二分类probit模型


The Comparison Logit and Probit Regression Analyses in
Estimating the Strength of Gear Teeth


A.A. Shariff
Centre For Foundation Studies In Science, University of Malaya
50603 Kuala Lumpur, Malaysia
E-mail: asma@um.edu.my

A. Zaharim
Faculty of Engineering and Built Environment

K. Sopian
SERI University Kebangsaan Malaysia, Bangi, Selangor, Malaysia
Abstract
Logit and probit are two regression  methods which are categorised under
Generalized Linear Models. Both models can be used when the response variables in the
analyses are categorical in nature. For the case of the strength of gear teeth data, it can be in
terms of counted proportions, such as r teeth fail out of n teeth tested. In this paper, the two
models, logit and probit are discussed and the methods of analysis are compared for
simulated data sets obtained from experimental procedure called staircase design (SCD)
experiment. For the analysis, the response variable is the proportion failing and the
explanatory variable is the  corresponding load. The analysis  is also compared with the
explanatory variable of logarithm of load. The population distributions of strengths
considered are normal and Weibull distribution and 1000 SCD experiments are simulated.
The sampling distributions of the various estimators are then compared for bias, standard
deviation, and mean squared error for the  two contrasting population distributions of
strength. It is found that, a regression of the logit on the logarithm of load seems to be the
most robust approach if normality of strengths is in doubt.