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I have a dataset with annual observations (1990-2016) on neonatal mortality rates (dependent variable) for countries 1, 2, 3, 4, 5, and 6. The independent variables are indicators 1, 2, 3, 4, and 5. You can download the dataset here.

Given that observations are not independent, the data follow a hierarchical structure, and since I have longitudinal data/repeated observations, I decided to carry out a mixed-effects linear regression to explore the impact of these national indicators on neonatal mortality rates over the 27 year period in Stata.

mixed neomortality indicator1 indicator2 indicator3 indicator4 indicator5 year || country_id:

As you can see, I added random effects for the variable country_id. The intraclass correlation coefficient is 0.49.

Output in STATA

My questions are related to whether this analysis is correct from a statistical point of view or not:

1) Is it correct to add random effects to country_id, or should I have added random effects to other variables?

2) Since this is longitudinal data, I included the variable year in the model, otherwise there would be no way to account for time in the model. Is this correct?

3) When writing a scientific paper, how should the results from this type of model be reported? I reported the regression coefficients, the 95% CI and the p-value for both the crude and adjusted model (all 5 indicators included, no further variables were included). I also reported the results from the LR test, the ICC, and the Akaike and Bayesian information criteria. Please comment on whether I missed something or if, for example, AIC and BIC are not usually reported for this type of models:

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Thank you so much in advance for your time and help!!!

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  • $\begingroup$ I am voting to reopen, as the questions are clearly statistical, and have almost nothing to do with Stata. $\endgroup$ – Robert Long Nov 23 '19 at 14:17
  • $\begingroup$ With only 6 countries, you need to be very careful. Small numbers of clusters in multilevel models requires corrections to standard errors for fixed effect estimates. In Stata, you should add the options REML and kroger to your mixed model to get the appropriate corrections. $\endgroup$ – Erik Ruzek Dec 6 '19 at 18:56
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1) Is it correct to add random effects to country_id,

Yes, this is a good way to model the non-independence of observations within each country. Observations within each country will be more similar to each other than observations in other countries - that is they will be correlated, and the ICC (intra-class correlation coefficient) estimates this. With an ICC of 49% this is quite substantial.

or should I have added random effects to other variables?

The model you have fitted specifies random intercepts for country. There is no other clustering in your dataset, so the only other possibilities are random slopes for the other fixed effects. For this, you should be guided by the theory of the data generation process. A random slope for a variable means that each country can have it's own slope for the variable in question. If this makes sense, then you could go ahead and do this, however you may then encounter problems with model convergence.

2) Since this is longitudinal data, I included the variable year in the model, otherwise there would be no way to account for time in the model. Is this correct?

Again yes, your model output indicates that there is a negative association of time with the outcome. You could also look at a non-linear association with time by, for example, adding a quadratic term.

When writing a scientific paper, how should the results from this type of model be reported? I reported the regression coefficients, the 95% CI and the p-value for both the crude and adjusted model (all 5 indicators included, no further variables were included). I also reported the results from the LR test, the ICC, and the Akaike and Bayesian information criteria. Please comment on whether I missed something or if, for example, AIC and BIC are not usually reported for this type of models:

AIC and BIC would not normally be reported. Your target journal should have some guidance for what to include. Personally I would not report p-values, but other than that I would go ahead with the statistics you mentioned.

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