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Is logistic regression the best for binomial response?

In: Tatra Mountains Mathematical Publications, vol. 26, no. 2
Júlia Volaufová - Stephen M. Redmann - Lynn Roy Lamotte
Detaily:
Rok, strany: 2003, 237 - 246
O článku:
In this paper we investigate a simple situation with one discrete explanatory variable, say $X$, with finite levels and the response variable being a vector of dichotomous responses, say $Y$, with replicated values at each level of $X$. The mean of $Y$ is modeled by a vector, say $p$ such that $E(Y) = p (X)$ and $var(Y)=V$. The main question, whether the probability $p$ depends on levels of $X$ is addressed in several ways. First, considering a logistic regression analysis with both the Wald's test and the likelihood ratio test, second, looking at grouped data for each level of $X$, and using the angular transformation on proportions. The proportions are then modeled by linear model. Finally, the assumptions of discrete vector $Y$ are ignored and a weighted least squares (WLS) method is used on $E(Y)=p (X)= X γ$ and $var(Y)=σ2I$. In the latter case the estimates of $p(x)$ are truncated into 0 whenever the resulting probability estimate is negative. For estimation of $p$ we look at the total mean squared error with respect to the true value used in simulation. The more important part is the hypothesis of no dependence of $p$ on $X$, and here we compare the standard tests used within each method with respect to their size and power. The focus is mainly on the tails for small values of simulated probabilities and actual small sample sizes. We propose that the WLS yields equally good results as the logistic regression approach and the angularly transformed response of proportions.
Ako citovať:
ISO 690:
Volaufová, J., Redmann, S., Lamotte, L. 2003. Is logistic regression the best for binomial response?. In Tatra Mountains Mathematical Publications, vol. 26, no.2, pp. 237-246. 1210-3195.

APA:
Volaufová, J., Redmann, S., Lamotte, L. (2003). Is logistic regression the best for binomial response?. Tatra Mountains Mathematical Publications, 26(2), 237-246. 1210-3195.