687 HW3
2023-11-20
load("/Users/zhoudongqiang/Desktop/2023 fall/687/687 homework/HW3/ess_belgium.rdata")1. Provide a brief description of the variables of interest using tables or graphs. Are there any missing data? Justify the way that you handle the missing values.
#select the data we are going to use.
data<-ess_belgium[,c("trstprl","trstlgl","trstplt","trstprt","imsmetn","imdfetn","impcntr","stfgov")]
for (i in 1:ncol(data)){ as.factor(data[,i])}“88” represents missing data for “trstprl”,“trstlgl”,“trstplt”, “trstprt”, and “stfgov”.
# For trust variables and government satisfaction
trust_value = c(rep(c("0","1", "2","3","4","5",
"6","7","8","9","10","88"), each = 5))
trust_vars <- c(rep(c("trstprl", "trstlgl", "trstplt", "trstprt", "stfgov")
, times = 12))
frequency = data[,c(1,2,3,4,8)]%>% # the frequecy of each category
apply(MARGIN = 2, FUN = table) %>%
apply(MARGIN = 2, FUN = unname)
frequency = c(frequency[,1],frequency[,2],frequency[,3],frequency[,4],frequency[,5])
trust_freq = data.frame(trust_value,trust_vars,frequency)
# Plotting trust variables frequency using ggplot2
ggplot(trust_freq, aes(x = trust_vars, y = frequency, fill = trust_value ,label = frequency)) +
geom_bar(stat = "identity") +
labs(fill = "Value")
“8” represents missing data for “imsmetn”,“imdfetn”, and “impcntr”.
# For immigratrion variables
immigration_value <- c(rep(c("1", "2","3","4", "8"), each = 3))
immigration_vars <- c(rep(c("imsmetn", "imdfetn", "impcntr"),times=5))
frequency = data[,c(5,6,7)]%>%
apply(MARGIN = 2, FUN = table) %>%
apply(MARGIN = 2, FUN = unname)
frequency = c(frequency[,1],frequency[,2],frequency[,3])
immigration_freq = data.frame(immigration_value,immigration_vars,frequency)
# Plotting immigration variables frequency using ggplot2
ggplot(immigration_freq, aes(x = immigration_vars, y = frequency,
fill = immigration_value,label = frequency)) +
geom_bar(stat = "identity") +
labs(fill = "Value")
Drop missing variables
rows_with_88 <- apply(data[, 1:4], 1, function(x) any(x == "88"))
rows_with_8 <- apply(data[, 5:7], 1, function(x) any(x == "8"))
# Combine the logical indices
rows_to_remove <- rows_with_88 | rows_with_8
# Subset the data to exclude these rows
data <- data[!rows_to_remove, ]
#Now there is 1657 non-null variables2.Create a dichotomous variable to indicate satisfaction with the national government: STF_IND = 0 if STFGOV<=5, and STF_IND = 1 otherwise.
data$STF_IND <- 1
data$STF_IND[data$stfgov<=5]<-0
table(data$STF_IND)##
## 0 1
## 1273 3843. Perform a multiple group analysis to examine invariance in the way that a latent construct of trust in leadership is measured between individuals who are satisfied with the government and those who are not. What is your conclusion?
trust_model <- ' trstlead =~ trstplt + trstprt + trstprl+ trstlgl '# Fit the configural invariance model (no constraints between groups)
fit_configural <- cfa(trust_model, group = "STF_IND", data = data)
# Check the fit
summary(fit_configural)## lavaan 0.6.16 ended normally after 54 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Number of observations per group:
## 1 384
## 0 1273
##
## Model Test User Model:
##
## Test statistic 131.603
## Degrees of freedom 4
## P-value (Chi-square) 0.000
## Test statistic for each group:
## 1 56.247
## 0 75.356
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## trstlead =~
## trstplt 1.000
## trstprt 0.935 0.053 17.724 0.000
## trstprl 0.527 0.048 11.037 0.000
## trstlgl 0.457 0.053 8.617 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .trstplt 5.086 0.105 48.610 0.000
## .trstprt 5.008 0.104 48.060 0.000
## .trstprl 5.880 0.094 62.662 0.000
## .trstlgl 5.914 0.101 58.517 0.000
## trstlead 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .trstplt 0.597 0.169 3.541 0.000
## .trstprt 1.016 0.161 6.319 0.000
## .trstprl 2.378 0.180 13.210 0.000
## .trstlgl 3.170 0.235 13.505 0.000
## trstlead 3.606 0.342 10.553 0.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## trstlead =~
## trstplt 1.000
## trstprt 0.995 0.023 43.735 0.000
## trstprl 0.824 0.027 30.976 0.000
## trstlgl 0.741 0.031 23.912 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .trstplt 3.499 0.058 60.067 0.000
## .trstprt 3.521 0.058 60.349 0.000
## .trstprl 4.016 0.061 65.899 0.000
## .trstlgl 4.623 0.065 70.617 0.000
## trstlead 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .trstplt 0.718 0.062 11.651 0.000
## .trstprt 0.764 0.062 12.304 0.000
## .trstprl 2.280 0.100 22.745 0.000
## .trstlgl 3.480 0.145 23.940 0.000
## trstlead 3.601 0.177 20.294 0.000# Fit the metric invariance model (constrain factor loadings)
fit_metric <- cfa(trust_model,
group.equal = c("loadings"),
group = "STF_IND", data = data)
summary(fit_metric)## lavaan 0.6.16 ended normally after 48 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
## Number of equality constraints 3
##
## Number of observations per group:
## 1 384
## 0 1273
##
## Model Test User Model:
##
## Test statistic 172.295
## Degrees of freedom 7
## P-value (Chi-square) 0.000
## Test statistic for each group:
## 1 89.401
## 0 82.894
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## trstlead =~
## trstplt 1.000
## trstprt (.p2.) 0.987 0.021 47.239 0.000
## trstprl (.p3.) 0.767 0.024 32.598 0.000
## trstlgl (.p4.) 0.682 0.027 25.198 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .trstplt 5.086 0.101 50.414 0.000
## .trstprt 5.008 0.102 49.043 0.000
## .trstprl 5.880 0.104 56.697 0.000
## .trstlgl 5.914 0.109 54.456 0.000
## trstlead 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .trstplt 0.835 0.114 7.299 0.000
## .trstprt 1.007 0.120 8.367 0.000
## .trstprl 2.324 0.185 12.578 0.000
## .trstlgl 3.098 0.236 13.105 0.000
## trstlead 3.073 0.260 11.839 0.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## trstlead =~
## trstplt 1.000
## trstprt (.p2.) 0.987 0.021 47.239 0.000
## trstprl (.p3.) 0.767 0.024 32.598 0.000
## trstlgl (.p4.) 0.682 0.027 25.198 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .trstplt 3.499 0.059 59.561 0.000
## .trstprt 3.521 0.059 60.088 0.000
## .trstprl 4.016 0.059 67.533 0.000
## .trstlgl 4.623 0.064 72.004 0.000
## trstlead 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .trstplt 0.691 0.063 10.974 0.000
## .trstprt 0.761 0.063 12.066 0.000
## .trstprl 2.325 0.100 23.142 0.000
## .trstlgl 3.524 0.146 24.158 0.000
## trstlead 3.702 0.178 20.761 0.000#configural invariance model: Test statistic: 131.603 Degrees of freedom: 4
#metric invariance model: Test statistic: 172.295 Degrees of freedom: 7
p_value<- pchisq(172.295-131.603,7-3 , lower.tail = FALSE)
p_value## [1] 3.11287e-08The p_value is 3.11287e-08 which is much smaller than 0.001. It suggest that in terms of model fitting, there is a significant difference between the constrained and unconstrained models.The constrained model fits much worse than the unconstrained model.Thus, the two groups of government satisfaction appear to measure different constructs.
4. Divide the individuals into three groups using a latent class analysis (LCA) based on the three measures of attitudes toward immigrants. What are your qualitative descriptions of each of the three classes?
# Prepare Data:
data$imsmetn <- factor(data$imsmetn)
data$imdfetn <- factor(data$imdfetn)
data$impcntr <- factor(data$impcntr)lca_model <- poLCA(cbind(imsmetn, imdfetn, impcntr) ~ 1,
data = data,
nclass = 3,
maxiter = 50000,
nrep = 10)## Model 1: llik = -4723.374 ... best llik = -4723.374
## Model 2: llik = -4859.954 ... best llik = -4723.374
## Model 3: llik = -4723.374 ... best llik = -4723.374
## Model 4: llik = -4723.374 ... best llik = -4723.374
## Model 5: llik = -4723.374 ... best llik = -4723.374
## Model 6: llik = -4723.374 ... best llik = -4723.374
## Model 7: llik = -4749.13 ... best llik = -4723.374
## Model 8: llik = -4749.13 ... best llik = -4723.374
## Model 9: llik = -4749.13 ... best llik = -4723.374
## Model 10: llik = -4778.172 ... best llik = -4723.374
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $imsmetn
## 1 2 3 4
## class 1: 0.9848 0.0152 0.0000 0.0000
## class 2: 0.1247 0.8577 0.0176 0.0000
## class 3: 0.0373 0.2987 0.4701 0.1939
##
## $imdfetn
## 1 2 3 4
## class 1: 0.9635 0.0365 0.0000 0.0000
## class 2: 0.0133 0.9276 0.0579 0.0011
## class 3: 0.0013 0.0239 0.6028 0.3719
##
## $impcntr
## 1 2 3 4
## class 1: 0.7929 0.1664 0.0337 0.0070
## class 2: 0.0322 0.8246 0.1296 0.0136
## class 3: 0.0034 0.1117 0.5659 0.3190
##
## Estimated class population shares
## 0.0882 0.4605 0.4513
##
## Predicted class memberships (by modal posterior prob.)
## 0.0899 0.4635 0.4466
##
## =========================================================
## Fit for 3 latent classes:
## =========================================================
## number of observations: 1657
## number of estimated parameters: 29
## residual degrees of freedom: 34
## maximum log-likelihood: -4723.374
##
## AIC(3): 9504.748
## BIC(3): 9661.718
## G^2(3): 719.3494 (Likelihood ratio/deviance statistic)
## X^2(3): 944.0326 (Chi-square goodness of fit)
## start<- Sys.time()
end <- Sys.time()
time_spend<- round (start-end,2)
lca_model## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $imsmetn
## 1 2 3 4
## class 1: 0.9848 0.0152 0.0000 0.0000
## class 2: 0.1247 0.8577 0.0176 0.0000
## class 3: 0.0373 0.2987 0.4701 0.1939
##
## $imdfetn
## 1 2 3 4
## class 1: 0.9635 0.0365 0.0000 0.0000
## class 2: 0.0133 0.9276 0.0579 0.0011
## class 3: 0.0013 0.0239 0.6028 0.3719
##
## $impcntr
## 1 2 3 4
## class 1: 0.7929 0.1664 0.0337 0.0070
## class 2: 0.0322 0.8246 0.1296 0.0136
## class 3: 0.0034 0.1117 0.5659 0.3190
##
## Estimated class population shares
## 0.0882 0.4605 0.4513
##
## Predicted class memberships (by modal posterior prob.)
## 0.0899 0.4635 0.4466
##
## =========================================================
## Fit for 3 latent classes:
## =========================================================
## number of observations: 1657
## number of estimated parameters: 29
## residual degrees of freedom: 34
## maximum log-likelihood: -4723.374
##
## AIC(3): 9504.748
## BIC(3): 9661.718
## G^2(3): 719.3494 (Likelihood ratio/deviance statistic)
## X^2(3): 944.0326 (Chi-square goodness of fit)
## plot(lca_model)
Class 1 (Population share ≈ 0.088): This class has a lower probability
of selecting the most positive outcomes across all three measures of
attitudes towards immigrants (imsmetn, imdfetn, impcntr). This suggests
that this class is the most restrictive or conservative regarding
immigration, with a relatively small proportion of the population
(approximately 8.8%).
Class 2 (Population share ≈ 0.451): This class shows an increasing probability of selecting more positive outcomes for attitudes towards immigrants. The probabilities are not as high as Class 3 for the most positive outcome but are higher than Class 1. This could be interpreted as a moderately open attitude towards immigration, representing the largest share of the population (approximately 45.1%).
Class 3 (Population share ≈ 0.46): This class has the highest probabilities of selecting the most positive outcomes for attitudes towards immigrants. This suggests that this class is the most open or liberal regarding immigration policies, and it makes up a significant portion of the population, nearly equal to Class 2 (approximately 46%).
5.Consider latent class analyses with four or five classes as well. Which of the three LCA models would appear to have the best fit? What do you notice computationally as the hypothesized number of classes increases?
lca_model_2 <- poLCA(cbind(imsmetn, imdfetn, impcntr) ~ 1,
data = data,
nclass = 4,
maxiter = 50000,
nrep = 10)## Model 1: llik = -4372.78 ... best llik = -4372.78
## Model 2: llik = -4372.78 ... best llik = -4372.78
## Model 3: llik = -4372.78 ... best llik = -4372.78
## Model 4: llik = -4372.78 ... best llik = -4372.78
## Model 5: llik = -4372.78 ... best llik = -4372.78
## Model 6: llik = -4372.78 ... best llik = -4372.78
## Model 7: llik = -4372.78 ... best llik = -4372.78
## Model 8: llik = -4372.78 ... best llik = -4372.78
## Model 9: llik = -4372.78 ... best llik = -4372.78
## Model 10: llik = -4372.78 ... best llik = -4372.78
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $imsmetn
## 1 2 3 4
## class 1: 0.9848 0.0152 0.0000 0.0000
## class 2: 0.0208 0.1495 0.2329 0.5968
## class 3: 0.1256 0.8588 0.0156 0.0000
## class 4: 0.0468 0.3850 0.5641 0.0041
##
## $imdfetn
## 1 2 3 4
## class 1: 0.9637 0.0363 0.0000 0.0000
## class 2: 0.0000 0.0226 0.0000 0.9774
## class 3: 0.0136 0.9482 0.0257 0.0125
## class 4: 0.0021 0.0283 0.9019 0.0677
##
## $impcntr
## 1 2 3 4
## class 1: 0.7931 0.1662 0.0337 0.0070
## class 2: 0.0042 0.0590 0.1039 0.8329
## class 3: 0.0321 0.8322 0.1201 0.0155
## class 4: 0.0042 0.1507 0.7730 0.0721
##
## Estimated class population shares
## 0.0882 0.1445 0.4489 0.3184
##
## Predicted class memberships (by modal posterior prob.)
## 0.0899 0.1412 0.4424 0.3265
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## number of observations: 1657
## number of estimated parameters: 39
## residual degrees of freedom: 24
## maximum log-likelihood: -4372.78
##
## AIC(4): 8823.561
## BIC(4): 9034.658
## G^2(4): 18.16198 (Likelihood ratio/deviance statistic)
## X^2(4): 15.74141 (Chi-square goodness of fit)
## lca_model_3 <- poLCA(cbind(imsmetn, imdfetn, impcntr) ~ 1,
data = data,
nclass = 5,
maxiter = 50000,
nrep = 10)## Model 1: llik = -4370.019 ... best llik = -4370.019
## Model 2: llik = -4370.019 ... best llik = -4370.019
## Model 3: llik = -4370.019 ... best llik = -4370.019
## Model 4: llik = -4369.333 ... best llik = -4369.333
## Model 5: llik = -4370.019 ... best llik = -4369.333
## Model 6: llik = -4370.209 ... best llik = -4369.333
## Model 7: llik = -4369.333 ... best llik = -4369.333
## Model 8: llik = -4369.804 ... best llik = -4369.333
## Model 9: llik = -4369.333 ... best llik = -4369.333
## Model 10: llik = -4370.209 ... best llik = -4369.333
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $imsmetn
## 1 2 3 4
## class 1: 0.9848 0.0152 0.0000 0.0000
## class 2: 0.1251 0.8595 0.0155 0.0000
## class 3: 0.0000 0.0937 0.0730 0.8333
## class 4: 0.0401 0.4008 0.5544 0.0047
## class 5: 0.0765 0.3088 0.6147 0.0000
##
## $imdfetn
## 1 2 3 4
## class 1: 0.9635 0.0365 0.0000 0.0000
## class 2: 0.0136 0.9489 0.0249 0.0126
## class 3: 0.0000 0.0140 0.0000 0.9860
## class 4: 0.0026 0.0176 0.9798 0.0000
## class 5: 0.0000 0.0637 0.3510 0.5852
##
## $impcntr
## 1 2 3 4
## class 1: 0.7930 0.1662 0.0337 0.0070
## class 2: 0.0320 0.8329 0.1217 0.0133
## class 3: 0.0058 0.0567 0.1042 0.8333
## class 4: 0.0054 0.1578 0.8368 0.0000
## class 5: 0.0000 0.1005 0.3395 0.5600
##
## Estimated class population shares
## 0.0882 0.4483 0.1036 0.2564 0.1035
##
## Predicted class memberships (by modal posterior prob.)
## 0.0899 0.4424 0.0863 0.283 0.0984
##
## =========================================================
## Fit for 5 latent classes:
## =========================================================
## number of observations: 1657
## number of estimated parameters: 49
## residual degrees of freedom: 14
## maximum log-likelihood: -4369.333
##
## AIC(5): 8836.665
## BIC(5): 9101.891
## G^2(5): 11.26667 (Likelihood ratio/deviance statistic)
## X^2(5): 8.52821 (Chi-square goodness of fit)
## c(lca_model$bic,lca_model_2$bic,lca_model_3$bic)## [1] 9661.718 9034.658 9101.891I chose the four classes LCA model because it has the smallest BIC, indicating the best model fit.
And number of estimated parameters increase from 29 to 49, which would widen the standard errors of the estimated parameters.
6. Fit a structural equation model, using the latent trust in leadership measure indicated by the four measures to predict the latent immigration attitude measure indicated by the three measures. Interpret the estimated coefficient for the structural component of this model.
# Convert unordered factors to ordered factors
data$imsmetn <- factor(data$imsmetn, ordered = TRUE)
data$imdfetn <- factor(data$imdfetn, ordered = TRUE)
data$impcntr <- factor(data$impcntr, ordered = TRUE)
sem_model <- '
trust_in_leadership =~ trstprl + trstlgl + trstplt + trstprt
immigration_attitude =~ imsmetn + imdfetn + impcntr
immigration_attitude ~ trust_in_leadership
'
fit <- sem(sem_model, data=data)
summary(fit)## lavaan 0.6.16 ended normally after 46 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of model parameters 25
##
## Number of observations 1657
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 65.151 143.909
## Degrees of freedom 13 13
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.467
## Shift parameter 4.417
## simple second-order correction
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## trust_in_leadership =~
## trstprl 1.000
## trstlgl 0.865 0.037 23.545 0.000
## trstplt 0.927 0.037 24.830 0.000
## trstprt 0.915 0.038 24.204 0.000
## immigration_attitude =~
## imsmetn 1.000
## imdfetn 1.170 0.015 79.550 0.000
## impcntr 1.039 0.010 102.300 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## immigration_attitude ~
## trust_n_ldrshp -0.140 0.011 -12.203 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .trstprl 4.448 0.057 78.164 0.000
## .trstlgl 4.922 0.059 82.773 0.000
## .trstplt 3.867 0.054 71.529 0.000
## .trstprt 3.865 0.054 72.044 0.000
## .imsmetn 0.000
## .imdfetn 0.000
## .impcntr 0.000
## trust_n_ldrshp 0.000
## .immigratn_tttd 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|)
## imsmetn|t1 -0.990 0.037 -26.780 0.000
## imsmetn|t2 0.502 0.032 15.569 0.000
## imsmetn|t3 1.356 0.044 31.061 0.000
## imdfetn|t1 -1.330 0.043 -30.887 0.000
## imdfetn|t2 0.083 0.031 2.677 0.007
## imdfetn|t3 0.961 0.037 26.273 0.000
## impcntr|t1 -1.364 0.044 -31.108 0.000
## impcntr|t2 0.078 0.031 2.529 0.011
## impcntr|t3 1.033 0.038 27.481 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .trstprl 1.451 0.108 13.465 0.000
## .trstlgl 2.714 0.115 23.578 0.000
## .trstplt 1.663 0.092 18.102 0.000
## .trstprt 1.685 0.096 17.574 0.000
## .imsmetn 0.302
## .imdfetn 0.044
## .impcntr 0.247
## trust_n_ldrshp 3.584 0.238 15.058 0.000
## .immigratn_tttd 0.628 0.015 41.001 0.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|)
## imsmetn 1.000
## imdfetn 1.000
## impcntr 1.000The 1 unit increase in the respondent’s trust in leadership is associated with -0.140 unit decrease in negative attitudes. (p-value less than 0.001), which implies that the higher the respondents’ trust in leadership, the more open their attitudes toward immigrants.
7. How might you improve the fitted model in part 6?
mod_indices <- modificationIndices(fit)
model_refined <-
'
trustleader =~ trstprl + trstlgl + trstplt + trstprt
immigrationatt =~ imsmetn + imdfetn + impcntr
trstprl ~~ trstlgl
trstplt ~~ trstprl
immigrationatt~ a*trustleader
'
fit_mod <- sem(model_refined, data=data)
summary(fit_mod)## lavaan 0.6.16 ended normally after 60 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of model parameters 27
##
## Number of observations 1657
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 63.258 140.134
## Degrees of freedom 11 11
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.462
## Shift parameter 3.304
## simple second-order correction
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## trustleader =~
## trstprl 1.000
## trstlgl 0.835 0.041 20.329 0.000
## trstplt 0.901 0.045 20.146 0.000
## trstprt 0.856 0.052 16.620 0.000
## immigrationatt =~
## imsmetn 1.000
## imdfetn 1.170 0.015 79.548 0.000
## impcntr 1.039 0.010 102.291 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## immigrationatt ~
## trustleadr (a) -0.131 0.012 -10.707 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .trstprl ~~
## .trstlgl -0.262 0.154 -1.702 0.089
## .trstplt -0.340 0.128 -2.646 0.008
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .trstprl 4.448 0.057 78.164 0.000
## .trstlgl 4.922 0.059 82.773 0.000
## .trstplt 3.867 0.054 71.529 0.000
## .trstprt 3.865 0.054 72.044 0.000
## .imsmetn 0.000
## .imdfetn 0.000
## .impcntr 0.000
## trustleader 0.000
## .immigrationatt 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|)
## imsmetn|t1 -0.990 0.037 -26.780 0.000
## imsmetn|t2 0.502 0.032 15.569 0.000
## imsmetn|t3 1.356 0.044 31.061 0.000
## imdfetn|t1 -1.330 0.043 -30.887 0.000
## imdfetn|t2 0.083 0.031 2.677 0.007
## imdfetn|t3 0.961 0.037 26.273 0.000
## impcntr|t1 -1.364 0.044 -31.108 0.000
## impcntr|t2 0.078 0.031 2.529 0.011
## impcntr|t3 1.033 0.038 27.481 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .trstprl 1.092 0.247 4.430 0.000
## .trstlgl 2.651 0.158 16.766 0.000
## .trstplt 1.542 0.126 12.205 0.000
## .trstprt 1.799 0.130 13.833 0.000
## .imsmetn 0.302
## .imdfetn 0.044
## .impcntr 0.247
## trustleader 3.942 0.336 11.735 0.000
## .immigrationatt 0.630 0.015 41.152 0.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|)
## imsmetn 1.000
## imdfetn 1.000
## impcntr 1.000measurement_invariance_model <- '
group: gender
trust_in_leadership =~ trstprl + trstlgl + trstplt + trstprt
immigration_attitude =~ imsmetn + imdfetn + impcntr
immigration_attitude ~ trust_in_leadership
'
fit_invariance <- sem(measurement_invariance_model, data=data)## Warning in lavParseModelString(model): lavaan WARNING: syntax contains only a
## single block identifier: groupsummary(fit_invariance)## lavaan 0.6.16 ended normally after 46 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of model parameters 25
##
## Number of observations 1657
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 65.151 143.909
## Degrees of freedom 13 13
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.467
## Shift parameter 4.417
## simple second-order correction
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## trust_in_leadership =~
## trstprl 1.000
## trstlgl 0.865 0.037 23.545 0.000
## trstplt 0.927 0.037 24.830 0.000
## trstprt 0.915 0.038 24.204 0.000
## immigration_attitude =~
## imsmetn 1.000
## imdfetn 1.170 0.015 79.550 0.000
## impcntr 1.039 0.010 102.300 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## immigration_attitude ~
## trust_n_ldrshp -0.140 0.011 -12.203 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .trstprl 4.448 0.057 78.164 0.000
## .trstlgl 4.922 0.059 82.773 0.000
## .trstplt 3.867 0.054 71.529 0.000
## .trstprt 3.865 0.054 72.044 0.000
## .imsmetn 0.000
## .imdfetn 0.000
## .impcntr 0.000
## trust_n_ldrshp 0.000
## .immigratn_tttd 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|)
## imsmetn|t1 -0.990 0.037 -26.780 0.000
## imsmetn|t2 0.502 0.032 15.569 0.000
## imsmetn|t3 1.356 0.044 31.061 0.000
## imdfetn|t1 -1.330 0.043 -30.887 0.000
## imdfetn|t2 0.083 0.031 2.677 0.007
## imdfetn|t3 0.961 0.037 26.273 0.000
## impcntr|t1 -1.364 0.044 -31.108 0.000
## impcntr|t2 0.078 0.031 2.529 0.011
## impcntr|t3 1.033 0.038 27.481 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .trstprl 1.451 0.108 13.465 0.000
## .trstlgl 2.714 0.115 23.578 0.000
## .trstplt 1.663 0.092 18.102 0.000
## .trstprt 1.685 0.096 17.574 0.000
## .imsmetn 0.302
## .imdfetn 0.044
## .impcntr 0.247
## trust_n_ldrshp 3.584 0.238 15.058 0.000
## .immigratn_tttd 0.628 0.015 41.001 0.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|)
## imsmetn 1.000
## imdfetn 1.000
## impcntr 1.000The original model (BIC = 35062.51) has been improved compared to refined model (BIC = 34953.34), which means that new model has a better fit.
8. Write a one-page summary of the results and conclusions of the above analyses.
First I created frequency plots for the two variables of interest and found that each contained a certain number of missing values. So I removed the observations with missing values, a total of 46 variables, which is not counting many not fundamentally corrupting the SEM model results.
I categorized the survey participants into two groups based on their satisfaction with the government. When I tried to implement Multi-Group Analysis (MGA), the constrained factor loadings resulted in a model markedly different from the initial one, leading to the termination of the MGA process. Consequently, it remains unclear whether the measurement invariance is strong, weak, or non-existent.
Subsequently, I conducted a Latent Class Analysis (LCA) and grouped the individuals into three categories, guided by three metrics reflecting their views on immigration.The first group seems to be more inclined to be more conservative and opposed to immigration. The second group is relatively more open, indicating a more moderate and friendly stance towards immigrants. The third group is more open, choosing mainly “allow many people to live here” on all questions, indicating a welcoming attitude towards immigrants.
Subsequently, I developed a structural equation modeling (SEM) framework that utilized four latent indicators of leadership trust to predict latent attitudes toward immigrants suggested by these three indicators. Findings suggest that there is a direct correlation between the level of trust in leadership and more receptive attitudes toward immigrants, with more trust in leaders being associated with more open attitudes toward immigrants. To enhance the SEM model, I reviewed the modification indices and incorporated the correlations between “trstprl ~~ trstlgl” and “trstplt ~~ trstprl”