如何解决比较非嵌套模型之间的标准化因子载荷
对于我的硕士论文，我使用 SEM (lavaan) 比较模型。我进行了一项在线调查，以验证评估 ICT 压力因素和资源的新量表。由于问卷很长，我怀疑回答风格可能存在问题，因此我使用了 Weijters 等人的方法。 (2008) 模拟不同的反应趋势（例如 Aquiescence、ARS）。
检查结构有效性的一部分包括分析测量模型中观察变量对潜在结构的指标负荷（MacKenzie 等，2011）。
如果我在模型中包含 ARS，我想检查这些因子载荷是否不同。我注意到的是，如果我包括 ARS，因子载荷的标准误差是两倍或三倍。在这个模型中，一些因子负载变得更高，并且所有负载都显着地加载在潜在构造上。我不确定的是，因子载荷的变化是由于较高的标准误差（我所期望的）还是由于 ARS。
如何比较非嵌套模型之间的因子载荷？比较 Modelfits 对我没有帮助，因为这不会告诉我单个参数是否不同。 （包含 ARS 的模型几乎总是更适合，即使 ARS 对指标的影响不显着）
我无法包含数据文件，但我提取了一些代码和 lavaan 的输出。问题涉及ICTPAss_day1 - ICTPAss_day3指标的因子载荷（std.all）变化
# Latent Variables:
# Estimate Std.Err z-value P(>|z|) Std.lv Std.all
# ICTPAss =~
# ICTPAss_day1 0.817 0.061 13.434 0.000 0.817 0.774
# ICTPAss_day3 0.833 0.058 14.410 0.000 0.833 0.779
# ICTPAss_day4 0.732 0.057 12.811 0.000 0.732 0.641
和
# Latent Variables:
# Estimate Std.Err z-value P(>|z|) Std.lv Std.all
# ICTPAss =~
# ICTPAss_d1 0.881 0.242 3.642 0.000 0.881 0.832
# ICTPAss_d3 0.875 0.239 3.654 0.000 0.875 0.821
# ICTPAss_d4 0.749 0.226 3.319 0.001 0.749 0.656
完整代码：
model_ictpass <- '
# measurement model
ICTPAss =~ ICTPAss_day1 + ICTPAss_day3 + ICTPAss_day4
'
fit_ictpass <- lavaan::cfa(model_ictpass,my_data_validity,estimator = "MLM",std.lv = T)
summary(fit_ictpass,fit.measures=T,standardized=T,rsquare = T)
# lavaan 0.6-8 ended normally after 13 iterations
#
# Estimator ML
# Optimization method NLMINB
# Number of model parameters 6
#
# Number of observations 356
#
# Model Test User Model:
# Standard Robust
# Test Statistic 0.000 0.000
# degrees of freedom 0 0
#
# Model Test Baseline Model:
#
# Test statistic 292.653 230.441
# degrees of freedom 3 3
# P-value 0.000 0.000
# Scaling correction factor 1.270
#
# User Model versus Baseline Model:
#
# Comparative Fit Index (CFI) 1.000 1.000
# Tucker-Lewis Index (TLI) 1.000 1.000
#
# Robust Comparative Fit Index (CFI) NA
# Robust Tucker-Lewis Index (TLI) NA
#
# Loglikelihood and information Criteria:
#
# Loglikelihood user model (H0) -1459.113 -1459.113
# Loglikelihood unrestricted model (H1) -1459.113 -1459.113
#
# Akaike (AIC) 2930.226 2930.226
# Bayesian (BIC) 2953.475 2953.475
# Sample-size adjusted Bayesian (BIC) 2934.440 2934.440
#
# Root Mean Square Error of Approximation:
#
# RMSEA 0.000 0.000
# 90 Percent confidence interval - lower 0.000 0.000
# 90 Percent confidence interval - upper 0.000 0.000
# P-value RMSEA <= 0.05 NA NA
#
# Robust RMSEA 0.000
# 90 Percent confidence interval - lower 0.000
# 90 Percent confidence interval - upper 0.000
#
# Standardized Root Mean Square Residual:
#
# SRMR 0.000 0.000
#
# Parameter Estimates:
#
# Standard errors Robust.sem
# information Expected
# information saturated (h1) model Structured
#
# Latent Variables:
# Estimate Std.Err z-value P(>|z|) Std.lv Std.all
# ICTPAss =~
# ICTPAss_day1 0.817 0.061 13.434 0.000 0.817 0.774
# ICTPAss_day3 0.833 0.058 14.410 0.000 0.833 0.779
# ICTPAss_day4 0.732 0.057 12.811 0.000 0.732 0.641
#
# Variances:
# Estimate Std.Err z-value P(>|z|) Std.lv Std.all
# .ICTPAss_day1 0.447 0.074 6.079 0.000 0.447 0.401
# .ICTPAss_day3 0.449 0.072 6.194 0.000 0.449 0.393
# .ICTPAss_day4 0.767 0.075 10.246 0.000 0.767 0.589
# ICTPAss 1.000 1.000 1.000
#
# R-Square:
# Estimate
# ICTPAss_day1 0.599
# ICTPAss_day3 0.607
# ICTPAss_day4 0.411
#
####6.3.0.1 Messmodell ARS
model_ictpass_ars <- '
# measurement model
ICTPAss =~ ICTPAss_day1 + ICTPAss_day3 + ICTPAss_day4
ARS =~ a*ARS_a + a*ARS_b + a*ARS_c
# time-invariant autoregressive effect
ARS_b ~ e*ARS_a
ARS_c ~ e*ARS_b
# Influence of ARS
ICTPAss_day1 ~ l*ARS
ICTPAss_day3 ~ l*ARS
ICTPAss_day4 ~ l*ARS
'
fit_ictpass_ars <- lavaan::cfa(model_ictpass_ars,std.lv = T)
summary(fit_ictpass_ars,rsquare = T)
# lavaan 0.6-8 ended normally after 36 iterations
#
# Estimator ML
# Optimization method NLMINB
# Number of model parameters 18
# Number of equality constraints 5
#
# Number of observations 356
#
# Model Test User Model:
# Standard Robust
# Test Statistic 8.158 7.800
# degrees of freedom 8 8
# P-value (Chi-square) 0.418 0.453
# Scaling correction factor 1.046
# Satorra-Bentler correction
#
# Model Test Baseline Model:
#
# Test statistic 379.734 341.671
# degrees of freedom 15 15
# P-value 0.000 0.000
# Scaling correction factor 1.111
#
# User Model versus Baseline Model:
#
# Comparative Fit Index (CFI) 1.000 1.000
# Tucker-Lewis Index (TLI) 0.999 1.001
#
# Robust Comparative Fit Index (CFI) 1.000
# Robust Tucker-Lewis Index (TLI) 1.001
#
# Loglikelihood and information Criteria:
#
# Loglikelihood user model (H0) -2035.784 -2035.784
# Loglikelihood unrestricted model (H1) -2031.706 -2031.706
#
# Akaike (AIC) 4097.569 4097.569
# Bayesian (BIC) 4147.943 4147.943
# Sample-size adjusted Bayesian (BIC) 4106.701 4106.701
#
# Root Mean Square Error of Approximation:
#
# RMSEA 0.007 0.000
# 90 Percent confidence interval - lower 0.000 0.000
# 90 Percent confidence interval - upper 0.063 0.060
# P-value RMSEA <= 0.05 0.863 0.886
#
# Robust RMSEA 0.000
# 90 Percent confidence interval - lower 0.000
# 90 Percent confidence interval - upper 0.063
#
# Standardized Root Mean Square Residual:
#
# SRMR 0.029 0.029
#
# Parameter Estimates:
#
# Standard errors Robust.sem
# information Expected
# information saturated (h1) model Structured
#
# Latent Variables:
# Estimate Std.Err z-value P(>|z|) Std.lv Std.all
# ICTPAss =~
# ICTPAss_d1 0.881 0.242 3.642 0.000 0.881 0.832
# ICTPAss_d3 0.875 0.239 3.654 0.000 0.875 0.821
# ICTPAss_d4 0.749 0.226 3.319 0.001 0.749 0.656
# ARS =~
# ARS_a (a) 0.207 0.024 8.679 0.000 0.207 0.554
# ARS_b (a) 0.207 0.024 8.679 0.000 0.207 0.433
# ARS_c (a) 0.207 0.024 8.679 0.000 0.207 0.465
#
# Regressions:
# Estimate Std.Err z-value P(>|z|) Std.lv Std.all
# ARS_b ~
# ARS_a (e) 0.028 0.059 0.478 0.633 0.028 0.022
# ARS_c ~
# ARS_b (e) 0.028 0.059 0.478 0.633 0.028 0.030
# ICTPAss_day1 ~
# ARS (l) 0.642 0.492 1.305 0.192 0.642 0.607
# ICTPAss_day3 ~
# ARS (l) 0.642 0.492 1.305 0.192 0.642 0.603
# ICTPAss_day4 ~
# ARS (l) 0.642 0.492 1.305 0.192 0.642 0.563
#
# Covariances:
# Estimate Std.Err z-value P(>|z|) Std.lv Std.all
# ICTPAss ~~
# ARS -0.446 0.475 -0.940 0.347 -0.446 -0.446
#
# Variances:
# Estimate Std.Err z-value P(>|z|) Std.lv Std.all
# .ICTPAss_day1 0.438 0.073 6.023 0.000 0.438 0.391
# .ICTPAss_day3 0.458 0.069 6.620 0.000 0.458 0.404
# .ICTPAss_day4 0.759 0.071 10.666 0.000 0.759 0.582
# .ARS_a 0.097 0.011 8.690 0.000 0.097 0.693
# .ARS_b 0.183 0.016 11.605 0.000 0.183 0.801
# .ARS_c 0.154 0.015 9.923 0.000 0.154 0.771
# ICTPAss 1.000 1.000 1.000
# ARS 1.000 1.000 1.000
#
# R-Square:
# Estimate
# ICTPAss_day1 0.609
# ICTPAss_day3 0.596
# ICTPAss_day4 0.418
# ARS_a 0.307
# ARS_b 0.199
# ARS_c 0.229
文学：
MacKenzie,S. B.,Podsakoff,P. M. & Podsakoff,N. P. (2011)。在 MIS 和行为研究中构建测量和验证程序：整合新的和现有的技术。 MIS 季刊，35(2)，293。https://doi.org/10.2307/23044045
Weijters,B.、Schillewaert,N. & Geuens,M. (2008)。跨数据收集模式评估响应风格。营销科学院学报，36（3），409-422。 https://doi.org/10.1007/s11747-007-0077-6
Weijters,B.、Geuens,M. & Schillewaert,N. (2010a)。自我报告问卷中默认和极端反应风格的个体一致性。应用心理测量，34（2），105-121。 https://doi.org/10.1177/0146621609338593
感谢您的回答和问候:)
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