在使用Lavaan -package进行测量不变性分析时，我无法找出出现此警告的原因。
警告信息： 在lav_model_vcov（lavmodel = lavmodel，lavsamplestats = lavsamplestats，： lavaan警告： 估计参数的方差-协方差矩阵（vcov） 似乎不是肯定的！最小特征值 （= 1.630820e-17）接近零。这可能是一个症状， 模式不明。
以前的模型（例如具有相同阈值的强不变性）可以很好地工作。
数据包含两个时间点：带有“ _12”（或“ _12_r”）的变量来自后一个时间点。所有观察到的变量都是序数。
vars <- c(
"t3", "t4", "t5_r", "t6", "t7_r", "t8", "t9", "t10", "t11",
"t3_12", "t4_12", "t5_12_r", "t6_12", "t7_12_r", "t8_12", "t9_12", "t10_12", "t11_12",
"t30", "t31", "t32", "t30_12", "t31_12", "t32_12")
model_residual <- '
#General structure with equal loadings between timepoints
ControlT1 =~ a * t3 + b * t4 + c * t5_r + d * t6 + e * t7_r + f * t8 + g * t9 + h * t10 + i * t11
ControlT2 =~ a * t3_12 + b * t4_12 + c * t5_12_r + d * t6_12 + e * t7_12_r + f * t8_12 + g * t9_12 + h * t10_12 + i * t11_12
DemandT1 =~ t30 + t31 + t32
DemandT2 =~ t30_12 + t31_12 + t32_12
ControlT2 ~ ControlT1 + DemandT1
DemandT2 ~ DemandT1 + ControlT1
#Equal thresholds
t3 | z1*t1 + z2*t2 + z3*t3 + z4*t4
t3_12 | z1*t1 + z2*t2 + z3*t3 + z4*t4
t4 | z21*t1 + z22*t2 + z23*t3 + z24*t4
t4_12 | z21*t1 + z22*t2 + z23*t3 + z24*t4
t5_r | z31*t1 + z32*t2 + z33*t3 + z34*t4
t5_12_r | z31*t1 + z32*t2 + z33*t3 + z34*t4
t6 | z41*t1 + z42*t2 + z43*t3 + z44*t4
t6_12 | z41*t1 + z42*t2 + z43*t3 + z44*t4
t7_r | z51*t1 + z52*t2 + z53*t3 + z54*t4
t7_12_r | z51*t1 + z52*t2 + z53*t3 + z54*t4
t8 | z61*t1 + z62*t2 + z63*t3 + z64*t4
t8_12 | z61*t1 + z62*t2 + z63*t3 + z64*t4
t9 | z71*t1 + z72*t2 + z73*t3 + z74*t4
t9_12 | z71*t1 + z72*t2 + z73*t3 + z74*t4
t10 | z81*t1 + z82*t2 + z83*t3 + z84*t4
t10_12 | z81*t1 + z82*t2 + z83*t3 + z84*t4
t11 | z91*t1 + z92*t2 + z93*t3 + z94*t4
t11_12 | z91*t1 + z92*t2 + z93*t3 + z94*t4
t30 | z101*t1 + z102*t2 + z103*t3 + z104*t4
t30_12 | z101*t1 + z102*t2 + z103*t3 + z104*t4
t31 | z111*t1 + z112*t2 + z113*t3 + z114*t4
t31_12 | z111*t1 + z112*t2 + z113*t3 + z114*t4
t32 | z121*t1 + z122*t2 + z123*t3 + z124*t4
t32_12 | z121*t1 + z122*t2 + z123*t3 + z124*t4
#Equal residuals
t3 ~~ f1*t3
t3_12 ~~ t3_12
t4 ~~ f2*t4
t4_12 ~~ f2*t4_12
t5_r ~~ f3*t5_r
t5_12_r ~~ f3*t5_12_r
t6 ~~ f4*t6
t6_12 ~~ f4*t6_12
t7_r ~~ f5*t7_r
t7_12_r ~~ f5*t7_12_r
t8 ~~ f6*t8
t8_12 ~~ f6*t8_12
t9 ~~ f7*t9
t9_12 ~~ f7*t9_12
t10 ~~ f8*t10
t10_12 ~~ f8*t10_12
t11 ~~ f9*t11
t11_12 ~~ f9*t11_12
t30 ~~ f10*t30
t30_12 ~~ f10*t30_12
t31 ~~ f11*t31
t31_12 ~~ f11*t31_12
t32 ~~ f12*t32
t32_12 ~~ f12*t32_12
#Other allowed correlations
t3 ~~ t3_12
t4 ~~ t4_12
t5_r ~~ t5_12_r
t6 ~~ t6_12
t7_r ~~ t7_12_r
t8 ~~ t8_12
t9 ~~ t9_12
t10 ~~ t10_12
t11 ~~ t11_12
t30 ~~ t30_12
t31 ~~ t31_12
t32 ~~ t32_12
t3 ~~ t4
t3_12 ~~ t4_12
t4 ~~ t5_r
t4_12 ~~ t5_12_r
t3_12 ~~ t5_12_r
t3 ~~ t5_r
t3 ~~ t4_12
t3 ~~ t5_12_r
t4 ~~ t3_12
t4 ~~ t5_12_r
t5_r ~~ t3_12
t5_r ~~ t4_12
'
fit_residual <- sem(model_residual, data=AAA, ordered=vars)
分析通过了，但我怀疑由于错误而使分析无效。