ABSTRACT
Generally, experimental responses are positive which may be analysed either by log-normal or gamma models. Some continuous positive process variables may have non-normal error distributions, and the class of generalized linear models includes distributions useful for the analysis of such process characteristic data. In regression models with multiplicative error, estimation is often based on either the log-normal or the gamma model. It is well known that the gamma model with constant coefficient of variation and the log-normal model with constant variance give almost same analysis. However, in the analysis of data from quality improvement experiments neither the coefficient of variation nor the variance needs to be constant, so that the two models do not necessarily give similar results. A choice needs to be made between the gamma and the log-normal models. The present chapter focuses the discrepancies of the regression estimates between the two models based on real examples. It is identified that even though the variance or the coefficient of variation remains constant, but regression estimates may be different between the two models. For non-constant variance, regression estimates may be different between the two models. It is also identified that for the same positive data set, the variance is constant under the lognormal model but non-constant under the gamma model. For this data set, the regression estimates are completely different between the two models. It is shown that for non-constant variance, even though the measures of fitting criteria and estimates are almost same in both the models, but the fittings may not always be identical. Moreover, this chapter points that some insignificant effects may also be sometimes very important in fitting. In the process, the causes of discrepancies have been explained between the two models. Some examples illustrate these points. A few applications of both the log-normal and the gamma models are illustrated with real examples in the different fields of science.
