Currently, I am analyzing the developmental performance of under 5 children. The dependent variable is the ratio of pass/fail counts of Denver-II. So, can I use the ratios as scores (continuous variable) and conduct independent t-test and multiple regression, accordingly? I badly need your scientific inputs!
Cheers,
Berhanu
Depends who/what you are writing for - term paper ok - but high end journal referees may ask for more - referees are expected to be critical
The issues are two fold
1 the ratio of observed / expected has a lower bound of 0 - you cannot go below a count of zero- not taking this into account can result in impossible negative predictions
2 while modeling counts - the error variance may not be normal but belong to the Poisson family ( including a Negative Binomial Distribution) - not taking in to account this inbuilt heterogeneity ( the variance depends on the mean) may result in incorrect standard error leading ro inferential error.
So in a Generalized Linear Model in the form of a Poisson or NBD the log of the underlying counts is modeled with an offset - the coefficient associated wit the log of the expected is constrained to 1,
Most statistical software these days has this capability
This is a clear read
D. Wayne Osgood1 (2000) Poisson-Based Regression Analysis of Aggregate Crime Rates, Journal of Quantitative Criminology, Vol. 16, No. 1, 2000
Software examples are
http://www.ats.ucla.edu/stat/stata/dae/poissonreg.htm
http://www.ats.ucla.edu/stat/r/dae/poissonreg.htm
http://www.ats.ucla.edu/stat/spss/dae/poissonreg.htm
Dear Kelvyn Jones, these are really really relevant resources!!
So, as I have been preparing a publishable manuscript, you are not suggesting me to Use the usual multiple regression b/c of the limitations with the "ratios or dependent variable"?? Can I go for it with all the limitations or.....???
Thanks for your greater efforts to help me useful paper!!
Check the assumptions of usual multiple regression regarding your data (homoscedasticity in particular, but also Gaussian-like residuals), and that the obtained model predicts
The expected passes using Denver II is always a non-zero number. The ratio you get is thus always > 0. I don't think a negative prediction is practically important for this specific data. The denominator (expected passes) always varies with age, and if you are not comparing age matched groups, the distributions of the two groups differ. Then the distribution of the ratio score(dependent variable) cannot be normal and the variance in both groups also varies. This makes it unfair to use t-test. With OLS regression you may control the effect of age difference but the assumption of homoscedasticity may not be met. I would opt the use of Poisson model using the count passes if mean=variance, if not the negative binomial regression.
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