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In a study, an outcome variable has three categories. There are several factors in the study. We are determining how these factors influence the outcome variable.We have fitted multiple logistic regression and calculated relative risk ratio to determine whether a factor is significant risk factor for the outcome variable.

If there were only one country in this study, the statistical analysis so far described were enough. But, the problem is we have several countries, we are doing the same statistical analysis to determine which factors are significant for the outcome variable.

Now, we want to compare among the countries. How can we compare among the countries? Is there any statistical measurement by which we can compare among countries. Could you please share any reference where several countries were being compared?

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    $\begingroup$ You need some sort of nonlinear multilevel model. These are fairly complex to run correctly and interpret, but they have been discussed here a lot. See the multilevel analysis tag. stats.stackexchange.com/questions/tagged/multilevel-analysis The description of that tag is "Statistical analysis of datasets comprising several levels of hierarchy (e.g., students nested in classes nested in schools or hierarchical forecasting). For questions about mixed models use [mixed-model] tag. For nested random effects, use [nested-data]. " $\endgroup$
    – Peter Flom
    Commented Jan 14 at 18:35

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As @Peter Flom says, some sort of nonlinear multilevel model is needed. Though the type of nonlinear multilevel model depends on whether your outcome is ordinal or nominal. If your data is ordinal (e.g., Likert scale data), then a multilevel ordinal regression would be appropriate. See Bauer & Sterba (2011) for an accessible introduction to this method and also see Habibov & Afandi (2011) for an application that involves different countries. If your data is nominal (i.e., unordered categories such as gender identity or favorite sports team) then consider the multilevel nominal response model. No applications of this model come to mind, though both Anderson, Kim, & Keller (2014) and Hedeker (2008) introduce it well.

References

Anderson, C. J., Kim, J. S., & Keller, B. (2014). Multilevel modeling of categorical response variables. Handbook of international large-scale assessment: Background, technical issues, and methods of data analysis, 481-519.

Bauer, D. J., & Sterba, S. K. (2011). Fitting multilevel models with ordinal outcomes: performance of alternative specifications and methods of estimation. Psychological methods, 16(4), 373.

Habibov, N. N., & Afandi, E. N. (2011). Self-rated health and social capital in transitional countries: Multilevel analysis of comparative surveys in Armenia, Azerbaijan, and Georgia. Social Science & Medicine, 72(7), 1193-1204.

Hedeker, D. (2008). Multilevel models for ordinal and nominal variables. In Handbook of multilevel analysis (pp. 237-274). New York, NY: Springer New York.

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    $\begingroup$ The references are really very helpful. Thanks. $\endgroup$
    – user232597
    Commented Jan 22 at 15:37
  • $\begingroup$ Great! Glad they helped. $\endgroup$
    – Preston Botter
    Commented Jan 22 at 17:40

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