interpreting standardized constants in sem

[Rod McCrea]

Hi, does anyone know how to interpret a standardized constant in sem?

When I run two equivalent models with sem and regress (see code below), the beta coefficients for the variables are the same. However, there is no standardized constant in regress (i.e., it is zero). That makes sense to me, but I am unsure how to interpret standardized coefficients in sem.

code:
regress balance_pursue benefit_financial benefits_infrastructure benefits_employ_community impacts_living_costs impacts_environment impacts_other_industries, beta
sem (balance_pursue <- benefit_financial benefits_infrastructure benefits_employ_community impacts_living_costs impacts_environment impacts_other_industries), standardize

The sem code above is part of a larger path analysis.

Much appreciated, Rod

[Phil Bromiley]

You didn't get a quick answer. This usually means you'd do better if you followed the FAQ on asking questions - provide Stata code in code delimiters, Stata output, and sample data using dataex.

I don't quite see what your question is. If you're getting the same coefficients in regress and sem, why wouldn't you discuss them the same way? By the way, several commentators on this website are generally in favor of non-standardized variables particularly if the metric of the measures is meaningful - just makes interpretation easier.

[Rod McCrea]

Thanks Phil

I get the same coefficient values in sem and regress for the standardized 'slopes', but I also get a non-zero estimate of a standardized 'constant' term in sem which I don't know how to interpret.

In regress, the standardized constant 'goes away' (or is zero) because when all the standardised predictors are zero (or at their mean), the standardized criterion is also zero (or at it's mean) as the line of prediction passes through the means of the predictors and criterion variables. This makes sense to me, but this does not sem to apply in sem for some reason.

I prefer to interpret the standardised coefficients because the variables are on different scales and I want to compare their relative predictive strength, even though standardised coefficients are an imperfect measure of relative predictive strength.
Rod

[Marcos Almeida]

From the Stata Manual:

regress simply reports standardized coefficients in an extra column. All other results are reported in unstandardized form. sem updates the entire output with the standardized values.

I believe the constant "disappears" under regress because the spotlight with "beta" option is the coefficient. On the other hand, sem just "unveils" this secret. We know the interpretation of the coefficients is similar to the unstandardized regression, where "one-unit" of each predictor is changed into "one SD". Being this true, I believe that, considering the beta coefficients under regress are equal to the standardized coefficients under sem, it shall also be true that the constant represents SDs of Y where the SD for the predictors is zero.

[Rod McCrea]

Hi Marcos. I can see now that the standardized constant is simply a measure of the unstandardized constant in units of Y's SD.

The SD of Y is 1.407709 using my example above, and the unstandardized constant (1.8575537) is the standardised constant (1.319558) multiplied by the SD of Y.

Thanks for helping me make sense of the standardized constant in sem. Rod

[Marcos Almeida]

Hello Rod,

Thank you for informing you consider the thread reached its closure.

[Clayton Neighbors]

I had a very similar question to the one Rod posted. It seems to me that if one has no missing data on any variables, standardized results should have intercepts of exactly zero, at least when no latent variables are in a model. I was running a model with missing data and using mlmv (fiml) and trying to get standardized results but the intercepts weren't really very close to zero. As a solution I constructed the following instructions:
To get perfectly standardized results with mlmv: 1) Run an sem model with only your variables listed, no single headed arrows. Stata will suggest you let them all be correlated, which is fine. The results will provide you with estimated means and variances using FIML. 2) Use estimated means and variances to generate zscores for all variables (gen zvar=(var-[mean])/sqrt(var[variance]). 3) Run your actual model with the zvariables. All predictors should have means of 0 and variances of 1. Intercepts will be exactly zero.