On the Sensitivity of Probit and Complementary Log-Log Models to Violated Tolerance Edo State.

Abstract

In this article, the sensitivity of each of the fixed effects probit and complementary log-log models to gamma,
Cauchy and lognormal tolerances was studied, through Monte Carlo experiments. Seven levels of sample size and
four levels of number of time points were utilized for the simulation. Criteria used for comparison were the bias;
variance and the root mean squared error. It was found that, typically for the probit and complementary log-log
models, the lognormal tolerance produced the least absolute bias, while Cauchy produced the highest. Cauchy
tolerance typically produced the least variance and lognormal tolerance, the highest for both the probit and the
complementary log-log models. The lognormal tolerance produced the least variability around the true parameter
value, and Cauchy, the highest for the probit model. For the complementary log-log model, gamma tolerance
produced the least variability around the true parameter value and Cauchy, the largest. It was concluded that both
the probit and the complementary log-log models were least sensitive to the lognormal tolerance, followed by
gamma, and lastly, Cauchy tolerance.