SEM & marker variable
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Noortje de Boer
Apr 3, 2017, 8:44:46 AM4/3/17
to lavaan
Dear all,
I am running a SEM model with 1 IV (OM_M), 3 DVs which covary (FC, EP, AC), 1 Mediator (RES) and several controls (LEEFTIJD, RULEOBEDIENCE, GESLACHT_D_VROUW)
I use the MLM Satorro Bentler estimator since my data does not meet all assumptions of multivariate normality.
OM.mate.model <- '
#define DVs
FC =~ F1 + F3 + F5 + C4 + C5
EP =~ E3 + E4 + E5 + P5
AC =~ A2 + A3 + A4 + A5
#define M
RES =~ RESIS1_RC + RESIS2_RC + RESIS3_RC
#define IV
OM_M =~ OM_M1 + OM_M2 + OM_M3 + OM_M4
#covariances DV
FC ~~ EP
FC ~~ AC
AC ~~ EP
#direct effect
FC ~ c1*OM_M + LEEFTIJD + RULEOBEDIENCE
EP ~ c2*OM_M + LEEFTIJD + WERKERVARING
AC ~ c3*OM_M + LEEFTIJD + GESLACHT_D_VROUW
#indirect effects
RES ~ a*OM_M + RULEOBEDIENCE #only rule obedience correlated with resistance
FC ~ b1*RES
EP ~ b2*RES
AC ~ b3*RES
ab1 := a*b1
ab2 := a*b2
ab3 := a*b3
'
My model runs fine, but now I want to check for common method variance by adding a latent variable and a marker variable. My syntax is as follows:
CMB.marker <- '
#define DVs
FC =~ F1 + F3 + F5 + C4 + C5
EP =~ E3 + E4 + E5 + P5
AC =~ A2 + A3 + A4 + A5
#define M
RES =~ RESIS1_RC + RESIS2_RC + RESIS3_RC
#define IV
OM_M =~ OM_M1 + OM_M2 + OM_M3
#covariances DV (all measure 1 dimension of inspection style)
FC ~~ EP
FC ~~ AC
AC ~~ EP
#direct effect
FC ~ c1*OM_M + LEEFTIJD + RULEOBEDIENCE
EP ~ c2*OM_M + LEEFTIJD + WERKERVARING
AC ~ c3*OM_M + LEEFTIJD + GESLACHT_D_VROUW
#indirect effects
RES ~ a*OM_M + RULEOBEDIENCE #only rule obedience correlated with resistance
FC ~ b1*RES
EP ~ b2*RES
AC ~ b3*RES
ab1 := a*b1
ab2 := a*b2
ab3 := a*b3
#define common latent variable
#constraining factor loadings to be equal
CLF =~ F1 + cmb*F3 + cmb*F5 + cmb*C4 + cmb*C5 +
cmb*E3 + cmb*E4 + cmb*E5 + cmb*P5 +
cmb*A2 + cmb*A3 + cmb*A4 + cmb*A5 +
cmb*RESIS1_RC + cmb*RESIS2_RC + cmb*RESIS3_RC +
cmb*OM_M1 + cmb*OM_M2 + cmb*OM_M3 +
Marker
#contraining variance of CLF to be 1
CLF ~~ 1*CLF
#adding marker variable: KM_gebruik_uren
#constraining factor loadings to be equal
Marker =~ cmb*KM_gebruik_uren
#covary with other latent variables
Marker ~~ FC
Marker ~~ EP
Marker ~~ AC
Marker ~~ RES
Marker ~~ OM_M
'
Now I get the warning message:
Warning message:
In lav_object_post_check(object) :
lavaan WARNING: covariance matrix of latent variables
is not positive definite;
use inspect(fit,"cov.lv") to investigate.
I indeed find negative covariances between my latent variables
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FC ~
OM_M (c1) -0.461 0.119 -3.871 0.000 -0.150 -0.150
LEEFTIJD 0.025 0.011 2.272 0.023 0.013 0.163
GESLACHT_ 0.332 0.201 1.657 0.097 0.170 0.076
GESLACHT_ -0.129 0.688 -0.187 0.851 -0.066 -0.004
WERKERVAR -0.016 0.009 -1.706 0.088 -0.008 -0.093
RULEOBEDI -0.037 0.053 -0.690 0.490 -0.019 -0.047
EP ~
OM_M (c2) -0.277 0.119 -2.319 0.020 -0.091 -0.091
LEEFTIJD 0.017 0.011 1.596 0.110 0.009 0.112
GESLACHT_ 0.256 0.230 1.113 0.266 0.132 0.059
GESLACHT_ 0.842 0.391 2.157 0.031 0.433 0.027
WERKERVAR 0.013 0.010 1.306 0.191 0.007 0.076
RULEOBEDI -0.060 0.052 -1.147 0.251 -0.031 -0.078
AC ~
OM_M (c3) -0.075 0.104 -0.722 0.471 -0.025 -0.025
LEEFTIJD 0.012 0.009 1.349 0.177 0.006 0.083
GESLACHT_ -0.062 0.223 -0.277 0.782 -0.032 -0.014
GESLACHT_ -1.943 2.687 -0.723 0.470 -1.014 -0.064
WERKERVAR -0.004 0.010 -0.443 0.658 -0.002 -0.025
RULEOBEDI -0.035 0.050 -0.692 0.489 -0.018 -0.046
RES ~
OM_M (a) -1.195 0.296 -4.042 0.000 -0.307 -0.307
LEEFTIJD -0.008 0.010 -0.775 0.439 -0.003 -0.042
GESLACHT_ -0.372 0.222 -1.674 0.094 -0.150 -0.067
GESLACHT_ 1.519 1.601 0.949 0.343 0.612 0.038
WERKERVAR 0.007 0.011 0.641 0.521 0.003 0.032
RULEOBEDI 0.261 0.063 4.139 0.000 0.105 0.265
FC ~
RES (b1) 0.429 0.144 2.984 0.003 0.545 0.545
EP ~
RES (b2) 0.286 0.126 2.267 0.023 0.365 0.365
AC ~
RES (b3) 0.302 0.101 2.999 0.003 0.391 0.391
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.FC ~~
.EP 1.958 0.462 4.240 0.000 0.714 0.714
.AC 1.272 0.343 3.713 0.000 0.467 0.467
.EP ~~
.AC 1.483 0.334 4.436 0.000 0.478 0.478
OM_M ~~
CLF 1.689 0.312 5.406 0.000 2.648 2.648
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.F1 5.354 0.594 9.012 0.000 5.354 2.543
.F3 7.014 0.615 11.410 0.000 7.014 4.394
.F5 6.600 0.613 10.758 0.000 6.600 3.508
.C4 7.239 0.594 12.192 0.000 7.239 4.182
.C5 6.616 0.624 10.607 0.000 6.616 4.086
.E3 6.379 0.582 10.955 0.000 6.379 3.091
.E4 6.595 0.597 11.050 0.000 6.595 3.303
.E5 5.844 0.543 10.763 0.000 5.844 2.756
.P5 5.595 0.560 9.989 0.000 5.595 2.336
.A2 4.825 0.501 9.624 0.000 4.825 1.934
.A3 3.910 0.419 9.323 0.000 3.910 1.572
.A4 5.924 0.558 10.617 0.000 5.924 2.538
.A5 5.068 0.554 9.155 0.000 5.068 2.041
.RESIS1_RC 4.704 0.678 6.936 0.000 4.704 1.622
.RESIS2_RC 3.243 0.687 4.720 0.000 3.243 1.417
.RESIS3_RC 3.247 0.682 4.762 0.000 3.247 1.395
.OM_M1 5.489 0.101 54.539 0.000 5.489 2.441
.OM_M2 5.156 0.102 50.741 0.000 5.156 2.252
.OM_M3 5.118 0.100 51.089 0.000 5.118 2.265
.FC 0.000 0.000 0.000
.EP 0.000 0.000 0.000
.AC 0.000 0.000 0.000
.RES 0.000 0.000 0.000
OM_M 0.000 0.000 0.000
CLF 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
CLF 1.000 1.000 1.000
.F1 2.903 0.282 10.306 0.000 2.903 0.655
.F3 1.017 0.174 5.859 0.000 1.017 0.399
.F5 1.995 0.368 5.421 0.000 1.995 0.564
.C4 1.700 0.340 4.996 0.000 1.700 0.568
.C5 1.027 0.196 5.235 0.000 1.027 0.392
.E3 1.540 0.225 6.853 0.000 1.540 0.362
.E4 1.160 0.196 5.934 0.000 1.160 0.291
.E5 2.285 0.241 9.490 0.000 2.285 0.508
.P5 3.294 0.355 9.280 0.000 3.294 0.574
.A2 3.068 0.272 11.288 0.000 3.068 0.493
.A3 3.979 0.281 14.177 0.000 3.979 0.643
.A4 1.659 0.246 6.753 0.000 1.659 0.304
.A5 2.356 0.305 7.723 0.000 2.356 0.382
.RESIS1_RC 5.063 0.363 13.941 0.000 5.063 0.602
.RESIS2_RC 1.239 0.233 5.317 0.000 1.239 0.237
.RESIS3_RC 1.530 0.278 5.514 0.000 1.530 0.282
.OM_M1 0.808 0.167 4.830 0.000 0.808 0.160
.OM_M2 1.085 0.209 5.184 0.000 1.085 0.207
.OM_M3 1.206 0.217 5.556 0.000 1.206 0.236
.FC 2.409 0.578 4.171 0.000 0.631 0.631
.EP 3.123 0.472 6.620 0.000 0.824 0.824
.AC 3.081 0.400 7.699 0.000 0.839 0.839
.RES 5.098 1.588 3.210 0.001 0.827 0.827
OM_M 0.407 0.419 0.971 0.332 1.000 1.000
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ab1 -0.512 0.275 -1.864 0.062 -0.167 -0.167
ab2 -0.342 0.223 -1.536 0.125 -0.112 -0.112
ab3 -0.361 0.195 -1.850 0.064 -0.120 -0.120
> #marker variable
> CMB.marker <- '
+ #define DVs
+ FC =~ F1 + F3 + F5 + C4 + C5
+ EP =~ E3 + E4 + E5 + P5
+ AC =~ A2 + A3 + A4 + A5
+
+ #define M
+ RES =~ RESIS1_RC + RESIS2_RC + RESIS3_RC
+
+ #define IV
+ OM_M =~ OM_M1 + OM_M2 + OM_M3
+
+ #covariances DV (all measure 1 dimension of inspection style)
+ FC ~~ EP
+ FC ~~ AC
+ AC ~~ EP
+
+ #direct effect
+ FC ~ c1*OM_M + LEEFTIJD + GESLACHT_D_VROUW + GESLACHT_D_ANDERS + WERKERVARING + RULEOBEDIENCE
+ EP ~ c2*OM_M + LEEFTIJD + GESLACHT_D_VROUW + GESLACHT_D_ANDERS + WERKERVARING + RULEOBEDIENCE
+ AC ~ c3*OM_M + LEEFTIJD + GESLACHT_D_VROUW + GESLACHT_D_ANDERS + WERKERVARING + RULEOBEDIENCE
+
+ #mediation b/w IV and 3 DV
+ #indirect effects
+ RES ~ a*OM_M + LEEFTIJD + GESLACHT_D_VROUW + GESLACHT_D_ANDERS + WERKERVARING + RULEOBEDIENCE
+ FC ~ b1*RES
+ EP ~ b2*RES
+ AC ~ b3*RES
+ ab1 := a*b1
+ ab2 := a*b2
+ ab3 := a*b3
+
+ #define common latent variable
+ #constraining factor loadings to be equal
+ CLF =~ F1 + cmb*F3 + cmb*F5 + cmb*C4 + cmb*C5 +
+ cmb*E3 + cmb*E4 + cmb*E5 + cmb*P5 +
+ cmb*A2 + cmb*A3 + cmb*A4 + cmb*A5 +
+ cmb*RESIS1_RC + cmb*RESIS2_RC + cmb*RESIS3_RC +
+ cmb*OM_M1 + cmb*OM_M2 + cmb*OM_M3 +
+ KM_gebruik_uren
+
+ #contraining variance of CLF to be 1
+ CLF ~~ 1*CLF
+
+ #adding marker variable: KM_gebruik_uren
+ #constraining factor loadings to be equal
+ Marker =~ cmb*KM_gebruik_uren
+ #covary with other latent variables
+ Marker ~~ FC
+ Marker ~~ EP
+ Marker ~~ AC
+ Marker ~~ RES
+ Marker ~~ OM_M
+
+ '
> fit.CMB.marker <- cfa(CMB.marker,
+ data = NVWA2016,
+ estimator="MLM")
Warning messages:
1: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, :
lavaan WARNING: could not compute standard errors!
lavaan NOTE: this may be a symptom that the model is not identified.
2: In lav_model_test(lavmodel = lavmodel, lavpartable = lavpartable, :
lavaan WARNING: could not compute scaled test statistic
3: In lav_object_post_check(object) :
lavaan WARNING: covariance matrix of latent variables
is not positive definite;
use inspect(fit,"cov.lv") to investigate.
> summary(fit.CMB.marker, standardized=TRUE, fit.measures=TRUE)
lavaan (0.5-23.1097) converged normally after 230 iterations
Number of observations 507
Estimator ML Robust
Minimum Function Test Statistic 587.480 NA
Degrees of freedom 232 232
P-value (Chi-square) 0.000 NA
Scaling correction factor NA
for the Satorra-Bentler correction
Model test baseline model:
Minimum Function Test Statistic 5175.970 2907.974
Degrees of freedom 290 290
P-value 0.000 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 0.927 NA
Tucker-Lewis Index (TLI) 0.909 NA
Robust Comparative Fit Index (CFI) NA
Robust Tucker-Lewis Index (TLI) NA
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -24378.783 -24378.783
Loglikelihood unrestricted model (H1) -24085.043 -24085.043
Number of free parameters 98 98
Akaike (AIC) 48953.566 48953.566
Bayesian (BIC) 49367.960 49367.960
Sample-size adjusted Bayesian (BIC) 49056.896 49056.896
Root Mean Square Error of Approximation:
RMSEA 0.055 NA
90 Percent Confidence Interval 0.049 0.061 0.000 0.000
P-value RMSEA <= 0.05 0.068 0.000
Robust RMSEA NA
90 Percent Confidence Interval 0.000 0.000
Standardized Root Mean Square Residual:
SRMR 0.047 0.047
Parameter Estimates:
Information Expected
Standard Errors Robust.sem
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FC =~
F1 1.000 1.860 0.895
F3 1.035 NA 1.926 1.204
F5 1.039 NA 1.932 1.027
C4 0.976 NA 1.816 1.047
C5 1.049 NA 1.951 1.205
EP =~
E3 1.000 1.968 0.954
E4 1.022 NA 2.011 1.006
E5 0.896 NA 1.764 0.835
P5 0.960 NA 1.889 0.785
AC =~
A2 1.000 1.920 0.772
A3 0.833 NA 1.600 0.640
A4 1.114 NA 2.139 0.915
A5 1.105 NA 2.123 0.857
RES =~
RESIS1_R 1.000 2.499 0.865
RESIS2_R 1.072 NA 2.678 1.178
RESIS3_R 1.062 NA 2.654 1.145
OM_M =~
OM_M1 1.000 0.570 0.254
OM_M2 0.967 NA 0.551 0.241
OM_M3 0.911 NA 0.519 0.229
CLF =~
F1 1.000 1.000 0.481
F3 (cmb) 1.000 1.000 0.625
F5 (cmb) 1.000 1.000 0.531
C4 (cmb) 1.000 1.000 0.577
C5 (cmb) 1.000 1.000 0.618
E3 (cmb) 1.000 1.000 0.485
E4 (cmb) 1.000 1.000 0.500
E5 (cmb) 1.000 1.000 0.473
P5 (cmb) 1.000 1.000 0.416
A2 (cmb) 1.000 1.000 0.402
A3 (cmb) 1.000 1.000 0.400
A4 (cmb) 1.000 1.000 0.428
A5 (cmb) 1.000 1.000 0.404
RESIS1_R (cmb) 1.000 1.000 0.346
RESIS2_R (cmb) 1.000 1.000 0.440
RESIS3_R (cmb) 1.000 1.000 0.432
OM_M1 (cmb) 1.000 1.000 0.445
OM_M2 (cmb) 1.000 1.000 0.438
OM_M3 (cmb) 1.000 1.000 0.441
KM_gbrk_ 0.478 NA 0.478 0.327
Marker =~
KM_gbrk_ (cmb) 1.000 0.987 0.676
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FC ~
OM_M (c1) -0.490 NA -0.150 -0.150
LEEFTIJD 0.024 NA 0.013 0.163
GESLACHT_ 0.322 NA 0.173 0.077
GESLACHT_ -0.140 NA -0.075 -0.005
WERKERVAR -0.015 NA -0.008 -0.092
RULEOBEDI -0.037 NA -0.020 -0.050
EP ~
OM_M (c2) -0.335 NA -0.097 -0.097
LEEFTIJD 0.017 NA 0.009 0.110
GESLACHT_ 0.273 NA 0.139 0.062
GESLACHT_ 0.840 NA 0.427 0.027
WERKERVAR 0.013 NA 0.007 0.074
RULEOBEDI -0.069 NA -0.035 -0.088
AC ~
OM_M (c3) -0.120 NA -0.036 -0.036
LEEFTIJD 0.012 NA 0.006 0.083
GESLACHT_ -0.056 NA -0.029 -0.013
GESLACHT_ -1.949 NA -1.015 -0.064
WERKERVAR -0.004 NA -0.002 -0.025
RULEOBEDI -0.036 NA -0.019 -0.047
RES ~
OM_M (a) -1.354 NA -0.309 -0.309
LEEFTIJD -0.009 NA -0.004 -0.045
GESLACHT_ -0.344 NA -0.138 -0.061
GESLACHT_ 1.557 NA 0.623 0.039
WERKERVAR 0.007 NA 0.003 0.029
RULEOBEDI 0.247 NA 0.099 0.249
FC ~
RES (b1) 0.412 NA 0.553 0.553
EP ~
RES (b2) 0.298 NA 0.378 0.378
AC ~
RES (b3) 0.309 NA 0.402 0.402
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.FC ~~
.EP 1.864 NA 0.717 0.717
.AC 1.204 NA 0.470 0.470
.EP ~~
.AC 1.492 NA 0.482 0.482
.FC ~~
Marker -0.482 NA -0.333 -0.333
.EP ~~
Marker -0.403 NA -0.230 -0.230
.AC ~~
Marker -0.354 NA -0.205 -0.205
.RES ~~
Marker -0.853 NA -0.378 -0.378
OM_M ~~
Marker -1.119 NA -1.988 -1.988
CLF 1.461 NA 2.562 2.562
CLF ~~
Marker 0.008 NA 0.008 0.008
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.F1 5.484 NA 5.484 2.637
.F3 7.057 NA 7.057 4.413
.F5 6.643 NA 6.643 3.530
.C4 7.279 NA 7.279 4.199
.C5 6.662 NA 6.662 4.115
.E3 6.476 NA 6.476 3.139
.E4 6.691 NA 6.691 3.347
.E5 5.941 NA 5.941 2.813
.P5 5.678 NA 5.678 2.360
.A2 4.863 NA 4.863 1.954
.A3 3.935 NA 3.935 1.575
.A4 5.956 NA 5.956 2.549
.A5 5.108 NA 5.108 2.063
.RESIS1_RC 4.840 NA 4.840 1.675
.RESIS2_RC 3.387 NA 3.387 1.490
.RESIS3_RC 3.388 NA 3.388 1.462
.OM_M1 5.489 NA 5.489 2.442
.OM_M2 5.156 NA 5.156 2.257
.OM_M3 5.118 NA 5.118 2.259
.KM_gebruik_urn 1.682 NA 1.682 1.151
.FC 0.000 0.000 0.000
.EP 0.000 0.000 0.000
.AC 0.000 0.000 0.000
.RES 0.000 0.000 0.000
OM_M 0.000 0.000 0.000
CLF 0.000 0.000 0.000
Marker 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
CLF 1.000 1.000 1.000
.F1 2.925 NA 2.925 0.676
.F3 1.019 NA 1.019 0.398
.F5 1.988 NA 1.988 0.561
.C4 1.697 NA 1.697 0.565
.C5 1.026 NA 1.026 0.392
.E3 1.541 NA 1.541 0.362
.E4 1.157 NA 1.157 0.290
.E5 2.283 NA 2.283 0.512
.P5 3.293 NA 3.293 0.569
.A2 3.079 NA 3.079 0.497
.A3 3.991 NA 3.991 0.640
.A4 1.638 NA 1.638 0.300
.A5 2.364 NA 2.364 0.386
.RESIS1_RC 5.063 NA 5.063 0.606
.RESIS2_RC 1.238 NA 1.238 0.239
.RESIS3_RC 1.531 NA 1.531 0.285
.OM_M1 0.808 NA 0.808 0.160
.OM_M2 1.088 NA 1.088 0.209
.OM_M3 1.204 NA 1.204 0.234
.KM_gebruik_urn 0.925 NA 0.925 0.433
.FC 2.148 NA 0.621 0.621
.EP 3.146 NA 0.813 0.813
.AC 3.051 NA 0.827 0.827
.RES 5.214 NA 0.835 0.835
OM_M 0.325 NA 1.000 1.000
Marker 0.974 NA 1.000 1.000
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ab1 -0.558 -0.171 -0.171
ab2 -0.404 -0.117 -0.117
ab3 -0.418 -0.124 -0.124
> #marker variable
> CMB.marker <- '
+ #define DVs
+ FC =~ F1 + F3 + F5 + C4 + C5
+ EP =~ E3 + E4 + E5 + P5
+ AC =~ A2 + A3 + A4 + A5
+
+ #define M
+ RES =~ RESIS1_RC + RESIS2_RC + RESIS3_RC
+
+ #define IV
+ OM_M =~ OM_M1 + OM_M2 + OM_M3
+
+ #covariances DV (all measure 1 dimension of inspection style)
+ FC ~~ EP
+ FC ~~ AC
+ AC ~~ EP
+
+ #direct effect
+ FC ~ c1*OM_M + LEEFTIJD + GESLACHT_D_VROUW + GESLACHT_D_ANDERS + WERKERVARING + RULEOBEDIENCE
+ EP ~ c2*OM_M + LEEFTIJD + GESLACHT_D_VROUW + GESLACHT_D_ANDERS + WERKERVARING + RULEOBEDIENCE
+ AC ~ c3*OM_M + LEEFTIJD + GESLACHT_D_VROUW + GESLACHT_D_ANDERS + WERKERVARING + RULEOBEDIENCE
+
+ #mediation b/w IV and 3 DV
+ #indirect effects
+ RES ~ a*OM_M + LEEFTIJD + GESLACHT_D_VROUW + GESLACHT_D_ANDERS + WERKERVARING + RULEOBEDIENCE
+ FC ~ b1*RES
+ EP ~ b2*RES
+ AC ~ b3*RES
+ ab1 := a*b1
+ ab2 := a*b2
+ ab3 := a*b3
+
+ #define common latent variable
+ #constraining factor loadings to be equal
+ CLF =~ F1 + cmb*F3 + cmb*F5 + cmb*C4 + cmb*C5 +
+ cmb*E3 + cmb*E4 + cmb*E5 + cmb*P5 +
+ cmb*A2 + cmb*A3 + cmb*A4 + cmb*A5 +
+ cmb*RESIS1_RC + cmb*RESIS2_RC + cmb*RESIS3_RC +
+ cmb*OM_M1 + cmb*OM_M2 + cmb*OM_M3 +
+ Marker
+
+ #contraining variance of CLF to be 1
+ CLF ~~ 1*CLF
+
+ #adding marker variable: KM_gebruik_uren
+ #constraining factor loadings to be equal
+ Marker =~ cmb*KM_gebruik_uren
+ #covary with other latent variables
+ Marker ~~ FC
+ Marker ~~ EP
+ Marker ~~ AC
+ Marker ~~ RES
+ Marker ~~ OM_M
+
+ '
> fit.CMB.marker <- cfa(CMB.marker,
+ data = NVWA2016,
+ estimator="MLM")
Warning message:
In lav_object_post_check(object) :
lavaan WARNING: covariance matrix of latent variables
is not positive definite;
use inspect(fit,"cov.lv") to investigate.
> summary(fit.CMB.marker, standardized=TRUE, fit.measures=TRUE)
lavaan (0.5-23.1097) converged normally after 220 iterations
Number of observations 507
Estimator ML Robust
Minimum Function Test Statistic 587.480 532.237
Degrees of freedom 234 234
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.104
for the Satorra-Bentler correction
Model test baseline model:
Minimum Function Test Statistic 5175.970 2907.974
Degrees of freedom 290 290
P-value 0.000 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 0.928 0.886
Tucker-Lewis Index (TLI) 0.910 0.859
Robust Comparative Fit Index (CFI) 0.929
Robust Tucker-Lewis Index (TLI) 0.912
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -24378.783 -24378.783
Loglikelihood unrestricted model (H1) -24085.043 -24085.043
Number of free parameters 96 96
Akaike (AIC) 48949.566 48949.566
Bayesian (BIC) 49355.503 49355.503
Sample-size adjusted Bayesian (BIC) 49050.788 49050.788
Root Mean Square Error of Approximation:
RMSEA 0.055 0.050
90 Percent Confidence Interval 0.049 0.060 0.045 0.056
P-value RMSEA <= 0.05 0.084 0.475
Robust RMSEA 0.053
90 Percent Confidence Interval 0.047 0.059
Standardized Root Mean Square Residual:
SRMR 0.047 0.047
Parameter Estimates:
Information Expected
Standard Errors Robust.sem
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FC =~
F1 1.000 1.860 0.895
F3 1.035 0.041 24.945 0.000 1.926 1.204
F5 1.039 0.052 20.055 0.000 1.932 1.027
C4 0.976 0.051 19.239 0.000 1.816 1.047
C5 1.049 0.044 23.817 0.000 1.951 1.205
EP =~
E3 1.000 1.968 0.954
E4 1.022 0.035 29.454 0.000 2.011 1.006
E5 0.896 0.048 18.703 0.000 1.764 0.835
P5 0.960 0.045 21.280 0.000 1.889 0.785
AC =~
A2 1.000 1.920 0.772
A3 0.833 0.054 15.364 0.000 1.600 0.640
A4 1.114 0.058 19.085 0.000 2.139 0.915
A5 1.105 0.061 18.257 0.000 2.123 0.857
RES =~
RESIS1_R 1.000 2.499 0.865
RESIS2_R 1.072 0.051 21.075 0.000 2.678 1.178
RESIS3_R 1.062 0.054 19.639 0.000 2.654 1.145
OM_M =~
OM_M1 1.000 0.570 0.253
OM_M2 0.967 0.054 18.020 0.000 0.551 0.241
OM_M3 0.911 0.056 16.289 0.000 0.519 0.229
CLF =~
F1 1.000 1.000 0.481
F3 (cmb) 1.000 1.000 0.625
F5 (cmb) 1.000 1.000 0.531
C4 (cmb) 1.000 1.000 0.577
C5 (cmb) 1.000 1.000 0.618
E3 (cmb) 1.000 1.000 0.485
E4 (cmb) 1.000 1.000 0.500
E5 (cmb) 1.000 1.000 0.473
P5 (cmb) 1.000 1.000 0.416
A2 (cmb) 1.000 1.000 0.402
A3 (cmb) 1.000 1.000 0.400
A4 (cmb) 1.000 1.000 0.428
A5 (cmb) 1.000 1.000 0.404
RESIS1_R (cmb) 1.000 1.000 0.346
RESIS2_R (cmb) 1.000 1.000 0.440
RESIS3_R (cmb) 1.000 1.000 0.432
OM_M1 (cmb) 1.000 1.000 0.445
OM_M2 (cmb) 1.000 1.000 0.438
OM_M3 (cmb) 1.000 1.000 0.441
Marker 0.486 0.396 1.229 0.219 0.333 0.333
Marker =~
KM_gbrk_ (cmb) 1.000 1.461 1.000
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FC ~
OM_M (c1) -0.490 0.136 -3.613 0.000 -0.150 -0.150
LEEFTIJD 0.024 0.011 2.213 0.027 0.013 0.163
GESLACHT_ 0.322 0.191 1.684 0.092 0.173 0.077
GESLACHT_ -0.140 0.665 -0.211 0.833 -0.075 -0.005
WERKERVAR -0.015 0.009 -1.694 0.090 -0.008 -0.092
RULEOBEDI -0.037 0.049 -0.744 0.457 -0.020 -0.050
EP ~
OM_M (c2) -0.335 0.138 -2.416 0.016 -0.097 -0.097
LEEFTIJD 0.017 0.011 1.588 0.112 0.009 0.110
GESLACHT_ 0.273 0.230 1.186 0.235 0.139 0.062
GESLACHT_ 0.840 0.391 2.146 0.032 0.427 0.027
WERKERVAR 0.013 0.010 1.289 0.197 0.007 0.074
RULEOBEDI -0.069 0.052 -1.321 0.186 -0.035 -0.088
AC ~
OM_M (c3) -0.120 0.114 -1.052 0.293 -0.036 -0.036
LEEFTIJD 0.012 0.009 1.366 0.172 0.006 0.083
GESLACHT_ -0.056 0.221 -0.254 0.800 -0.029 -0.013
GESLACHT_ -1.949 2.685 -0.726 0.468 -1.015 -0.064
WERKERVAR -0.004 0.009 -0.451 0.652 -0.002 -0.025
RULEOBEDI -0.036 0.050 -0.730 0.465 -0.019 -0.047
RES ~
OM_M (a) -1.354 0.294 -4.601 0.000 -0.309 -0.309
LEEFTIJD -0.009 0.010 -0.842 0.400 -0.004 -0.045
GESLACHT_ -0.344 0.220 -1.567 0.117 -0.138 -0.061
GESLACHT_ 1.557 1.674 0.930 0.352 0.623 0.039
WERKERVAR 0.007 0.011 0.600 0.549 0.003 0.029
RULEOBEDI 0.247 0.061 4.025 0.000 0.099 0.249
FC ~
RES (b1) 0.412 0.135 3.040 0.002 0.553 0.553
EP ~
RES (b2) 0.298 0.130 2.295 0.022 0.379 0.379
AC ~
RES (b3) 0.309 0.104 2.978 0.003 0.402 0.402
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.FC ~~
.EP 1.864 0.433 4.303 0.000 0.717 0.717
.AC 1.204 0.322 3.742 0.000 0.470 0.470
.EP ~~
.AC 1.492 0.341 4.374 0.000 0.482 0.482
.FC ~~
Marker -0.482 0.439 -1.098 0.272 -0.239 -0.239
.EP ~~
Marker -0.403 0.433 -0.930 0.353 -0.165 -0.165
.AC ~~
Marker -0.354 0.341 -1.040 0.298 -0.147 -0.147
.RES ~~
Marker -0.853 0.976 -0.874 0.382 -0.271 -0.271
OM_M ~~
Marker -1.131 1.004 -1.127 0.260 -1.440 -1.440
CLF 1.461 0.193 7.573 0.000 2.563 2.563
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.F1 5.484 0.583 9.403 0.000 5.484 2.637
.F3 7.057 0.615 11.476 0.000 7.057 4.413
.F5 6.643 0.614 10.818 0.000 6.643 3.530
.C4 7.279 0.593 12.286 0.000 7.279 4.199
.C5 6.662 0.623 10.693 0.000 6.662 4.115
.E3 6.476 0.579 11.188 0.000 6.476 3.139
.E4 6.691 0.595 11.251 0.000 6.691 3.347
.E5 5.941 0.534 11.133 0.000 5.941 2.813
.P5 5.678 0.561 10.117 0.000 5.678 2.360
.A2 4.863 0.497 9.775 0.000 4.863 1.954
.A3 3.935 0.420 9.360 0.000 3.935 1.575
.A4 5.956 0.561 10.624 0.000 5.956 2.549
.A5 5.108 0.551 9.267 0.000 5.108 2.063
.RESIS1_RC 4.840 0.669 7.237 0.000 4.840 1.675
.RESIS2_RC 3.387 0.681 4.973 0.000 3.387 1.490
.RESIS3_RC 3.388 0.677 5.008 0.000 3.388 1.462
.OM_M1 5.489 0.101 54.539 0.000 5.489 2.442
.OM_M2 5.156 0.102 50.741 0.000 5.156 2.257
.OM_M3 5.118 0.100 51.089 0.000 5.118 2.259
.KM_gebruik_urn 1.682 0.065 25.884 0.000 1.682 1.151
.FC 0.000 0.000 0.000
.EP 0.000 0.000 0.000
.AC 0.000 0.000 0.000
.RES 0.000 0.000 0.000
OM_M 0.000 0.000 0.000
CLF 0.000 0.000 0.000
Marker 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
CLF 1.000 1.000 1.000
.F1 2.925 0.278 10.506 0.000 2.925 0.676
.F3 1.019 0.174 5.846 0.000 1.019 0.398
.F5 1.988 0.369 5.391 0.000 1.988 0.561
.C4 1.697 0.341 4.984 0.000 1.697 0.565
.C5 1.026 0.197 5.212 0.000 1.026 0.392
.E3 1.541 0.225 6.854 0.000 1.541 0.362
.E4 1.157 0.195 5.934 0.000 1.157 0.290
.E5 2.283 0.239 9.553 0.000 2.283 0.512
.P5 3.293 0.355 9.265 0.000 3.293 0.569
.A2 3.079 0.271 11.343 0.000 3.079 0.497
.A3 3.991 0.281 14.214 0.000 3.991 0.640
.A4 1.638 0.244 6.720 0.000 1.638 0.300
.A5 2.364 0.305 7.755 0.000 2.364 0.386
.RESIS1_RC 5.063 0.362 13.981 0.000 5.063 0.606
.RESIS2_RC 1.238 0.231 5.354 0.000 1.238 0.239
.RESIS3_RC 1.531 0.277 5.528 0.000 1.531 0.285
.OM_M1 0.808 0.166 4.864 0.000 0.808 0.160
.OM_M2 1.088 0.210 5.187 0.000 1.088 0.209
.OM_M3 1.204 0.216 5.568 0.000 1.204 0.234
.KM_gebruik_urn 0.000 0.000 0.000
.FC 2.148 0.460 4.671 0.000 0.621 0.621
.EP 3.147 0.476 6.604 0.000 0.813 0.813
.AC 3.051 0.412 7.399 0.000 0.827 0.827
.RES 5.214 1.710 3.049 0.002 0.835 0.835
OM_M 0.325 0.375 0.866 0.387 1.000 1.000
Marker 1.899 0.404 4.703 0.000 0.889 0.889
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ab1 -0.558 0.290 -1.926 0.054 -0.171 -0.171
ab2 -0.404 0.252 -1.604 0.109 -0.117 -0.117
ab3 -0.418 0.218 -1.922 0.055 -0.124 -0.124
> inspect(fit.CMB.marker, "cov.lv")
FC EP AC RES OM_M CLF Marker
FC 3.460
EP 2.786 3.872
AC 2.084 2.127 3.688
RES 2.690 1.894 1.911 6.243
OM_M -0.340 -0.240 -0.175 -0.440 0.325
CLF -1.531 -1.078 -0.787 -1.978 1.461 1.000
Marker -0.393 -0.347 -0.391 -0.283 -0.421 0.486 2.136
> CMB.marker <- '
+ #define DVs
+ FC =~ F1 + F3 + F5 + C4 + C5
+ EP =~ E3 + E4 + E5 + P5
+ AC =~ A2 + A3 + A4 + A5
+
+ #define M
+ RES =~ RESIS1_RC + RESIS2_RC + RESIS3_RC
+
+ #define IV
+ OM_M =~ OM_M1 + OM_M2 + OM_M3
+
+ #covariances DV (all measure 1 dimension of inspection style)
+ FC ~~ EP
+ FC ~~ AC
+ AC ~~ EP
+
+ #direct effect
+ FC ~ c1*OM_M + LEEFTIJD + RULEOBEDIENCE
+ EP ~ c2*OM_M + LEEFTIJD + WERKERVARING
+ AC ~ c3*OM_M + LEEFTIJD + GESLACHT_D_VROUW
+
+ #mediation b/w IV and 3 DV
+ #indirect effects
+ RES ~ a*OM_M + RULEOBEDIENCE #only rule obedience correlated with resistance
+ FC ~ b1*RES
+ EP ~ b2*RES
+ AC ~ b3*RES
+ ab1 := a*b1
+ ab2 := a*b2
+ ab3 := a*b3
+
+ #define common latent variable
+ #constraining factor loadings to be equal
+ CLF =~ F1 + cmb*F3 + cmb*F5 + cmb*C4 + cmb*C5 +
+ cmb*E3 + cmb*E4 + cmb*E5 + cmb*P5 +
+ cmb*A2 + cmb*A3 + cmb*A4 + cmb*A5 +
+ cmb*RESIS1_RC + cmb*RESIS2_RC + cmb*RESIS3_RC +
+ cmb*OM_M1 + cmb*OM_M2 + cmb*OM_M3 +
+ Marker
+
+ #contraining variance of CLF to be 1
+ CLF ~~ 1*CLF
+
+ #adding marker variable: KM_gebruik_uren
+ #constraining factor loadings to be equal
+ Marker =~ cmb*KM_gebruik_uren
+ #covary with other latent variables
+ Marker ~~ FC
+ Marker ~~ EP
+ Marker ~~ AC
+ Marker ~~ RES
+ Marker ~~ OM_M
+
+ '
> fit.CMB.marker <- cfa(CMB.marker,
+ data = NVWA2016,
+ estimator="MLM")
Warning message:
In lav_object_post_check(object) :
lavaan WARNING: covariance matrix of latent variables
is not positive definite;
use inspect(fit,"cov.lv") to investigate.
> summary(fit.CMB.marker, standardized=TRUE, fit.measures=TRUE)
lavaan (0.5-23.1097) converged normally after 149 iterations
Number of observations 507
Estimator ML Robust
Minimum Function Test Statistic 596.408 508.883
Degrees of freedom 227 227
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.172
for the Satorra-Bentler correction
Model test baseline model:
Minimum Function Test Statistic 5165.641 2777.151
Degrees of freedom 270 270
P-value 0.000 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 0.925 0.888
Tucker-Lewis Index (TLI) 0.910 0.866
Robust Comparative Fit Index (CFI) 0.929
Robust Tucker-Lewis Index (TLI) 0.916
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -25079.037 -25079.037
Loglikelihood unrestricted model (H1) -24780.834 -24780.834
Number of free parameters 83 83
Akaike (AIC) 50324.075 50324.075
Bayesian (BIC) 50675.041 50675.041
Sample-size adjusted Bayesian (BIC) 50411.589 50411.589
Root Mean Square Error of Approximation:
RMSEA 0.057 0.049
90 Percent Confidence Interval 0.051 0.062 0.044 0.055
P-value RMSEA <= 0.05 0.024 0.555
Robust RMSEA 0.054
90 Percent Confidence Interval 0.047 0.060
Standardized Root Mean Square Residual:
SRMR 0.050 0.050
Parameter Estimates:
Information Expected
Standard Errors Robust.sem
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FC =~
F1 1.000 1.636 0.785
F3 1.042 0.051 20.467 0.000 1.705 1.061
F5 1.044 0.065 15.987 0.000 1.707 0.906
C4 0.969 0.061 15.773 0.000 1.585 0.910
C5 1.057 0.055 19.272 0.000 1.730 1.065
EP =~
E3 1.000 1.816 0.876
E4 1.029 0.043 23.748 0.000 1.869 0.930
E5 0.878 0.054 16.155 0.000 1.594 0.753
P5 0.942 0.055 17.008 0.000 1.711 0.712
AC =~
A2 1.000 1.755 0.707
A3 0.817 0.058 14.192 0.000 1.434 0.575
A4 1.150 0.069 16.639 0.000 2.019 0.863
A5 1.152 0.073 15.780 0.000 2.021 0.812
RES =~
RESIS1_R 1.000 2.318 0.800
RESIS2_R 1.072 0.056 19.245 0.000 2.485 1.094
RESIS3_R 1.053 0.059 17.889 0.000 2.442 1.058
OM_M =~
OM_M1 1.000 0.827 0.366
OM_M2 0.952 0.059 16.162 0.000 0.787 0.345
OM_M3 0.889 0.061 14.566 0.000 0.735 0.326
CLF =~
F1 1.000 1.000 0.480
F3 (cmb) 1.000 1.000 0.622
F5 (cmb) 1.000 1.000 0.531
C4 (cmb) 1.000 1.000 0.574
C5 (cmb) 1.000 1.000 0.616
E3 (cmb) 1.000 1.000 0.483
E4 (cmb) 1.000 1.000 0.498
E5 (cmb) 1.000 1.000 0.473
P5 (cmb) 1.000 1.000 0.416
A2 (cmb) 1.000 1.000 0.403
A3 (cmb) 1.000 1.000 0.401
A4 (cmb) 1.000 1.000 0.427
A5 (cmb) 1.000 1.000 0.402
RESIS1_R (cmb) 1.000 1.000 0.345
RESIS2_R (cmb) 1.000 1.000 0.440
RESIS3_R (cmb) 1.000 1.000 0.433
OM_M1 (cmb) 1.000 1.000 0.443
OM_M2 (cmb) 1.000 1.000 0.438
OM_M3 (cmb) 1.000 1.000 0.443
Marker 0.432 0.328 1.319 0.187 0.296 0.296
Marker =~
KM_gbrk_ (cmb) 1.000 1.461 1.000
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FC ~
OM_M (c1) -0.558 0.125 -4.479 0.000 -0.282 -0.282
LEEFTIJD 0.011 0.008 1.433 0.152 0.007 0.088
RULEOBEDI 0.014 0.027 0.502 0.616 0.008 0.021
EP ~
OM_M (c2) -0.423 0.128 -3.304 0.001 -0.193 -0.193
LEEFTIJD 0.007 0.009 0.782 0.434 0.004 0.051
WERKERVAR 0.023 0.007 3.246 0.001 0.013 0.142
AC ~
OM_M (c3) -0.175 0.108 -1.623 0.105 -0.083 -0.083
LEEFTIJD 0.009 0.007 1.202 0.230 0.005 0.063
GESLACHT_ -0.204 0.184 -1.108 0.268 -0.116 -0.052
RES ~
OM_M (a) -1.152 0.199 -5.788 0.000 -0.411 -0.411
RULEOBEDI 0.245 0.060 4.077 0.000 0.106 0.266
FC ~
RES (b1) 0.259 0.103 2.516 0.012 0.366 0.366
EP ~
RES (b2) 0.143 0.095 1.514 0.130 0.183 0.183
AC ~
RES (b3) 0.195 0.077 2.535 0.011 0.257 0.257
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.FC ~~
.EP 1.563 0.354 4.417 0.000 0.681 0.681
.AC 0.961 0.248 3.883 0.000 0.426 0.426
.EP ~~
.AC 1.228 0.268 4.574 0.000 0.436 0.436
.FC ~~
Marker -0.521 0.438 -1.190 0.234 -0.275 -0.275
.EP ~~
Marker -0.471 0.440 -1.071 0.284 -0.200 -0.200
.AC ~~
Marker -0.370 0.333 -1.113 0.266 -0.159 -0.159
.RES ~~
Marker -0.639 0.734 -0.871 0.384 -0.227 -0.227
OM_M ~~
Marker -0.937 0.776 -1.208 0.227 -0.812 -0.812
CLF 1.313 0.138 9.495 0.000 1.588 1.588
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.F1 5.669 0.444 12.766 0.000 5.669 2.720
.F3 7.241 0.471 15.366 0.000 7.241 4.505
.F5 6.829 0.471 14.511 0.000 6.829 3.623
.C4 7.467 0.453 16.499 0.000 7.467 4.285
.C5 6.846 0.477 14.338 0.000 6.846 4.215
.E3 6.519 0.458 14.238 0.000 6.519 3.146
.E4 6.727 0.471 14.289 0.000 6.727 3.347
.E5 5.997 0.417 14.392 0.000 5.997 2.834
.P5 5.736 0.438 13.091 0.000 5.736 2.387
.A2 4.831 0.404 11.970 0.000 4.831 1.946
.A3 3.920 0.339 11.572 0.000 3.920 1.572
.A4 5.896 0.466 12.645 0.000 5.896 2.520
.A5 5.041 0.461 10.935 0.000 5.041 2.026
.RESIS1_RC 4.448 0.489 9.103 0.000 4.448 1.535
.RESIS2_RC 2.966 0.470 6.311 0.000 2.966 1.306
.RESIS3_RC 2.986 0.464 6.432 0.000 2.986 1.294
.OM_M1 5.489 0.101 54.539 0.000 5.489 2.430
.OM_M2 5.156 0.102 50.741 0.000 5.156 2.259
.OM_M3 5.118 0.100 51.089 0.000 5.118 2.269
.KM_gebruik_urn 1.682 0.065 25.884 0.000 1.682 1.151
.FC 0.000 0.000 0.000
.EP 0.000 0.000 0.000
.AC 0.000 0.000 0.000
.RES 0.000 0.000 0.000
OM_M 0.000 0.000 0.000
CLF 0.000 0.000 0.000
Marker 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
CLF 1.000 1.000 1.000
.F1 2.918 0.278 10.512 0.000 2.918 0.672
.F3 1.021 0.174 5.860 0.000 1.021 0.395
.F5 1.985 0.371 5.353 0.000 1.985 0.559
.C4 1.703 0.342 4.985 0.000 1.703 0.561
.C5 1.024 0.200 5.128 0.000 1.024 0.388
.E3 1.542 0.228 6.761 0.000 1.542 0.359
.E4 1.136 0.197 5.757 0.000 1.136 0.281
.E5 2.294 0.239 9.589 0.000 2.294 0.512
.P5 3.304 0.356 9.282 0.000 3.304 0.572
.A2 3.130 0.276 11.340 0.000 3.130 0.508
.A3 4.016 0.279 14.393 0.000 4.016 0.646
.A4 1.604 0.249 6.452 0.000 1.604 0.293
.A5 2.313 0.318 7.278 0.000 2.313 0.374
.RESIS1_RC 5.049 0.365 13.836 0.000 5.049 0.601
.RESIS2_RC 1.228 0.240 5.128 0.000 1.228 0.238
.RESIS3_RC 1.547 0.276 5.609 0.000 1.547 0.291
.OM_M1 0.792 0.173 4.592 0.000 0.792 0.155
.OM_M2 1.094 0.215 5.092 0.000 1.094 0.210
.OM_M3 1.213 0.219 5.547 0.000 1.213 0.238
.KM_gebruik_urn 0.000 0.000 0.000
.FC 1.840 0.382 4.819 0.000 0.688 0.688
.EP 2.863 0.413 6.930 0.000 0.868 0.868
.AC 2.773 0.366 7.570 0.000 0.900 0.900
.RES 4.086 0.811 5.035 0.000 0.760 0.760
OM_M 0.684 0.273 2.504 0.012 1.000 1.000
Marker 1.949 0.328 5.935 0.000 0.913 0.913
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ab1 -0.298 0.155 -1.917 0.055 -0.151 -0.151
ab2 -0.165 0.128 -1.285 0.199 -0.075 -0.075
ab3 -0.224 0.115 -1.952 0.051 -0.106 -0.106
> inspect(fit.CMB.marker, "cov.lv")
FC EP AC RES OM_M CLF Marker
FC 2.675
EP 2.114 3.297
AC 1.447 1.553 3.081
RES 1.855 1.112 1.191 5.375
OM_M -0.586 -0.402 -0.273 -0.788 0.684
CLF -1.124 -0.773 -0.525 -1.513 1.313 1.000
Marker -0.370 -0.345 -0.347 -0.213 -0.370 0.432 2.136
I do not get why and how to fix this. Can anyone help me?
Best,
Noortje
Terrence Jorgensen
Apr 5, 2017, 4:56:01 AM4/5/17
to lavaan
I indeed find negative covariances between my latent variables
Negative covariances are not an indication of a nonpositive definite matrix. Negative variances are (you have none of those) and out-of-bounds correlations are (i.e., > +/-1). You can check for out-of-bounds correlations with lavInspect(fit, "cor.lv"). But you can have a NPD matrix even if neither of those particular "Heywood cases" are present. If your variances and correlations are all within their natural boundaries, then your NPD matrix could have linear dependencies (redundancies, conceptually).
I do not get why and how to fix this. Can anyone help me?
NPD matrices can be due to sampling error, or due to model misspecification.
- To investigate whether misspecification is a plausible explanation, you can test the fit of your model(s). To narrow down the source of misspecification, you can first fit a CFA. Since the latent structure is saturated, all misfit is due to misspecification in the measurement model. You may have to reconceptualize the measurement model before proceeding to test hypotheses about the latent constructs your hope are represented by your measurement model. After establishing satisfactory fit in your CFA, then you can test the structural hypotheses by comparing the fit of the latent regression model to the CFA model. Any decrement in fit will be due to imposing structural constraints. This is sometimes called "the 2-step approach", and you can find more about it in the literature or by asking around on SEMNET.
- To investigate whether sampling error is a plausible explanation, you can check whether the 95% CI of an out-of-bounds estimate includes plausible values. If you find a correlation > 1, you can transform the lower confidence limit of the covariance estimate into a correlation metric by dividing by its respective SDs. http://journals.sagepub.com/doi/abs/10.1177/0049124112442138
Terrence D. Jorgensen
Postdoctoral Researcher, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
UvA web page: http://www.uva.nl/profile/t.d.jorgensen
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