I’m writing a report about modelling. I’d like to have your opinion on something.
Which are the best quotes for these 2 paragraphs ?
1- In the classical general linear model the response variable is continuous and it follows a normal distribution (linear regression analysis, ANOVA, ANCOVA), with the main estimation method of least squares.
I have only quoted a book: “MacCullagh, P., & Nelder, J. A. (1989). Generalized linear models (Vol. 37). CRC press.".
2- There are a recent increased interest in the application of statistical modeling to medicine, biomedicine, public health, and biology.
I’d like to quote a similar quote of tutorial or review of Ben Bolker: “Bolker, B. M., Brooks,et al., (2009). Generalized linear mixed models: a practical guide for ecology and evolution. Trends in ecology & evolution, 24(3), 127-135.”
Not that I had better references, but there are minor flaws in the first sentence:
not the response variable follows a normal distribution but the residuals! Further, this is not a mandatory prerequisite; it is an *assumption* under which the the estimates are (most) *reasonable* and the p-values would have a well-defined meaning. It would be even more correct to state that the expectations about the residuals(errors) are modelled using the normal probability distribution. This is not identical to the statement that the residuals actually have a frequency distribution of the shape of the normal distribution.
Apart from this I would think of citing RA Fisher for general linear models, since this was largely his invention (apart from Legendre and Gauss). McCullagh & Nelder are better if you want to point to generalIZED linear models, although the unification of the models for exponential disperion family was published by Nelder & Wedderburn (1972).
Not that I had better references, but there are minor flaws in the first sentence:
not the response variable follows a normal distribution but the residuals! Further, this is not a mandatory prerequisite; it is an *assumption* under which the the estimates are (most) *reasonable* and the p-values would have a well-defined meaning. It would be even more correct to state that the expectations about the residuals(errors) are modelled using the normal probability distribution. This is not identical to the statement that the residuals actually have a frequency distribution of the shape of the normal distribution.
Apart from this I would think of citing RA Fisher for general linear models, since this was largely his invention (apart from Legendre and Gauss). McCullagh & Nelder are better if you want to point to generalIZED linear models, although the unification of the models for exponential disperion family was published by Nelder & Wedderburn (1972).
For no 1 there are plenty, my favourite is 'Estimation and Inference in Econometrics'
by Davidson and MacKinnon(1993). The value of this book is that author's intuition is great and you can never go wrong if you follow it.
I agree with Jochen's comments and encourage you to observe them, especially the one about the normality of the variables. It is something very basic but known by only a few practitioners.
The second statement is quite questionable, and I thing it "expired" at least one decade ago, despite the fact that the reference given is fairly recent. In general, if no statistical modelling is done how can one get defendable research output, except for heavily focused medical research or some theoretical work that explores a more general problem?
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