker-Lewis Index (TLI) 0.523
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -84845.972
## Loglikelihood unrestricted model (H1) -83075.783
##
## Akaike (AIC) 169719.945
## Bayesian (BIC) 169814.448
## Sample-size adjusted Bayesian (SABIC) 169769.959
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.200
## 90 Percent confidence interval - lower 0.194
## 90 Percent confidence interval - upper 0.205
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.212
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FamWorkRelEth =~
## in501rer 1.000 0.936 0.504
## in502rer 1.399 0.056 25.151 0.000 1.309 0.627
## in503rer 0.948 0.038 25.143 0.000 0.887 0.604
## in507rer 0.855 0.040 21.560 0.000 0.800 0.424
## Altru =~
## in504rer 1.000 1.213 0.703
## in505rer 1.385 0.039 35.257 0.000 1.681 0.924
## in506rer 0.721 0.020 35.499 0.000 0.874 0.485
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FamWorkRelEth ~~
## Altru 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .in501rer 2.576 0.057 44.887 0.000 2.576 0.746
## .in502rer 2.648 0.078 34.156 0.000 2.648 0.607
## .in503rer 1.367 0.038 36.439 0.000 1.367 0.635
## .in507rer 2.925 0.060 49.057 0.000 2.925 0.821
## .in504rer 1.505 0.046 32.755 0.000 1.505 0.506
## .in505rer 0.486 0.072 6.734 0.000 0.486 0.147
## .in506rer 2.486 0.048 51.455 0.000 2.486 0.765
## FamWorkRelEth 0.876 0.054 16.368 0.000 1.000 1.000
## Altru 1.472 0.059 24.939 0.000 1.000 1.000
semPaths(Model3_2F_UNCOR_fit)
anova(Model3_2F_UNCOR_fit) #fitting model, plotting. Alternative two-factor model (ethnicity/nationality moved to factor 1 and uncorrelated factor one and two) had a high χ2 value, thus was uninterpretable. In addition, the corresponding p-value was highly significant. All other fit indices (AIC, BIC, CFI, TLI, RMSEA) were not acceptable. This model did not fit the data well.
## Chi-Squared Test Statistic (unscaled)
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## Saturated 0 0.0
## Model 14 169720 169814 3540.4 3540.4 14 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#The full two-factor model had lower AIC and BIC values than any of the other tested models. In addition, the two-factor model had CFI and TLI values in unacceptable ranges (.885 and .815, respectively). Finally, the two-factor model had an RMSEA at an unacceptable level (.124, CI [.119, .130]). The two-factor model fitted the data the best in comparison to the other tested models; however, this model was still not a good fit to the data.
inspect(cfa(Model3_2F_UNCOR_fit , PI1), what = "std") #alternative two-factor model factor patterns and correlations
## $lambda
## FmWrRE Altru
## in501rer 0.504 0.000
## in502rer 0.627 0.000
## in503rer 0.604 0.000
## in507rer 0.424 0.000
## in504rer 0.000 0.703
## in505rer 0.000 0.924
## in506rer 0.000 0.485
##
## $theta
## in501r in502r in503r in507r in504r in505r in506r
## in501rer 0.746
## in502rer 0.000 0.607
## in503rer 0.000 0.000 0.635
## in507rer 0.000 0.000 0.000 0.821
## in504rer 0.000 0.000 0.000 0.000 0.506
## in505rer 0.000 0.000 0.000 0.000 0.000 0.147
## in506rer 0.000 0.000 0.000 0.000 0.000 0.000 0.765
##
## $psi
## FmWrRE Altru
## FamWorkRelEth 1
## Altru 0 1
sessionInfo()
## R version 4.2.2 (2022-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Ventura 13.2.1
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] dplyr_1.0.10 naniar_0.6.1 semPlot_1.1.6 semTools_0.5-6 lavaan_0.6-15
## [6] psych_2.2.5
##
## loaded via a namespace (and not attached):
## [1] nlme_3.1-160 RColorBrewer_1.1-3 mi_1.1
## [4] tools_4.2.2 backports_1.4.1 bslib_0.4.0
## [7] utf8_1.2.2 R6_2.5.1 rpart_4.1.19
## [10] Hmisc_4.7-1 DBI_1.1.3 colorspace_2.0-3
## [13] nnet_7.3-18 withr_2.5.0 tidyselect_1.1.2
## [16] gridExtra_2.3 mnormt_2.1.0 compiler_4.2.2
## [19] fdrtool_1.2.17 qgraph_1.9.4 cli_3.4.0
## [22] htmlTable_2.4.1 labeling_0.4.2 sass_0.4.2
## [25] scales_1.2.1 checkmate_2.1.0 quadprog_1.5-8
## [28] pbapply_1.7-0 sem_3.1-15 stringr_1.4.1
## [31] digest_0.6.29 pbivnorm_0.6.0 foreign_0.8-83
## [34] minqa_1.2.5 rmarkdown_2.16 base64enc_0.1-3
## [37] jpeg_0.1-9 pkgconfig_2.0.3 htmltools_0.5.5
## [40] lme4_1.1-30 lisrelToR_0.1.5 highr_0.9
## [43] fastmap_1.1.0 htmlwidgets_1.6.2 rlang_1.0.6
## [46] rstudioapi_0.14 farver_2.1.1 jquerylib_0.1.4
## [49] generics_0.1.3 jsonlite_1.8.0 gtools_3.9.4
## [52] zip_2.2.2 magrittr_2.0.3 OpenMx_2.21.8
## [55] Formula_1.2-4 interp_1.1-3 Matrix_1.5-1
## [58] Rcpp_1.0.9 munsell_0.5.0 fansi_1.0.3
## [61] abind_1.4-5 rockchalk_1.8.157 visdat_0.5.3
## [64] lifecycle_1.0.3 stringi_1.7.8 yaml_2.3.5
## [67] carData_3.0-5 MASS_7.3-58.1 plyr_1.8.7
## [70] grid_4.2.2 parallel_4.2.2 deldir_1.0-6
## [73] lattice_0.20-45 kutils_1.70 splines_4.2.2
## [76] knitr_1.40 pillar_1.8.1 igraph_1.4.2
## [79] boot_1.3-28 corpcor_1.6.10 reshape2_1.4.4
## [82] stats4_4.2.2 XML_3.99-0.14 glue_1.6.2
## [85] evaluate_0.16 latticeExtra_0.6-30 RcppParallel_5.1.7
## [88] data.table_1.14.2 png_0.1-7 vctrs_0.5.1
## [91] nloptr_2.0.3 tidyr_1.2.1 gtable_0.3.1
## [94] purrr_0.3.4 assertthat_0.2.1 cachem_1.0.6
## [97] ggplot2_3.4.0 xfun_0.33 openxlsx_4.2.5.1
## [100] xtable_1.8-4 coda_0.19-4 glasso_1.11
## [103] survival_3.4-0 tibble_3.1.8 arm_1.13-1
## [106] cluster_2.1.4 ellipsis_0.3.2
citation("lavaan")
##
## To cite lavaan in publications use:
##
## Yves Rosseel (2012). lavaan: An R Package for Structural Equation
## Modeling. Journal of Statistical Software, 48(2), 1-36.
## https://doi.org/10.18637/jss.v048.i02
##
## A BibTeX entry for LaTeX users is
##
## @Article{,
## title = {{lavaan}: An {R} Package for Structural Equation Modeling},
## author = {Yves Rosseel},
## journal = {Journal of Statistical Software},
## year = {2012},
## volume = {48},
## number = {2},
## pages = {1--36},
## doi = {10.18637/jss.v048.i02},
## }
citation("semTools")
##
## The maintainer and *primary* contributors to this package are listed as
## authors, but this package is a collaborative work. The maintainer(s)
## cannot take credit for others' contributions. Whenever possible, please
## cite the paper(s) associated with the development of a particular
## function (e.g., permuteMeasEq or parcelAllocation) or tutorials about
## how to use them (e.g., probe2WayMC and related functions), which are
## listed in the References section of its associated help page.
## Otherwise, please use the following citation for the package as a
## whole:
##
## Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel,
## Y. (2022). semTools: Useful tools for structural equation modeling. R
## package version 0.5-6. Retrieved from
## https://CRAN.R-project.org/package=semTools
##
## A BibTeX entry for LaTeX users is
##
## @Manual{,
## title = {\texttt{semTools}: {U}seful tools for structural equation modeling},
## author = {Terrence D. Jorgensen and Sunthud Pornprasertmanit and Alexander M. Schoemann and Yves Rosseel},
## year = {2022},
## note = {R package version 0.5-6},
## url = {https://CRAN.R-project.org/package=semTools},
## }
citation("semPlot")
##
## To cite package 'semPlot' in publications use:
##
## Epskamp S (2022). _semPlot: Path Diagrams and Visual Analysis of
## Various SEM Packages' Output_. R package version 1.1.6,
## <https://CRAN.R-project.org/package=semPlot>.
##
## A BibTeX entry for LaTeX users is
##
## @Manual{,
## title = {semPlot: Path Diagrams and Visual Analysis of Various SEM Packages'
## Output},
## author = {Sacha Epskamp},
## year = {2022},
## note = {R package version 1.1.6},
## url = {https://CRAN.R-project.org/package=semPlot},
## }
citation("psych")
##
## To cite the psych package in publications use:
##
## Revelle, W. (2022) psych: Procedures for Personality and
## Psychological Research, Northwestern University, Evanston, Illinois,
## USA, https://CRAN.R-project.org/package=psych Version = 2.2.5.
##
## A BibTeX entry for LaTeX users is
##
## @Manual{,
## title = {psych: Procedures for Psychological, Psychometric, and Personality Research},
## author = {William Revelle},
## organization = { Northwestern University},
## address = { Evanston, Illinois},
## year = {2022},
## note = {R package version 2.2.5},
## url = {https://CRAN.R-project.org/package=psych},
## }
citation("naniar")
##
## To cite package 'naniar' in publications use:
##
## Tierney N, Cook D, McBain M, Fay C (2021). _naniar: Data Structures,
## Summaries, and Visualisations for Missing Data_. R package version
## 0.6.1, <https://CRAN.R-project.org/package=naniar>.
##
## A BibTeX entry for LaTeX users is
##
## @Manual{,
## title = {naniar: Data Structures, Summaries, and Visualisations for Missing Data},
## author = {Nicholas Tierney and Di Cook and Miles McBain and Colin Fay},
## year = {2021},
## note = {R package version 0.6.1},
## url = {https://CRAN.R-project.org/package=naniar},
## }
citation("dplyr") #getting package citations
##
## To cite package 'dplyr' in publications use:
##
## Wickham H, François R, Henry L, Müller K (2022). _dplyr: A Grammar of
## Data Manipulation_. R package version 1.0.10,
## <https://CRAN.R-project.org/package=dplyr>.
##
## A BibTeX entry for LaTeX users is
##
## @Manual{,
## title = {dplyr: A Grammar of Data Manipulation},
## author = {Hadley Wickham and Romain François and Lionel Henry and Kirill Müller},
## year = {2022},
## note = {R package version 1.0.10},
## url = {https://CRAN.R-project.org/package=dplyr},
## }