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I am trying to replicate a study that created a structural equation model (SEM) to explain effects on the intention to reduce meat consumption. The interactions of the latent variables are as follows:

  1. mident affects att, norm, pbcon, and redint.
  2. att, norm, and pbcon also affect redint. att, norm, pbcon, and redint were measured with 3 items each, while mident was measured with 2 items. All items used 5-point Likert scales.

I implemented this in R via the lavaan function:

m_free <-    'mident =~ identity1_0 + identity2_0
              att =~ attitude1_0 + attitude2_0 + attitude3_0 
              norm =~ injnorm1 + injnorm2 + injnorm3
              pbcon =~ pbc1_0 + pbc2_0 + pbc3_0
              redint =~ intention1_0 + intention2_0 + intention3_0
              
              identity1_0~1       
              identity2_0~1
                
              identity1_0~~identity1_0   
              identity2_0~~identity2_0
              
              attitude1_0~1       
              attitude2_0~1
              attitude3_0~1
              
              attitude1_0~~attitude1_0   
              attitude2_0~~attitude2_0
              attitude3_0~~attitude3_0
              
              injnorm1~1       
              injnorm2~1
              injnorm3~1
              
              injnorm1~~injnorm1  
              injnorm2~~injnorm2
              injnorm3~~injnorm3
              
              pbc1_0~1       
              pbc2_0~1
              pbc3_0~1
              
              pbc1_0~~pbc1_0  
              pbc2_0~~pbc2_0
              pbc3_0~~pbc3_0
              
              intention1_0~1       
              intention2_0~1
              intention3_0~1
              
              intention1_0~~intention1_0  
              intention2_0~~intention2_0
              intention3_0~~intention3_0
              
              mident~0       
              mident~~1*mident
              
              att~0       
              att~~1*att
              
              norm~0       
              norm~~1*norm
              
              pbcon~0         
              pbcon~~1*pbcon
              
              redint~0       
              redint~~1*redint
              
              # Regressions
              att~a*mident
              norm~d*mident
              pbcon~f*mident
              redint~b*att + c*mident + e*norm + g*pbcon
              
              d_mident := c
              ind_mident_att := a*b
              ind_mident_norm := d*e
              ind_mident_pbcon := f*g
              total := (a*b) + c + (d*e) + (f*g)
'
fit_m_free <- lavaan(model = m_free,
                         data = Indikatoren,
                         estimator = "DWLS")
summary(fit_m_free, fit.measures=TRUE, standardized= TRUE, rsquare=TRUE)

The model fit seems acceptable (CFI = 0.957, TLI = 0.945, RMSEA = 0.075, SRMR = 0.062) But the effects are huge compared to the study I am replicating. Most concerning is that the effect for mident goes into the opposite direction of what is theoretically plausible. I found out that att and mident show a strong negative correlation (with moderate negative correlations for their items) so this might explain it, but this shouldn't affect all the other variables. Moreover, I have 2.439 observations so sample size should also not be a problem. Therefore, I thought that I might have wrongly specified something in my code although nothing seems out of place to me. So my question is: Is there a mistake in my code or should I further investigate my data for some possible cause?

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  • $\begingroup$ If this is a SEM, why not use sem()? There are defaults in sem() not present in lavaan() that are easy to miss but are required for fitting an SEM the usual way. Try this and see if the results change. $\endgroup$
    – Noah
    Commented Nov 13, 2023 at 18:28
  • 1
    $\begingroup$ What do your correlations look like? If the effects are huge, then you should have some pretty high correlations. $\endgroup$
    – Jeremy Miles
    Commented Nov 13, 2023 at 19:01
  • $\begingroup$ @JeremyMiles The correlations between the latent variables based on predicted values from the path model have correlations between -0.26 and -0.89 on the negative side and between 0.23 and 0.65 on the positive side. Correlations for the items behind these latent variables are smaller. $\endgroup$
    – nioco
    Commented Nov 15, 2023 at 12:11
  • $\begingroup$ @Noah That really did make a difference. Thank you! $\endgroup$
    – nioco
    Commented Nov 15, 2023 at 12:14
  • $\begingroup$ I didn't mean latent variable correlations. The correlations in your raw data. But it sounds like your problem is solved anyway. $\endgroup$
    – Jeremy Miles
    Commented Nov 15, 2023 at 15:26

1 Answer 1

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Could the implausible negative association be due to a coding problem at the item level? Does this unexpected sign of the association occur both at the zero-order (bivariate) correlation level and in the path model? If not, then one explanation may be suppression. Suppressor effects can cause path coefficients to have the opposite sign relative to the corresponding zero-order correlation. This can happen when independent variables for the same outcome are strongly correlated.

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  • $\begingroup$ The item coding and correlations for mident, att and redint are correct. Interestingly, when I predict factor scores based on the path model and use these to correlate the latent variables redint and mident are moderately negatively correlated. So, the positive relationship between redint and mident only exists for the regression coefficients. A suppressor effect seems like a good idea because when I delete the regression of att on mident the regression of redint on mident becomes negative. Also the correlation between att and mident is -0.89. Do you have advice on how to handle this? $\endgroup$
    – nioco
    Commented Nov 15, 2023 at 12:05
  • $\begingroup$ Taking a look at the following paper may be useful for you: Maassen, G. H., & Bakker, A. B. (2001). Suppressor variables in path models: Definitions and interpretations. Sociological Methods & Research, 30(2), 241-270. isonderhouden.nl/doc/pdf/arnoldbakker/articles/… $\endgroup$
    – Christian Geiser
    Commented Nov 15, 2023 at 16:03

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