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I'm working with household survey data where households report their expenditure for various products. The goal is to look into income elasticities for various products thus in essence I'm interested in households' expenditure given their incomes.

The problem is to find a consistent approach in determining which product categories are invalid for this type of analysis. By invalid I mean the following: suppose we have two products - milk and lobsters. It would be quite reasonable to assume that as households consume much more milk than lobsters, the given sample will be more likely to depict the households' behaviour towards their purchases of milk rather than lobsters throughout the income spectrum.

I could try to look at for example variation in expenditure among households for a given product by analysing coefficients of variation or somehow look at variance of the dependent variable in linear regression like expenditure ~ income or even more simply I could look at the sample sizes for each product category (that is, how many households reported buying a particular good). However, I wonder if there is a consistent statistical approach to this kind of problem in determining the 'validity' of product categories? Any suggestions or references would be very helpful.

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    $\begingroup$ I think it is worth examining the actual pattern of association between income and fact/amount of purchasing of each product. Look at the scatterplots and nonlinear approximations on them. You might find that some products do not depend on income, some depend smoothly and some abruptly. $\endgroup$
    – ttnphns
    Jun 6, 2014 at 14:13
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    $\begingroup$ thing is that there are thousands of households and the data is very widespread so this wouldn't really allow to 'as objectively as possible' to determine whether the variance is too big/number of observations (fact of purchases) is too low and etc. I need to find a way of how could I consistently draw a line - 'ok, these categories will probably won't work, so don't analyse them' ... $\endgroup$
    – Sarunas
    Jun 8, 2014 at 20:39

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After some searching on the internet, I decided to use relative standard error of the mean or coefficient of variation of the mean as a criteria to make a decision. I found out that some departments of statistics consider household survey data for a particular product category to be reliable if its relative S.E./CV of the mean of expenditure is below some constant. This constant varies, but as a lower bound for practical purposes one can consider it to be 16.5% and the upper bound around 25%. If the given value is above this constant, then it should be treated with suspicion.

Note - as household surveys in most cases has complex structure, one has to account for the right way of obtaining estimates of the S.E. to compute the relative S.E./CV. There is an R package survey which is capable of adjusting for the survey design.

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