Non-linear Model vs Linear Model for a dataset I have a time series dataset for a city. The dataset contains rainfall amount and the number of repairman requests to a company. The company has 20 shops in different blocks of city and the rainfall data is also individually available for all 20 block. One point to consider is that rainfall is seasonal , hence when there is a rainfall in one block there is a high probability that there will be rainfall in some other block. Also it is assumed that a person in a given block will always place a request in the shop present nearest to him
I am trying to establish a relationship between the amount of rainfall and the number of repairman requests in that city at a block level. 
I am getting good results when I model the aggregated data for the whole city using a linear model. In contrast when I model the data on individual block level using linear model, the results are not that good. Hence I have to use non linear models when establishing a relationship on block level. 
What I want to do is to try to justify the use of non linear model instead of linear model for modelling relationship at a block level. One method which I feel could provide the justification is that 'law of large number' is not applicable at a block level of city but is applicable when the whole city is considered as a single unit.
Is this justification correct? Or do I need a different justification?
What sort of analysis do I need to perform  to support the justification?
 A: I am too "young" to join the discussion in the comments, so I will post my ideas and guesses as an answer.
I think there are better ways to estimate model fit (and hence justify it) than appealing to asymptotic laws. For example, you can fit a model an inspect the prediction errors. Or you can do cross validation and figure out which of the models has a better predictive capabilities.
In your case, it seems that you have already (somehow) determined that pooled linear model is inadequate and want to go to block level. I don't know why it didn't work, but I can guess - you have too little data on a block level and individual-block-regressions model overfits. If that is the case, the decision to go to individual-block-nonlinear-model is slightly suspicious, as you could overfit even more. Maybe you could consider an approach like hierarchical regression, which regularizes individual regressions.
When you are happy about the block level fit, then it is only appropriate to plot errors over time, and look if time is significant predictor. If it is, you can include it into the model as well.
