Analyzing LV1 and LV2 Interaction with Clustered Standard Errors

[Sanghyo Han]

Hello,

I have a multilevel dataset with individuals at Level 1 (LV1) and villages at Level 2 (LV2), and I am interested in the interaction between LV1 and LV2 variables. However, the average number of individuals per village is quite low. Specifically, I have approximately 4,000 individuals and 600 villages, resulting in an average of 6.7 individuals per village. Even if I were to use counties instead of villages as the Level 2 unit, there are still only 170 counties, leading to an average of 23.5 individuals per county.

Given this data structure, I believe that conducting a multilevel analysis might be challenging. (Am I right?)

As a result, I am considering using the clustered standard errors approach. However, I am unsure whether this method is appropriate for analyzing the interaction between LV1 and LV2 variables. Can I still analyze the interaction between LV1 and LV2 variables using clustered standard errors, or would this approach be unsuitable for that purpose?

Thank you for your guidance.

[Erik Ruzek]

You have a more than adequate sample size for multilevel analysis! Your model of interest would be specified in Stata as follows:

mixed DV LV1_var##LV2_var || LV2_cluster: LV1_var, cov(un)

This formulation allows for the slope of the LV1 variable to vary across LV2 clusters and with the interaction term, tests whether the slope variance can be explained by the LV2_var. Note that for subsequent use of handy postestimation techniques, such as margins, you will want to indicate the nature of the variables involved in the interaction. Use i. for categorical variables and c. for continuous variables.

[Sanghyo Han]

Erik, thank you for your advice. If you don't mind, I'd like to ask one more question. My LV1 variable is a nominal variable with four categories, and LV2 is a continuous variable. In this case, when I use the command mixed DV i.LV1_var##c.LV2_var || LV2_cluster: i.LV1_var, cov(un), the results show the variance of three variables and the constant, along with six covariances, but the estimates are extremely small. Additionally, the standard errors and 95% confidence intervals are not provided and are simply displayed as ".". In such a situation, is it still appropriate to use the cov(un) option?

[Erik Ruzek]

Is it that the model gives you confidence intervals when you exclude the random effect covariances? If that is the case, then I would probably omit cov(un) from the specification. It is possible that there is not much variance in the LV1 predictor by group and asking for covariances on top of that is a bridge too far. In general, when you have sizeable between group variance in a slope (whether a continuous or categorical predictor), you should be able to get reliable covariance estimates.