RE: Reducing RMSEA and Chisquare values

[JanHK]

Dear Lavaan and SEM experts,

I am new to lavaan (and SEM in general), so please bear with me.

I basically have a design where I am looking at the effect of invasive species on soil nutrients and microbial communities across a bunch of sites (see data attached and R code). I already know that the invasives definitely alter the communities in terms of composition as well as altering some soil nutrients. Now I would really like to see whether the invasives alter the microbe communities directly, i.e. potentially because of altered mutualistic associations, or indirectly, i.e. via a changed soil nutrient pathway (since the invasives can change soil nutrient levels, and the bacteria can then respond to this).

At first I made a latent variable model (model 1) where I grouped the soil variables as one latent variable (i.e. "soil"), and used it as predictor for change in community composition (either the of the first or second axes of an NMDS ordination as composition; the same idea would go for determining the effects of invasives on bacterial species richness and diversity). But I keep getting very significant chi-square values, so I thought my model was wrong. So the other option I have is based upon comments from an author of a paper who did something similar who told me that he did not include any latent variables in his model, which is why I dropped them and used direct paths. But I still get highly significant chi-square values and high RMSEA. Does this mean that none of these models are usable? Or is there a way to remedy the situation?

Many thanks in advance!

[Edward Rigdon]

Jan--

     Both of your models propose that all joint variation in aspects of soil condition is due to invasion. In the absence of invasion, one would expect NO covariation among these different aspects of soil quality, according to both models. Is that what you mean to assert? This is the core reason why both models perform poorly--because both imply this same condition. The statistical model is also linear for all variables--it does not allow for linear effects for some elements of soil quality but nonlinear effects for other aspects of soil quality. If you did not intend to impose such constraints, then these models are definitely wrong for your research.

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[JanHK]

Many thanks for the reply Edward. Excuse my lack of knowledge but what do you mean when you say "all joint variation in aspects of soil condition is due to invasion"? Basically, what I at least want to show with these models is that the presence of invasion causes the soil communities to change, either by directly changing the composition (the plants associate with their own set of bacteria and thus when they dominate they change the soil communities) OR that the plants change the chemistry of the soil and that then induces change in the soil communities. So do you mean I should make the soil variables to co-vary, as in adding double headed arrows between them? Also, with the nonlinear effects, do mean that I should include polynomials?

Thanks again for your insight!

[Edward Rigdon]

Jan--

     In a factor model with observed variables A and B that load on the same (standardized) common factor f (via parameters loading A and loading B) and no other paths between A and B, then the covariance of A and B is equal to the product loading A * loading B. Covariance among each pair of observed variables that load on the same factor f must be equal to the product of the two variables' loadings, and nothing else. Failure to conform to this constraint contributes mightily to lack of fit. Your second model implies that covariance between pairs of soil quality variables is due solely to their joint dependence on invasion, so each covariance is a product of regression slopes. There is also random sampling error, of course, but both models imply some very restrictive constraints, which may well explain poor results.

     From your description, it sounds more like you are looking for differences in values of soil quality variables across the no invasion / invasion condition--something more like an ANCOVA than either of these models. I am sure you would not mind if patterns emerged in the ways that the different soil quality variables change in response to invasion, but I am thinking that you do not currently have any specific patterns in mind. Probably those patterns will represent a middle ground between a argely unconstrained ANCOVA and a highly constrained factor model or model 2.

[JanHK]

Okay many thanks again Edward for all your insights. So are you saying that you think SEM models are just not the way to go for this idea/analysis? Also, there is definitely random sampling error that should be included, but I am not sure how to include it in the code. Thing is, I am definitely looking for differences in values of soil quality variables across the no invasion / invasion condition, but I have already done other analyses (PERMANOVA for community and normal ANOVA for soil variables) that show the invasion changes the bacterial communities and soil chemistry, respectively, but the SEM model would have been ideal to show which of the two pathways are strongest: either that invasion directly affects bacterial community composition or that it does so indirectly via first altering soil chemistry. That would be an ideal outcome...