Cauchy, Cauchy–Santos–Sartori–Faria, Logit, and Probit Functions for Estimating Seed Longevity in Soybean

Abstract

Seed longevity is characterized as the time for which seed remains viable during storage. Seed longevity can be estimated by a Probit model that determines the period in which 50% of seeds have lost viability (P50). The transformed data are binary and when they are not normally distributed, it is necessary to modify the Probit model or apply other functions to estimate longevity. This work aimed studied the use of the Logit, Cauchy, and Cauchy–Santos–Sartori–Faria (Cauchy‐SSF) functions to estimate the longevity of soybean seed [Glycine max (L.) Merr.] and compared Probit longevity models for the ordinary least squares (OLS) adjustment method and the generalized linear model (GLM). Ten seed lots were used to estimate water content, germination, and longevity. The P50 data were transformed via the Probit, Logit, Cauchy, and Cauchy‐SSF functions to estimate the coefficients of determination, the Akaike information criterion, deviance, dispersion, and the regression residuals. The effect on the results was observed, depending on the link function. The Cauchy‐SSF function as part of the OLS method estimated longevity in eight seed lots within the interval of interest (II), and the Cauchy function as part of the GLM estimated longevity in nine seed lots. The Cauchy, Cauchy‐SSF, and Logit models were capable of estimating the longevity of soybean seeds (P50) slightly better than the Probit model. We suggest the Cauchy‐SSF function for the OLS method and the Cauchy function for the GLM method to estimate soybean seed longevity when the data are not normally distributed.Core Ideas The Cauchy, Cauchy–Santos–Sartori–Faria Cauchy‐SSF, and Logit functions estimated longevity in soybean seeds more robustly than the Probit function. The ordinary least squares method combined with the Cauchy‐SSF function is as good as the generalized linear model method with the Cauchy function. The selection of the function changes the estimated time when 50% of seeds have lost viability, emphasizing the importance of the correct choice.