纳入观测协变量后SEM拟合度异常：lavaan.mi设定疑问
2026-6-13
lavaan.mi纳入观测协变量后拟合异常的问题咨询
使用lavaan.mi拟合多重插补数据集，采用稳健WLSMV估计。将年龄（age_random.cent）、性别（male）作为协变量纳入结构模型后，模型拟合指标异常优异，怀疑lavaan代码设定存在错误。曾尝试将潜变量/结果回归到外生观测变量，或让潜因子与协变量协变，但出现NPD（非正定矩阵）警告，特寻求相关分析建议。
1. 无协变量模型
模型代码
sc.cdss.1 <- '#specifying measurement model portion pos =~ NA*SCS_SF_q2 + SCS_SF_q5 + SCS_SF_q10 + SCS_SF_q3 + SCS_SF_q7 neg =~ NA*SCS_SF_q11 + SCS_SF_q4 + SCS_SF_q8 + SCS_SF_q1 + SCS_SF_q9 pos ~~ 1*pos neg ~~ 1*neg dep =~ NA*CDSS_q1 + CDSS_q2 + CDSS_q3 + CDSS_q4 + CDSS_q5 + CDSS_q6 + CDSS_q7 + CDSS_q8 + CDSS_q9 dep ~~ 1*dep #Specifying structural portion dep ~ pos + neg' sc.cdss.1.out = sem.mi(sc.cdss.1, data=imp2final, ordered=c("SCS_SF_q1", "SCS_SF_q2", "SCS_SF_q3", "SCS_SF_q4", "SCS_SF_q5", "SCS_SF_q7", "SCS_SF_q8", "SCS_SF_q9", "SCS_SF_q10", "SCS_SF_q11", "CDSS_q1", "CDSS_q2", "CDSS_q3", "CDSS_q4", "CDSS_q5", "CDSS_q6", "CDSS_q7", "CDSS_q8", "CDSS_q9"), estimator = "WLSMV", std.lv = TRUE) summary(sc.cdss.1.out, standardized = TRUE, rsquare=TRUE, fit.measures = TRUE)
拟合结果
lavaan.mi object fit to 20 imputed data sets using: - lavaan (0.6-19) - lavaan.mi (0.1-0) See class?lavaan.mi help page for available methods. Convergence information: The model converged on 20 imputed data sets. Standard errors were available for all imputations. Estimator DWLS Optimization method NLMINB Number of model parameters 86 Number of observations 170 Model Test User Model: Standard Scaled Test statistic 47.661 105.532 Degrees of freedom 149 149 P-value 1.000 0.997 Average scaling correction factor 1.285 Average shift parameter 68.452 simple second-order correction Pooling method D2 Pooled statistic “standard” “scaled.shifted” correction applied AFTER pooling Model Test Baseline Model: Test statistic 1039.465 564.542 Degrees of freedom 171 171 P-value 0.000 0.000 Scaling correction factor 2.207 User Model versus Baseline Model: Comparative Fit Index (CFI) 1.000 1.000 Tucker-Lewis Index (TLI) 1.134 1.127 Robust Comparative Fit Index (CFI) 0.796 Robust Tucker-Lewis Index (TLI) 0.766 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 H_0: RMSEA <= 0.050 1.000 1.000 P-value H_0: RMSEA >= 0.080 0.000 0.000 Robust RMSEA 0.117 90 Percent confidence interval - lower 0.098 90 Percent confidence interval - upper 0.136 P-value H_0: Robust RMSEA <= 0.050 0.000 P-value H_0: Robust RMSEA >= 0.080 0.999 Standardized Root Mean Square Residual: SRMR 0.083 0.083
2. 纳入协变量模型
模型代码
sc.cdss.1.covariate <- '#specifying measurement model portion pos =~ NA*SCS_SF_q2 + SCS_SF_q5 + SCS_SF_q10 + SCS_SF_q3 + SCS_SF_q7 neg =~ NA*SCS_SF_q11 + SCS_SF_q4 + SCS_SF_q8 + SCS_SF_q1 + SCS_SF_q9 pos ~~ 1*pos neg ~~ 1*neg dep =~ NA*CDSS_q1 + CDSS_q2 + CDSS_q3 + CDSS_q5 + CDSS_q6 + CDSS_q8 + CDSS_q9 dep ~~ 1*dep #specifying structural model portion dep ~ pos + neg + age_random.cent + male' sc.cdss.1.covariate.out = sem.mi(sc.cdss.1.covariate, data=imp2final, ordered=c("SCS_SF_q1", "SCS_SF_q2", "SCS_SF_q3", "SCS_SF_q4", "SCS_SF_q5", "SCS_SF_q7", "SCS_SF_q8", "SCS_SF_q9", "SCS_SF_q10", "SCS_SF_q11", "CDSS_q1", "CDSS_q2", "CDSS_q3", "CDSS_q4", "CDSS_q5", "CDSS_q6", "CDSS_q7", "CDSS_q8", "CDSS_q9"), estimator = "WLSMV", std.lv = TRUE) summary(sc.cdss.1.covariate.out, standardized = FALSE, rsquare=TRUE, fit.measures = TRUE)
拟合结果
lavaan.mi object fit to 20 imputed data sets using: - lavaan (0.6-19) - lavaan.mi (0.1-0) See class?lavaan.mi help page for available methods. Convergence information: The model converged on 20 imputed data sets. Standard errors were available for all imputations. Estimator DWLS Optimization method NLMINB Number of model parameters 81 Number of observations 170 Model Test User Model: Standard Scaled Test statistic 45.356 98.401 Degrees of freedom 148 148 P-value 1.000 0.999 Average scaling correction factor 1.256 Average shift parameter 62.277 simple second-order correction Pooling method D2 Pooled statistic “standard” “scaled.shifted” correction applied AFTER pooling Model Test Baseline Model: Test statistic 1007.645 553.194 Degrees of freedom 136 136 P-value 0.000 0.000 Scaling correction factor 2.089 User Model versus Baseline Model: Comparative Fit Index (CFI) 1.000 1.000 Tucker-Lewis Index (TLI) 1.108 1.109 Robust Comparative Fit Index (CFI) NA Robust Tucker-Lewis Index (TLI) NA 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 H_0: RMSEA <= 0.050 1.000 1.000 P-value H_0: RMSEA >= 0.080 0.000 0.000 Robust RMSEA NA 90 Percent confidence interval - lower NA 90 Percent confidence interval - upper NA P-value H_0: Robust RMSEA <= 0.050 NA P-value H_0: Robust RMSEA >= 0.080 NA Standardized Root Mean Square Residual: SRMR 0.078 0.078
核心疑问
纳入协变量后，模型拟合指标（如RMSEA、CFI）提升幅度过大，且稳健拟合统计量出现NA，对路径估计的可信度存疑。怀疑模型代码中遗漏了与观测协变量相关的必要设定，尝试过两种协变量纳入方式：
- 将潜变量/结果变量回归到外生观测协变量
- 设定潜因子与观测协变量的协方差
但上述尝试均触发NPD警告，希望得到关于模型设定错误排查、协变量正确纳入方式的建议。
内容的提问来源于stack exchange，提问作者Bryan
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