Help for bayesian SEM

Modeling
1

I am trying to test an interaction term within an SEM framework using lavaan by creating a product indicator. However, a Heywood case occurred, so I am attempting to resolve this using the Bayesian approach.

While running the Bayesian SEM, I encountered several error messages, and I would like some advice on how to address them:

  1. Would it be better to increase the number of chains, or should I increase alpha_delta? I’ve read that increasing alpha_delta is a last resort, so I’m hesitant to do so.
  2. When I ran a CFA without the interaction term, the model fit was acceptable. But once I added the interaction term, variables related to friend_bond started having estimation issues. Would it be reasonable to remove those variables? I’m concerned that arbitrarily removing variables might be statistically problematic.
  3. I used the default prior distributions because I’m not very familiar with setting them. Should I modify them?

Please excuse my English, as I used a translator.

Below is the model specification:

##family:Physic_health (13~20 + )
subj_dat <- indProd(subj_dat, var1 = 13:20, var2 = c("health", "health_satis"), match = FALSE,
                    meanC = TRUE, residualC = FALSE, doubleMC = TRUE)

##friend_bond:Physic_health (21~24 + )
subj_dat <- indProd(subj_dat, var1 = 21:24, var2 = c("health", "health_satis"), match = FALSE,
                    meanC = TRUE, residualC = FALSE, doubleMC = TRUE)

##family_bond:Mental_health (13~24 + )
subj_dat <- indProd(subj_dat, var1 = 13:20, var2 = c("stress", "depress"), match = FALSE,
                    meanC = TRUE, residualC = FALSE, doubleMC = TRUE)

##friend_bond:Mental_health (21~24 + )
subj_dat <- indProd(subj_dat, var1 = 21:24, var2 = c("stress", "depress"), match = FALSE,
                    meanC = TRUE, residualC = FALSE, doubleMC = TRUE)


intmodel <- "
              ##latent_var
              Physic_health =~ health + health_satis
              Mental_health =~ stress + depress
              family_bond =~ family_bond_253+family_bond_254+family_bond_255+family_bond_256
                             +family_bond_257+family_bond_258+family_bond_259+family_bond_260
              friend_bond =~ friend_bond_271+friend_bond_272
              
              ##int_var
              family_bond_Physic_health =~ family_bond_253.health + family_bond_253.health_satis + family_bond_254.health 
                                          + family_bond_254.health_satis + family_bond_255.health + family_bond_255.health_satis 
                                          + family_bond_256.health + family_bond_256.health_satis + family_bond_257.health 
                                          + family_bond_257.health_satis + family_bond_258.health + family_bond_258.health_satis 
                                          + family_bond_259.health + family_bond_259.health_satis + family_bond_260.health 
                                          + family_bond_260.health_satis

              family_bond_Mental_health =~ family_bond_253.stress + family_bond_253.depress + family_bond_254.stress + 
                                          family_bond_254.depress + family_bond_255.stress + family_bond_255.depress + 
                                          family_bond_256.stress + family_bond_256.depress + family_bond_257.stress + 
                                          family_bond_257.depress + family_bond_258.stress + family_bond_258.depress + 
                                          family_bond_259.stress + family_bond_259.depress + family_bond_260.stress + 
                                          family_bond_260.depress
              
              friend_bond_Physic_health =~ friend_bond_263.health + friend_bond_263.health_satis + friend_bond_264.health +
                                          friend_bond_264.health_satis + friend_bond_271.health + friend_bond_271.health_satis 
                                          + friend_bond_272.health + friend_bond_272.health_satis
              
              friend_bond_Mental_health =~ friend_bond_263.stress + friend_bond_263.depress + friend_bond_264.stress + 
                                          friend_bond_264.depress + friend_bond_271.stress + friend_bond_271.depress + 
                                          friend_bond_272.stress + friend_bond_272.depress


              #regression
              suic_ideation ~ Physic_health + Mental_health + family_bond + friend_bond +
                             family_bond_Physic_health + family_bond_Mental_health +
                             friend_bond_Physic_health + friend_bond_Mental_health
                    
            "

blav_cfa_fit <- bcfa(intmodel, data=subj_dat, n.chains = 5)
summary(blav_cfa_fit, standardized = TRUE, rsquare = TRUE)
fitmeasures(blav_cfa_fit)

And here are the results:

1: blavaan WARNING: the chains may not have converged. 
2: 
591 (23.5%) p_waic estimates greater than 0.4. We recommend trying loo instead. 
3: Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.
 
4: blavaan WARNING: some effective number of parameter computations are < 0. This may indicate prior-data conflict or other model problems. 
> summary(blav_cfa_fit)$psrf %>% 
+   as.data.frame() %>% 
+   filter(Point.Estimate > 1.1 | is.na(Point.Estimate))
blavaan 0.5.8 did NOT end normally after 1000 iterations
** WARNING ** Estimates below are most likely unreliable

  Estimator                                      BAYES
  Optimization method                             MCMC
  Number of model parameters                       161

  Number of observations                          2510

  Statistic                                 MargLogLik         PPP
  Value                                     -155596.980       0.000

Parameter Estimates:


Latent Variables:
                               Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       
  Physic_health =~                                                                         
    health                        1.000                                                    
    health_satis                  3.347    0.318    2.797    4.046    1.002    normal(0,10)
  Mental_health =~                                                                         
    stress                        1.000                                                    
    depress                       3.590    0.327    3.023    4.304    1.009    normal(0,10)
  family_bond =~                                                                           
    family_bnd_253                1.000                                                    
    family_bnd_254                1.006    0.040    0.927    1.086    1.007    normal(0,10)
    family_bnd_255                1.199    0.045    1.112    1.291    1.011    normal(0,10)
    family_bnd_256                1.170    0.042    1.090    1.256    1.012    normal(0,10)
    family_bnd_257                1.194    0.042    1.112    1.281    1.009    normal(0,10)
    family_bnd_258                1.150    0.040    1.068    1.233    1.006    normal(0,10)
    family_bnd_259                1.061    0.039    0.989    1.138    1.014    normal(0,10)
    family_bnd_260                1.091    0.037    1.020    1.166    1.007    normal(0,10)
  friend_bond =~                                                                           
    friend_bnd_271                1.000                                                    
    friend_bnd_272                1.357    0.060    1.212    1.445    1.036    normal(0,10)
  family_bond_Physic_health =~                                                             
    fmly_bnd_253.h                1.000                                                    
    fmly_bnd_253._                3.227    0.144    2.968    3.519    1.021    normal(0,10)
    fmly_bnd_254.h                0.755    0.048    0.663    0.852    1.005    normal(0,10)
    fmly_bnd_254._                2.622    0.133    2.370    2.893    1.011    normal(0,10)
    fmly_bnd_255.h                1.146    0.057    1.041    1.263    1.009    normal(0,10)
    fmly_bnd_255._                3.639    0.159    3.341    3.971    1.005    normal(0,10)
    fmly_bnd_256.h                1.101    0.055    0.995    1.212    1.006    normal(0,10)
    fmly_bnd_256._                3.598    0.160    3.306    3.930    1.013    normal(0,10)
    fmly_bnd_257.h                1.125    0.056    1.020    1.236    1.005    normal(0,10)
    fmly_bnd_257._                3.579    0.156    3.289    3.900    1.012    normal(0,10)
    fmly_bnd_258.h                1.074    0.053    0.969    1.181    1.007    normal(0,10)
    fmly_bnd_258._                3.434    0.152    3.145    3.746    1.010    normal(0,10)
    fmly_bnd_259.h                1.011    0.049    0.918    1.112    1.006    normal(0,10)
    fmly_bnd_259._                3.376    0.148    3.096    3.668    1.006    normal(0,10)
    fmly_bnd_260.h                1.181    0.054    1.078    1.292    1.008    normal(0,10)
    fmly_bnd_260._                3.694    0.155    3.410    4.020    1.013    normal(0,10)
  family_bond_Mental_health =~                                                             
    fmly_bnd_253.s                1.000                                                    
    fmly_bnd_253.d                1.998    0.121    1.775    2.238    1.163    normal(0,10)
    fmly_bnd_254.s                0.888    0.036    0.819    0.963    1.005    normal(0,10)
    fmly_bnd_254.d                1.786    0.126    1.554    2.042    1.122    normal(0,10)
    fmly_bnd_255.s                1.246    0.045    1.166    1.334    1.008    normal(0,10)
    fmly_bnd_255.d                2.553    0.148    2.288    2.859    1.152    normal(0,10)
    fmly_bnd_256.s                1.154    0.042    1.077    1.241    1.006    normal(0,10)
    fmly_bnd_256.d                2.254    0.135    2.010    2.534    1.147    normal(0,10)
    fmly_bnd_257.s                1.130    0.041    1.050    1.214    1.006    normal(0,10)
    fmly_bnd_257.d                2.292    0.134    2.046    2.572    1.120    normal(0,10)
    fmly_bnd_258.s                1.125    0.041    1.048    1.210    1.004    normal(0,10)
    fmly_bnd_258.d                2.337    0.140    2.087    2.631    1.166    normal(0,10)
    fmly_bnd_259.s                0.910    0.035    0.844    0.981    1.006    normal(0,10)
    fmly_bnd_259.d                1.787    0.119    1.575    2.041    1.152    normal(0,10)
    fmly_bnd_260.s                1.018    0.037    0.949    1.094    1.014    normal(0,10)
    fmly_bnd_260.d                2.052    0.123    1.827    2.303    1.159    normal(0,10)
  friend_bond_Physic_health =~                                                             
    frnd_bnd_263.h                1.000                                                    
    frnd_bnd_263._                2.885    0.146    2.607    3.177    1.014    normal(0,10)
    frnd_bnd_264.h                1.142    0.064    1.014    1.271    1.018    normal(0,10)
    frnd_bnd_264._                3.028    0.168    2.713    3.374    1.036    normal(0,10)
    frnd_bnd_271.h                1.542    0.074    1.404    1.688    1.005    normal(0,10)
    frnd_bnd_271._                4.435    0.262    3.938    4.960    1.042    normal(0,10)
    frnd_bnd_272.h                1.596    0.073    1.459    1.744    1.003    normal(0,10)
    frnd_bnd_272._                4.590    0.264    4.105    5.119    1.039    normal(0,10)
  friend_bond_Mental_health =~                                                             
    frnd_bnd_263.s                1.000                                                    
    frnd_bnd_263.d                3.012    1.852    1.273    6.067    5.565    normal(0,10)
    frnd_bnd_264.s                1.300    0.118    1.050    1.517    1.118    normal(0,10)
    frnd_bnd_264.d                3.283    1.882    1.463    6.459    5.141    normal(0,10)
    frnd_bnd_271.s                2.137    0.621    1.190    2.895    4.413    normal(0,10)
    frnd_bnd_271.d                5.320    3.856    1.849   11.719    5.810    normal(0,10)
    frnd_bnd_272.s                2.290    0.675    1.250    3.111    4.409    normal(0,10)
    frnd_bnd_272.d                5.315    3.735    1.951   11.503    5.752    normal(0,10)

Regressions:
                   Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       
  suic_ideation ~                                                              
    Physic_health    -0.010    0.013   -0.037    0.017    1.006    normal(0,10)
    Mental_health     0.044    0.013    0.016    0.071    1.015    normal(0,10)
    family_bond      -0.016    0.009   -0.033    0.001    1.010    normal(0,10)
    friend_bond       0.006    0.005   -0.004    0.015    1.002    normal(0,10)
    fmly_bnd_Phys_    0.028    0.016   -0.003    0.059    1.008    normal(0,10)
    fmly_bnd_Mntl_   -0.055    0.009   -0.073   -0.038    1.011    normal(0,10)
    frnd_bnd_Phys_    0.002    0.019   -0.037    0.038    1.015    normal(0,10)
    frnd_bnd_Mntl_    0.013    0.022   -0.025    0.063    1.062    normal(0,10)

Covariances:
                               Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       
  Physic_health ~~                                                                         
    Mental_health                 0.053    0.006    0.042    0.066    1.004     lkj_corr(1)
    family_bond                  -0.038    0.005   -0.048   -0.030    1.005     lkj_corr(1)
    friend_bond                  -0.029    0.005   -0.039   -0.019    1.003     lkj_corr(1)
    fmly_bnd_Phys_               -0.011    0.002   -0.015   -0.007    1.004     lkj_corr(1)
    fmly_bnd_Mntl_               -0.001    0.003   -0.007    0.004    1.003     lkj_corr(1)
    frnd_bnd_Phys_               -0.006    0.002   -0.009   -0.003    1.002     lkj_corr(1)
    frnd_bnd_Mntl_               -0.001    0.002   -0.005    0.002    1.255     lkj_corr(1)
  Mental_health ~~                                                                         
    family_bond                  -0.066    0.007   -0.079   -0.053    1.009     lkj_corr(1)
    friend_bond                  -0.038    0.006   -0.051   -0.025    1.010     lkj_corr(1)
    fmly_bnd_Phys_               -0.004    0.002   -0.009   -0.000    1.005     lkj_corr(1)
    fmly_bnd_Mntl_               -0.011    0.004   -0.019   -0.003    1.006     lkj_corr(1)
    frnd_bnd_Phys_               -0.004    0.002   -0.008    0.000    1.004     lkj_corr(1)
    frnd_bnd_Mntl_                0.001    0.002   -0.004    0.005    1.089     lkj_corr(1)
  family_bond ~~                                                                           
    friend_bond                   0.035    0.005    0.027    0.045    1.006     lkj_corr(1)
    fmly_bnd_Phys_                0.006    0.002    0.003    0.010    1.002     lkj_corr(1)
    fmly_bnd_Mntl_                0.006    0.003    0.001    0.012    1.005     lkj_corr(1)
    frnd_bnd_Phys_                0.003    0.002   -0.000    0.006    1.002     lkj_corr(1)
    frnd_bnd_Mntl_                0.002    0.002   -0.001    0.006    1.080     lkj_corr(1)
  friend_bond ~~                                                                           
    fmly_bnd_Phys_                0.002    0.002   -0.003    0.006    1.005     lkj_corr(1)
    fmly_bnd_Mntl_                0.003    0.004   -0.004    0.011    1.009     lkj_corr(1)
    frnd_bnd_Phys_                0.001    0.002   -0.003    0.005    1.013     lkj_corr(1)
    frnd_bnd_Mntl_               -0.007    0.003   -0.011   -0.001    1.314     lkj_corr(1)
  family_bond_Physic_health ~~                                                             
    fmly_bnd_Mntl_                0.013    0.002    0.011    0.017    1.011     lkj_corr(1)
    frnd_bnd_Phys_                0.012    0.001    0.010    0.014    1.005     lkj_corr(1)
    frnd_bnd_Mntl_                0.002    0.001   -0.000    0.004    1.532     lkj_corr(1)
  family_bond_Mental_health ~~                                                             
    frnd_bnd_Phys_                0.003    0.001    0.001    0.006    1.005     lkj_corr(1)
    frnd_bnd_Mntl_                0.013    0.003    0.007    0.019    2.074     lkj_corr(1)
  friend_bond_Physic_health ~~                                                             
    frnd_bnd_Mntl_                0.007    0.002    0.004    0.011    2.246     lkj_corr(1)

Variances:
                   Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       
   .health            0.272    0.012    0.249    0.295    1.001 gamma(1,.5)[sd]
   .health_satis      0.860    0.103    0.641    1.050    1.002 gamma(1,.5)[sd]
   .stress            0.524    0.020    0.486    0.564    1.008 gamma(1,.5)[sd]
   .depress           2.941    0.194    2.545    3.294    1.003 gamma(1,.5)[sd]
   .family_bnd_253    0.188    0.006    0.177    0.201    1.007 gamma(1,.5)[sd]
   .family_bnd_254    0.273    0.009    0.256    0.290    1.016 gamma(1,.5)[sd]
   .family_bnd_255    0.281    0.009    0.264    0.300    1.002 gamma(1,.5)[sd]
   .family_bnd_256    0.264    0.009    0.247    0.284    1.022 gamma(1,.5)[sd]
   .family_bnd_257    0.241    0.008    0.226    0.257    1.001 gamma(1,.5)[sd]
   .family_bnd_258    0.242    0.008    0.227    0.257    1.000 gamma(1,.5)[sd]
   .family_bnd_259    0.193    0.006    0.180    0.206    1.011 gamma(1,.5)[sd]
   .family_bnd_260    0.156    0.005    0.146    0.167    1.003 gamma(1,.5)[sd]
   .friend_bnd_271    0.228    0.013    0.199    0.248    1.031 gamma(1,.5)[sd]
   .friend_bnd_272    0.019    0.020    0.000    0.069    1.041 gamma(1,.5)[sd]
   .fmly_bnd_253.h    0.098    0.003    0.092    0.104    1.013 gamma(1,.5)[sd]
   .fmly_bnd_253._    0.481    0.015    0.453    0.511    1.003 gamma(1,.5)[sd]
   .fmly_bnd_254.h    0.134    0.004    0.127    0.142    1.005 gamma(1,.5)[sd]
   .fmly_bnd_254._    0.629    0.019    0.593    0.664    1.006 gamma(1,.5)[sd]
   .fmly_bnd_255.h    0.143    0.004    0.135    0.152    1.011 gamma(1,.5)[sd]
   .fmly_bnd_255._    0.554    0.017    0.521    0.589    1.000 gamma(1,.5)[sd]
   .fmly_bnd_256.h    0.134    0.004    0.126    0.142    1.020 gamma(1,.5)[sd]
   .fmly_bnd_256._    0.579    0.018    0.545    0.614    1.002 gamma(1,.5)[sd]
   .fmly_bnd_257.h    0.136    0.004    0.128    0.144    1.000 gamma(1,.5)[sd]
   .fmly_bnd_257._    0.523    0.017    0.490    0.558    1.003 gamma(1,.5)[sd]
   .fmly_bnd_258.h    0.129    0.004    0.121    0.136    1.007 gamma(1,.5)[sd]
   .fmly_bnd_258._    0.563    0.018    0.529    0.600    1.009 gamma(1,.5)[sd]
   .fmly_bnd_259.h    0.098    0.003    0.092    0.104    1.003 gamma(1,.5)[sd]
   .fmly_bnd_259._    0.442    0.014    0.416    0.471    1.007 gamma(1,.5)[sd]
   .fmly_bnd_260.h    0.100    0.003    0.094    0.106    1.002 gamma(1,.5)[sd]
   .fmly_bnd_260._    0.381    0.013    0.356    0.406    1.010 gamma(1,.5)[sd]
   .fmly_bnd_253.s    0.159    0.006    0.149    0.171    1.081 gamma(1,.5)[sd]
   .fmly_bnd_253.d    1.354    0.045    1.266    1.444    1.094 gamma(1,.5)[sd]
   .fmly_bnd_254.s    0.207    0.007    0.195    0.220    1.055 gamma(1,.5)[sd]
   .fmly_bnd_254.d    1.805    0.060    1.657    1.916    1.091 gamma(1,.5)[sd]
   .fmly_bnd_255.s    0.230    0.008    0.215    0.247    1.074 gamma(1,.5)[sd]
   .fmly_bnd_255.d    1.991    0.068    1.858    2.122    1.078 gamma(1,.5)[sd]
   .fmly_bnd_256.s    0.209    0.008    0.194    0.225    1.133 gamma(1,.5)[sd]
   .fmly_bnd_256.d    1.724    0.056    1.617    1.834    1.077 gamma(1,.5)[sd]
   .fmly_bnd_257.s    0.205    0.007    0.191    0.219    1.083 gamma(1,.5)[sd]
   .fmly_bnd_257.d    1.709    0.058    1.600    1.821    1.084 gamma(1,.5)[sd]
   .fmly_bnd_258.s    0.210    0.007    0.196    0.224    1.082 gamma(1,.5)[sd]
   .fmly_bnd_258.d    1.776    0.061    1.660    1.897    1.125 gamma(1,.5)[sd]
   .fmly_bnd_259.s    0.174    0.006    0.163    0.186    1.095 gamma(1,.5)[sd]
   .fmly_bnd_259.d    1.434    0.047    1.341    1.530    1.087 gamma(1,.5)[sd]
   .fmly_bnd_260.s    0.158    0.006    0.147    0.170    1.155 gamma(1,.5)[sd]
   .fmly_bnd_260.d    1.283    0.045    1.196    1.374    1.114 gamma(1,.5)[sd]
   .frnd_bnd_263.h    0.083    0.003    0.078    0.089    1.011 gamma(1,.5)[sd]
   .frnd_bnd_263._    0.479    0.016    0.450    0.512    1.004 gamma(1,.5)[sd]
   .frnd_bnd_264.h    0.138    0.004    0.130    0.147    1.003 gamma(1,.5)[sd]
   .frnd_bnd_264._    0.660    0.021    0.621    0.703    1.010 gamma(1,.5)[sd]
   .frnd_bnd_271.h    0.130    0.005    0.121    0.141    1.051 gamma(1,.5)[sd]
   .frnd_bnd_271._    0.533    0.027    0.481    0.584    1.028 gamma(1,.5)[sd]
   .frnd_bnd_272.h    0.128    0.005    0.119    0.138    1.040 gamma(1,.5)[sd]
   .frnd_bnd_272._    0.547    0.030    0.492    0.610    1.036 gamma(1,.5)[sd]
   .frnd_bnd_263.s    0.177    0.011    0.161    0.198    2.119 gamma(1,.5)[sd]
   .frnd_bnd_263.d    1.278    0.179    1.011    1.497    4.642 gamma(1,.5)[sd]
   .frnd_bnd_264.s    0.280    0.021    0.250    0.317    2.553 gamma(1,.5)[sd]
   .frnd_bnd_264.d    1.985    0.192    1.678    2.241    3.435 gamma(1,.5)[sd]
   .frnd_bnd_271.s    0.201    0.105    0.106    0.344   14.510 gamma(1,.5)[sd]
   .frnd_bnd_271.d    1.842    0.684    0.929    2.509   11.856 gamma(1,.5)[sd]
   .frnd_bnd_272.s    0.209    0.121    0.099    0.374   14.995 gamma(1,.5)[sd]
   .frnd_bnd_272.d    1.736    0.653    0.859    2.384   11.242 gamma(1,.5)[sd]
   .suic_ideation     0.013    0.000             0.014    1.002 gamma(1,.5)[sd]
    Physic_health     0.097    0.011    0.076    0.120    1.002 gamma(1,.5)[sd]
    Mental_health     0.151    0.018    0.117    0.187    1.007 gamma(1,.5)[sd]
    family_bond       0.145    0.009    0.128    0.162    1.010 gamma(1,.5)[sd]
    friend_bond       0.268    0.016    0.239    0.300    1.019 gamma(1,.5)[sd]
    fmly_bnd_Phys_    0.035    0.003    0.030    0.040    1.015 gamma(1,.5)[sd]
    fmly_bnd_Mntl_    0.108    0.007    0.095    0.121    1.040 gamma(1,.5)[sd]
    frnd_bnd_Phys_    0.028    0.002    0.023    0.033    1.026 gamma(1,.5)[sd]
    frnd_bnd_Mntl_    0.028    0.010    0.012    0.042    2.994 gamma(1,.5)[sd]
2

This looks like a common situation where the sign indeterminacy of the loadings leads to model nonconvergence. This is a place where it can be helpful to use more informative priors.

If you expect all your observed variables to be positively correlated with each other, I would recommend something like a normal(1, .4) prior on the free loadings. The rationale is that you are already fixing one loading to +1 (hence the prior mean), and the sd of .4 represents your expectation that the observed variables will be positively correlated. You would add the following argument to the bcfa call:

dp = dpriors(lambda = "normal(1, .4)")

Some more discussion is at the links below

1 Like
3

Hi, @JJJff and welcome to the Stan forums.

Just a heads up that lavaan and blavaan are not Stan projects, so this might not be the best place to get help for them. I’d try to help, but I don’t know SEM or the blavaan package. Here’s the official site for blavaan:

I was surprised to see that we did publish a case study for blavaan:

4

blavaan uses Stan internally and it’s listed on the redesigned Stan website as a tool built on Stan (Stan Toolkit – Stan), so I think it’s fair game for a Stan case study. As far as I know we don’t have a strict requirement that a case study involve writing Stan code by hand rather than using a package to generate the code.

(Or maybe I misinterpreted what you meant by “surprised”?)

5

Depending on the type of SEM you are looking at working with I know the brms package (based on Stan) will run piece-wise (?) SEM models. I’d be happy to share my R code and data (a simplified model of the full one we use) so you can see if that will work for you. I find building them in brms works better for my brain.

1 Like
6

I see you are using the double mean center method to create the interaction indicators. I think you could also use the residual method

residualC = TRUE

When using the residual indicator products you can then fix the factor correlations to 0, making the model smaller (hopefully easier to estimate). You fix the factor correlations between the interaction factor and their respective “main” factors to 0, as these relations have been remove by the residuals method