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I'm looking at the NMMAPS dataset, where pollution levels were measured in several cities over multiple days. I want to create a model to see which characteristics are linked to high pollution levels. Instead of creating a traditional model with all the data points, I thought of splitting the data into cities. Then I wanted to use the same model on each of these data sets and then finally combine the CI of each of the coefficients in order to find a new CI (by taking their intersections).

Would this be a valid approach?

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    $\begingroup$ Short answer: this is invalid. You should rater use single hierarchical regression model. $\endgroup$
    – Tim
    Commented Apr 29, 2018 at 16:17
  • $\begingroup$ @Tim On a similar note, would it be valid if you wanted to find out which variables are significant? $\endgroup$
    – user139790
    Commented Apr 29, 2018 at 16:27
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    $\begingroup$ I agree with @Tim that a hierarchical regression model is appropriate here - you can think of this type of model as essentially a collection of city-specific models. The city-specific models can be set up so that they allow the effects of each pollutant to be different across cities. The hierarchical regression model would produce an estimates of the pollutant effects for a "typical" city but also give an indication of how variable the effects of the other cities would be about these effects. $\endgroup$
    – Isabella Ghement
    Commented Apr 29, 2018 at 16:52
  • $\begingroup$ Check if this answers your question: stats.stackexchange.com/questions/205359/… $\endgroup$
    – Tim
    Commented Apr 30, 2018 at 9:25
  • $\begingroup$ What do you hope to accomplish by splitting and then re-aggregating coefficients that a single model cannot handle? If you insist on splitting, you could also consider Zellner's seemingly unrelated regression or multivariate regression, where each city's outcome is a variable. $\endgroup$
    – dimitriy
    Commented Jun 5 at 20:30

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You might be better off using a hierarchical model. If your sample size is too large, you can use the split sample approach.

Here is an extract from an article by Molenberghs, Verbeke and Iddi (2011) titled "Pseudo-likelihood methodology for partitioned large and complex samples".

Here is the abstract verbatim

Large data sets, either coming from a large number of independent replications, or because of hierarchies in the data with large numbers of within-unit replication, may pose challenges to the data analyst up to the point of making conventional inferential methods, such as maximum likelihood, prohibitive. Based on general pseudo-likelihood concepts, we propose a method to partition such a set of data, analyze each partition member, and properly combine the inferences into a single one. It is shown that the method is fully efficient for independent partitions, while with dependent sub-samples efficiency is sometimes but not always equal to one. It is argued that, for important realistic settings, efficiency is often very high. Illustrative examples enhance insight in the method’s operation, while real-data analysis underscores its power for practice.

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