Probit and Logit analysis: Multiple observations over time at various concentrations of biopesticide Metarhizium anisopliae strain

Abstract

A study was done to assess the goodness of fit of the regression lines using the data of silkworm larvae (J12 x C12 race) killed by various concentrations of M. anisopliae and LC71 of Metarhizium. anisopliae at different time intervals (hr) applying probit and logit function. The data were transformed before analysis using probit and logit transformations of proportion kill and with and without a logarithmic transformation of predictors. Analysis showed that the LC50 value were 5.969×106, 6.000×106, 7.250 and 7.235 spores mL-1 for probit, logit, log-probit and log-logit, respectively. The LT50 values were 204.247, 204.381, 2.304 and 2.305 hr for probit, logit, log-probit and log-logit, respectively. Significant Chi-square value indicates the necessity of heterogeneity factor for correction of variances under all functions. Residual deviance values were lower at the log-probit (2.826 for concentration and 0.292 for time) and log-logit (2.406 for concentration and 0.440 for time) models with higher p-values (≥ 0.587) compared to probit and logit model. In our study, p-values was higher (p>0.05) with lower residual deviance in log transformed data which indicated that the log-probit and log-logit models could best fit to the mortality data of silkworm larvae when the both concentration and time were as predictors. Results indicated that the log-transformation of predictors would be best for describing the mortality values of insects by concentration of Metarhizium. anisopliae and under different time values. However, it requires more précised complete datasets and good knowledge of statistics of samples values along with the conversion of results of probit and logit analyses back to original units before coming into concrete application of these analytical inferences into practice.