The comparison logit and probit regression analyses in estimating the strength of gear teeth

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5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)548-553
Number of pages6
JournalEuropean Journal of Scientific Research
Volume27
Issue number4
Publication statusPublished - 2009

Fingerprint

Probit Regression
Logit
Gear teeth
Population distribution
tooth
Tooth
teeth
population distribution
Regression Analysis
experimental design
Demography
Logarithm
Proportion
Weibull distribution
Regression
Normal Distribution
Normal distribution
logit analysis
Probit
Probit Model

Keywords

  • Counted proportion
  • Gear teeth
  • Logit
  • Probit
  • Regression analysis
  • Staircase design

ASJC Scopus subject areas

  • General

Cite this

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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.",
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AU - Zaharim, Azami

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N2 - 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.

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