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I have a dataset containing information on district wise monthly dengue incidence from 2010 to 2021. I have found that there is a sudden increase in the dengue incidence due to a new variant in 2019. I am trying to fit a model to identify the factors affecting dengue incidence, and I applied time series regression. The data were not stationary, therefore I included the differencing transformation on the data. But the model violated both the normality assumption and the auto correlation assumption. I included first log in to the model and it solved the auto correlation problem. But even with the log transformation the model did not satisfy the normality assumption. As the data are both time series and cross sectional, I tried using panel data regression but the model still violated the normality assumption. I think this could be because of the outliers present in the data, however since this is time series, data I cannot remove the outliers.

Following are the residual plots of the time series regression model.

enter image description here

My supervisor suggested that I should consider the simplest method and try to treat for the normality assumption violation rather than look for new methods. But I still cant find any solution for this problem. Does anyone have an idea about what approach I should take?

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  • $\begingroup$ Normality is irrelevant -- and forcing your data to look Normal will only be counterproductive. You appear to have the chance to discover something, because you have nine cases (represented by the circles in the upper left of the Residuals vs. Fitted plot) whose values greatly exceed their predictions. Study those cases for information about what makes them special. Removing the outliers, as you suggest, might ruin this opportunity. $\endgroup$
    – whuber
    Jan 8 at 14:43
  • $\begingroup$ Could you tell us how "incidence" is measured ? It looks to me like the distribution of the response variable might be bimodal, am I wrong ? $\endgroup$
    – CaroZ
    Jan 8 at 14:55
  • $\begingroup$ @whuber Thank you for your comment. While I understand your advice, the objective of this project was to identify the factors affecting dengue incidence. Therefore I was asked to fit a valid model that explains the model. Would applying a structural break approach work in this situation? I will look for any insights I can gain through the residual plots also. $\endgroup$ Jan 8 at 16:01
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    $\begingroup$ I suppose you are correct in saying that they both have the same objective. As you said, interestingly the outlying data all seemed to be coming from districts belonging to one province. I tried including the province as one of the variables in the model but still, the assumptions are violated. // And I'm sorry I got confused earlier, it is a bimodal response. $\endgroup$ Jan 8 at 17:31
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    $\begingroup$ "I tried including the province as one of the variables in the model" - not bad an idea, and a good start to arrive at a more informative model. Can you by following @whuber 's initial suggestion try to nail down further what distinguishes the outlying from the not outlying data within that province? This assumes that there can be made such a distinction between non-outlying and outlying, otherwise you could try to model a larger variance within the province. Step by step try to add things to your model that explain the irregularities. $\endgroup$ Jan 12 at 10:35

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Your variable is a ratio, I do not see the point in transforming anything to meet model assumptions. Better use an appropriate model. I would approach it differently. In the dataset, I would have one column per variable you want to test, one column for district, one column for the month. and then one column "infected" with the number of infected people. Then I would have an other column "uninfected" which is total population minus infected.

Then I would run a binomial glm with the district as a random factor (that is, a glmer) with the cbind function, which in R would look something like glmer(cbind(infected,uninfected)~month +(1|district), family=binomial)

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  • $\begingroup$ Re "do not see the point:" Ratios often are better analyzed in terms of their logs, roots, or folded versions thereof (which includes the logit). From that perspective (assuming the counts are unavailable), I do not see the point of not transforming the ratios! $\endgroup$
    – whuber
    Jan 9 at 14:59

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