ESEM-MIMIC: Regression coefficients changed after reordering indicators
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Mario Barahona
Aug 18, 2026, 8:11:03 AM (9 days ago) Aug 18
to lavaan
Hi,
I fitted an ESEM-MIMIC model (n = 1450; 74 ordinal indicators; 10 latent variables; one EFA block; six demographic predictors; DWLS estimation) and got good fit measures (CFI = .978; TLI = .976; RMSEA = .032; SRMR = .015). I, then, reordered the indicators (and the latent variables labels accordingly) in the model specification to better represent my underlying constructs and fitted the model again. As expected, the results for the measurement model were exactly the same (same fit inidces, same indicator distribution within the latent variables, equivalent factor loadings, and same factor covariances). However, the regression coefficients of the latent variables with the demographic predictors described an erratic pattern. Although each latent variable comprises the correct set of indicators, six latent variables have regression coefficients equal to those associated with the latent variable that occupied their position in the first (unordered) model, and two latent variables have regression coefficients completely different to those in the previous model. The remaining two latent variables got the same coefficients they had in the first model.
I would greatly appreciate your guidance on what might be going on. Below please find the lavaan's output for the regression results:
Unordered Model Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
OCAV ~
CRC.EFFEC (a1) 0.337 0.062 5.456 0.000 0.322 0.202
MEX.EFFEC (a2) 0.015 0.045 0.330 0.741 0.014 0.011
GENERO.FI 0.231 0.060 3.842 0.000 0.220 0.105
EDAD -0.001 0.005 -0.192 0.847 -0.001 -0.007
CURSOS.FI 0.019 0.009 2.059 0.039 0.018 0.058
EXPERIENC 0.059 0.016 3.703 0.000 0.057 0.100
AA ~
CRC.EFFEC (b1) 0.147 0.060 2.442 0.015 0.145 0.091
MEX.EFFEC (b2) -0.018 0.044 -0.414 0.679 -0.018 -0.014
GENERO.FI -0.213 0.061 -3.486 0.000 -0.210 -0.100
EDAD -0.015 0.004 -3.411 0.001 -0.015 -0.114
CURSOS.FI 0.003 0.009 0.302 0.763 0.003 0.009
EXPERIENC -0.046 0.015 -3.084 0.002 -0.045 -0.080
SE ~
CRC.EFFEC (c1) 0.682 0.061 11.211 0.000 0.616 0.387
MEX.EFFEC (c2) -0.535 0.045 -11.961 0.000 -0.483 -0.367
GENERO.FI -0.071 0.060 -1.186 0.236 -0.064 -0.031
EDAD -0.001 0.004 -0.320 0.749 -0.001 -0.010
CURSOS.FI -0.017 0.010 -1.778 0.075 -0.016 -0.050
EXPERIENC 0.033 0.015 2.159 0.031 0.030 0.053
AISI ~
CRC.EFFEC (d1) 0.415 0.055 7.515 0.000 0.397 0.250
MEX.EFFEC (d2) -0.095 0.043 -2.192 0.028 -0.091 -0.069
GENERO.FI 0.161 0.062 2.611 0.009 0.154 0.074
EDAD 0.007 0.004 1.632 0.103 0.006 0.048
CURSOS.FI -0.010 0.009 -1.167 0.243 -0.010 -0.032
EXPERIENC 0.013 0.014 0.930 0.352 0.013 0.022
OP ~
CRC.EFFEC (e1) 0.033 0.059 0.550 0.583 0.032 0.020
MEX.EFFEC (e2) -0.037 0.045 -0.810 0.418 -0.037 -0.028
GENERO.FI 0.195 0.063 3.087 0.002 0.194 0.093
EDAD -0.002 0.004 -0.495 0.621 -0.002 -0.016
CURSOS.FI 0.007 0.009 0.707 0.480 0.007 0.021
EXPERIENC -0.020 0.015 -1.356 0.175 -0.020 -0.035
TC ~
CRC.EFFEC (f1) 0.152 0.065 2.329 0.020 0.147 0.092
MEX.EFFEC (f2) -0.243 0.048 -5.076 0.000 -0.235 -0.179
GENERO.FI 0.102 0.063 1.606 0.108 0.099 0.047
EDAD 0.011 0.005 2.306 0.021 0.011 0.082
CURSOS.FI 0.007 0.010 0.715 0.475 0.007 0.023
EXPERIENC 0.017 0.016 1.083 0.279 0.017 0.029
AC ~
CRC.EFFEC (g1) -0.041 0.061 -0.669 0.503 -0.040 -0.025
MEX.EFFEC (g2) 0.161 0.045 3.581 0.000 0.158 0.120
GENERO.FI 0.230 0.062 3.692 0.000 0.226 0.108
EDAD -0.009 0.005 -1.906 0.057 -0.009 -0.067
CURSOS.FI -0.004 0.010 -0.375 0.708 -0.004 -0.011
EXPERIENC 0.035 0.016 2.218 0.027 0.034 0.061
ELCI ~
CRC.EFFEC (i1) 0.051 0.069 0.739 0.460 0.050 0.032
MEX.EFFEC (i2) 0.129 0.050 2.588 0.010 0.127 0.097
GENERO.FI -0.170 0.067 -2.548 0.011 -0.167 -0.080
EDAD -0.001 0.005 -0.133 0.894 -0.001 -0.005
CURSOS.FI -0.028 0.011 -2.557 0.011 -0.027 -0.088
EXPERIENC -0.041 0.018 -2.281 0.023 -0.041 -0.072
RFC ~
CRC.EFFEC (h1) -0.326 0.067 -4.880 0.000 -0.312 -0.196
MEX.EFFEC (h2) 0.147 0.049 3.030 0.002 0.141 0.107
GENERO.FI -0.032 0.065 -0.491 0.623 -0.030 -0.015
EDAD -0.006 0.005 -1.188 0.235 -0.006 -0.043
CURSOS.FI -0.017 0.010 -1.819 0.069 -0.017 -0.054
EXPERIENC -0.068 0.016 -4.163 0.000 -0.065 -0.115
ITR ~
CRC.EFFEC (j1) -0.341 0.066 -5.136 0.000 -0.327 -0.205
MEX.EFFEC (j2) 0.317 0.051 6.194 0.000 0.305 0.231
GENERO.FI -0.035 0.070 -0.509 0.611 -0.034 -0.016
EDAD -0.003 0.005 -0.535 0.593 -0.002 -0.019
CURSOS.FI 0.004 0.010 0.353 0.724 0.003 0.011
EXPERIENC 0.023 0.016 1.443 0.149 0.022 0.040
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
OCAV ~
CRC.EFFEC (a1) 0.337 0.062 5.456 0.000 0.322 0.202
MEX.EFFEC (a2) 0.015 0.045 0.330 0.741 0.014 0.011
GENERO.FI 0.231 0.060 3.842 0.000 0.220 0.105
EDAD -0.001 0.005 -0.192 0.847 -0.001 -0.007
CURSOS.FI 0.019 0.009 2.059 0.039 0.018 0.058
EXPERIENC 0.059 0.016 3.703 0.000 0.057 0.100
AA ~
CRC.EFFEC (b1) 0.147 0.060 2.442 0.015 0.145 0.091
MEX.EFFEC (b2) -0.018 0.044 -0.414 0.679 -0.018 -0.014
GENERO.FI -0.213 0.061 -3.486 0.000 -0.210 -0.100
EDAD -0.015 0.004 -3.411 0.001 -0.015 -0.114
CURSOS.FI 0.003 0.009 0.302 0.763 0.003 0.009
EXPERIENC -0.046 0.015 -3.084 0.002 -0.045 -0.080
SE ~
CRC.EFFEC (c1) 0.682 0.061 11.211 0.000 0.616 0.387
MEX.EFFEC (c2) -0.535 0.045 -11.961 0.000 -0.483 -0.367
GENERO.FI -0.071 0.060 -1.186 0.236 -0.064 -0.031
EDAD -0.001 0.004 -0.320 0.749 -0.001 -0.010
CURSOS.FI -0.017 0.010 -1.778 0.075 -0.016 -0.050
EXPERIENC 0.033 0.015 2.159 0.031 0.030 0.053
AISI ~
CRC.EFFEC (d1) 0.415 0.055 7.515 0.000 0.397 0.250
MEX.EFFEC (d2) -0.095 0.043 -2.192 0.028 -0.091 -0.069
GENERO.FI 0.161 0.062 2.611 0.009 0.154 0.074
EDAD 0.007 0.004 1.632 0.103 0.006 0.048
CURSOS.FI -0.010 0.009 -1.167 0.243 -0.010 -0.032
EXPERIENC 0.013 0.014 0.930 0.352 0.013 0.022
OP ~
CRC.EFFEC (e1) 0.033 0.059 0.550 0.583 0.032 0.020
MEX.EFFEC (e2) -0.037 0.045 -0.810 0.418 -0.037 -0.028
GENERO.FI 0.195 0.063 3.087 0.002 0.194 0.093
EDAD -0.002 0.004 -0.495 0.621 -0.002 -0.016
CURSOS.FI 0.007 0.009 0.707 0.480 0.007 0.021
EXPERIENC -0.020 0.015 -1.356 0.175 -0.020 -0.035
TC ~
CRC.EFFEC (f1) 0.152 0.065 2.329 0.020 0.147 0.092
MEX.EFFEC (f2) -0.243 0.048 -5.076 0.000 -0.235 -0.179
GENERO.FI 0.102 0.063 1.606 0.108 0.099 0.047
EDAD 0.011 0.005 2.306 0.021 0.011 0.082
CURSOS.FI 0.007 0.010 0.715 0.475 0.007 0.023
EXPERIENC 0.017 0.016 1.083 0.279 0.017 0.029
AC ~
CRC.EFFEC (g1) -0.041 0.061 -0.669 0.503 -0.040 -0.025
MEX.EFFEC (g2) 0.161 0.045 3.581 0.000 0.158 0.120
GENERO.FI 0.230 0.062 3.692 0.000 0.226 0.108
EDAD -0.009 0.005 -1.906 0.057 -0.009 -0.067
CURSOS.FI -0.004 0.010 -0.375 0.708 -0.004 -0.011
EXPERIENC 0.035 0.016 2.218 0.027 0.034 0.061
ELCI ~
CRC.EFFEC (i1) 0.051 0.069 0.739 0.460 0.050 0.032
MEX.EFFEC (i2) 0.129 0.050 2.588 0.010 0.127 0.097
GENERO.FI -0.170 0.067 -2.548 0.011 -0.167 -0.080
EDAD -0.001 0.005 -0.133 0.894 -0.001 -0.005
CURSOS.FI -0.028 0.011 -2.557 0.011 -0.027 -0.088
EXPERIENC -0.041 0.018 -2.281 0.023 -0.041 -0.072
RFC ~
CRC.EFFEC (h1) -0.326 0.067 -4.880 0.000 -0.312 -0.196
MEX.EFFEC (h2) 0.147 0.049 3.030 0.002 0.141 0.107
GENERO.FI -0.032 0.065 -0.491 0.623 -0.030 -0.015
EDAD -0.006 0.005 -1.188 0.235 -0.006 -0.043
CURSOS.FI -0.017 0.010 -1.819 0.069 -0.017 -0.054
EXPERIENC -0.068 0.016 -4.163 0.000 -0.065 -0.115
ITR ~
CRC.EFFEC (j1) -0.341 0.066 -5.136 0.000 -0.327 -0.205
MEX.EFFEC (j2) 0.317 0.051 6.194 0.000 0.305 0.231
GENERO.FI -0.035 0.070 -0.509 0.611 -0.034 -0.016
EDAD -0.003 0.005 -0.535 0.593 -0.002 -0.019
CURSOS.FI 0.004 0.010 0.353 0.724 0.003 0.011
EXPERIENC 0.023 0.016 1.443 0.149 0.022 0.040
Ordered Model Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
OCAV ~
CRC.EFFEC (a1) 0.337 0.062 5.447 0.000 0.322 0.202
MEX.EFFEC (a2) 0.015 0.045 0.330 0.742 0.014 0.011
GENERO.FI 0.231 0.060 3.841 0.000 0.220 0.105
EDAD -0.001 0.005 -0.192 0.848 -0.001 -0.007
CURSOS.FI 0.019 0.009 2.059 0.039 0.018 0.058
EXPERIENC 0.059 0.016 3.703 0.000 0.057 0.100
AA ~
CRC.EFFEC (b1) 0.636 0.061 10.485 0.000 0.595 0.374
MEX.EFFEC (b2) -0.441 0.045 -9.706 0.000 -0.413 -0.314
GENERO.FI -0.184 0.061 -3.026 0.002 -0.172 -0.082
EDAD -0.010 0.004 -2.288 0.022 -0.009 -0.072
CURSOS.FI -0.012 0.009 -1.338 0.181 -0.011 -0.037
EXPERIENC -0.001 0.015 -0.058 0.954 -0.001 -0.001
AISI ~
CRC.EFFEC (c1) -0.287 0.056 -5.106 0.000 -0.272 -0.171
MEX.EFFEC (c2) 0.303 0.044 6.912 0.000 0.287 0.218
GENERO.FI -0.129 0.062 -2.091 0.037 -0.122 -0.058
EDAD -0.011 0.004 -2.781 0.005 -0.011 -0.082
CURSOS.FI 0.012 0.009 1.386 0.166 0.012 0.038
EXPERIENC -0.057 0.014 -4.017 0.000 -0.054 -0.095
SE ~
CRC.EFFEC (d1) 0.416 0.061 6.844 0.000 0.398 0.250
MEX.EFFEC (d2) -0.096 0.045 -2.147 0.032 -0.092 -0.070
GENERO.FI 0.161 0.060 2.679 0.007 0.154 0.074
EDAD 0.007 0.004 1.497 0.134 0.006 0.048
CURSOS.FI -0.010 0.010 -1.080 0.280 -0.010 -0.032
EXPERIENC 0.013 0.015 0.858 0.391 0.013 0.022
OP ~
CRC.EFFEC (e1) 0.032 0.059 0.543 0.587 0.032 0.020
MEX.EFFEC (e2) -0.037 0.046 -0.804 0.421 -0.036 -0.028
GENERO.FI 0.195 0.063 3.095 0.002 0.194 0.093
EDAD -0.002 0.004 -0.496 0.620 -0.002 -0.016
CURSOS.FI 0.007 0.009 0.708 0.479 0.007 0.021
EXPERIENC -0.020 0.015 -1.355 0.175 -0.020 -0.035
AC ~
CRC.EFFEC (f1) 0.152 0.061 2.490 0.013 0.147 0.093
MEX.EFFEC (f2) -0.244 0.045 -5.436 0.000 -0.236 -0.179
GENERO.FI 0.102 0.062 1.633 0.102 0.098 0.047
EDAD 0.011 0.005 2.356 0.018 0.011 0.082
CURSOS.FI 0.007 0.010 0.773 0.440 0.007 0.023
EXPERIENC 0.017 0.016 1.080 0.280 0.017 0.029
ELCI ~
CRC.EFFEC (g1) -0.041 0.069 -0.594 0.553 -0.040 -0.025
MEX.EFFEC (g2) 0.161 0.050 3.232 0.001 0.158 0.120
GENERO.FI 0.230 0.068 3.405 0.001 0.226 0.108
EDAD -0.009 0.005 -1.716 0.086 -0.009 -0.067
CURSOS.FI -0.004 0.011 -0.333 0.739 -0.004 -0.011
EXPERIENC 0.035 0.018 1.928 0.054 0.034 0.061
RFC ~
CRC.EFFEC (h1) 0.051 0.066 0.769 0.442 0.050 0.031
MEX.EFFEC (h2) 0.130 0.048 2.684 0.007 0.128 0.097
GENERO.FI -0.170 0.065 -2.623 0.009 -0.167 -0.080
EDAD -0.001 0.005 -0.143 0.887 -0.001 -0.005
CURSOS.FI -0.028 0.010 -2.886 0.004 -0.027 -0.088
EXPERIENC -0.041 0.016 -2.526 0.012 -0.041 -0.072
TC ~
CRC.EFFEC (i1) -0.325 0.067 -4.883 0.000 -0.311 -0.196
MEX.EFFEC (i2) 0.147 0.049 3.021 0.003 0.141 0.107
GENERO.FI -0.032 0.064 -0.503 0.615 -0.031 -0.015
EDAD -0.006 0.005 -1.217 0.224 -0.006 -0.043
CURSOS.FI -0.017 0.010 -1.670 0.095 -0.017 -0.054
EXPERIENC -0.068 0.016 -4.273 0.000 -0.065 -0.115
ITR ~
CRC.EFFEC (j1) -0.341 0.065 -5.217 0.000 -0.327 -0.206
MEX.EFFEC (j2) 0.317 0.051 6.215 0.000 0.304 0.231
GENERO.FI -0.035 0.070 -0.508 0.612 -0.034 -0.016
EDAD -0.003 0.005 -0.536 0.592 -0.002 -0.019
CURSOS.FI 0.004 0.010 0.354 0.723 0.003 0.011
EXPERIENC 0.023 0.016 1.434 0.152 0.022 0.040
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
OCAV ~
CRC.EFFEC (a1) 0.337 0.062 5.447 0.000 0.322 0.202
MEX.EFFEC (a2) 0.015 0.045 0.330 0.742 0.014 0.011
GENERO.FI 0.231 0.060 3.841 0.000 0.220 0.105
EDAD -0.001 0.005 -0.192 0.848 -0.001 -0.007
CURSOS.FI 0.019 0.009 2.059 0.039 0.018 0.058
EXPERIENC 0.059 0.016 3.703 0.000 0.057 0.100
AA ~
CRC.EFFEC (b1) 0.636 0.061 10.485 0.000 0.595 0.374
MEX.EFFEC (b2) -0.441 0.045 -9.706 0.000 -0.413 -0.314
GENERO.FI -0.184 0.061 -3.026 0.002 -0.172 -0.082
EDAD -0.010 0.004 -2.288 0.022 -0.009 -0.072
CURSOS.FI -0.012 0.009 -1.338 0.181 -0.011 -0.037
EXPERIENC -0.001 0.015 -0.058 0.954 -0.001 -0.001
AISI ~
CRC.EFFEC (c1) -0.287 0.056 -5.106 0.000 -0.272 -0.171
MEX.EFFEC (c2) 0.303 0.044 6.912 0.000 0.287 0.218
GENERO.FI -0.129 0.062 -2.091 0.037 -0.122 -0.058
EDAD -0.011 0.004 -2.781 0.005 -0.011 -0.082
CURSOS.FI 0.012 0.009 1.386 0.166 0.012 0.038
EXPERIENC -0.057 0.014 -4.017 0.000 -0.054 -0.095
SE ~
CRC.EFFEC (d1) 0.416 0.061 6.844 0.000 0.398 0.250
MEX.EFFEC (d2) -0.096 0.045 -2.147 0.032 -0.092 -0.070
GENERO.FI 0.161 0.060 2.679 0.007 0.154 0.074
EDAD 0.007 0.004 1.497 0.134 0.006 0.048
CURSOS.FI -0.010 0.010 -1.080 0.280 -0.010 -0.032
EXPERIENC 0.013 0.015 0.858 0.391 0.013 0.022
OP ~
CRC.EFFEC (e1) 0.032 0.059 0.543 0.587 0.032 0.020
MEX.EFFEC (e2) -0.037 0.046 -0.804 0.421 -0.036 -0.028
GENERO.FI 0.195 0.063 3.095 0.002 0.194 0.093
EDAD -0.002 0.004 -0.496 0.620 -0.002 -0.016
CURSOS.FI 0.007 0.009 0.708 0.479 0.007 0.021
EXPERIENC -0.020 0.015 -1.355 0.175 -0.020 -0.035
AC ~
CRC.EFFEC (f1) 0.152 0.061 2.490 0.013 0.147 0.093
MEX.EFFEC (f2) -0.244 0.045 -5.436 0.000 -0.236 -0.179
GENERO.FI 0.102 0.062 1.633 0.102 0.098 0.047
EDAD 0.011 0.005 2.356 0.018 0.011 0.082
CURSOS.FI 0.007 0.010 0.773 0.440 0.007 0.023
EXPERIENC 0.017 0.016 1.080 0.280 0.017 0.029
ELCI ~
CRC.EFFEC (g1) -0.041 0.069 -0.594 0.553 -0.040 -0.025
MEX.EFFEC (g2) 0.161 0.050 3.232 0.001 0.158 0.120
GENERO.FI 0.230 0.068 3.405 0.001 0.226 0.108
EDAD -0.009 0.005 -1.716 0.086 -0.009 -0.067
CURSOS.FI -0.004 0.011 -0.333 0.739 -0.004 -0.011
EXPERIENC 0.035 0.018 1.928 0.054 0.034 0.061
RFC ~
CRC.EFFEC (h1) 0.051 0.066 0.769 0.442 0.050 0.031
MEX.EFFEC (h2) 0.130 0.048 2.684 0.007 0.128 0.097
GENERO.FI -0.170 0.065 -2.623 0.009 -0.167 -0.080
EDAD -0.001 0.005 -0.143 0.887 -0.001 -0.005
CURSOS.FI -0.028 0.010 -2.886 0.004 -0.027 -0.088
EXPERIENC -0.041 0.016 -2.526 0.012 -0.041 -0.072
TC ~
CRC.EFFEC (i1) -0.325 0.067 -4.883 0.000 -0.311 -0.196
MEX.EFFEC (i2) 0.147 0.049 3.021 0.003 0.141 0.107
GENERO.FI -0.032 0.064 -0.503 0.615 -0.031 -0.015
EDAD -0.006 0.005 -1.217 0.224 -0.006 -0.043
CURSOS.FI -0.017 0.010 -1.670 0.095 -0.017 -0.054
EXPERIENC -0.068 0.016 -4.273 0.000 -0.065 -0.115
ITR ~
CRC.EFFEC (j1) -0.341 0.065 -5.217 0.000 -0.327 -0.206
MEX.EFFEC (j2) 0.317 0.051 6.215 0.000 0.304 0.231
GENERO.FI -0.035 0.070 -0.508 0.612 -0.034 -0.016
EDAD -0.003 0.005 -0.536 0.592 -0.002 -0.019
CURSOS.FI 0.004 0.010 0.354 0.723 0.003 0.011
EXPERIENC 0.023 0.016 1.434 0.152 0.022 0.040
Best regards,
Mario Barahona
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