Determination of sample size for a multinomial model coupled with the phenology model

Predicting the timing of phenological events is important in agriculture, especially high-revenue products. A project sponsored by USDA-ARS had the objective of adapting a previously developed model for estimating proportions of insects in different development stages as a function of temperature (degree) and time (days) for predicting bloom in almond orchards. Data for the model normally form a two-way table of counts, with rows corresponding to sample percentages of different development stages and columns to sampling times. In this study, we report a technique developed to estimate sample sizes of multinomial and product multinomial models using a method of moments and determine the empirical coverage of sample size. This study aims to determine an appropriate sample size for data collection. This involves establishing a sampling distribution for the Pearson statistic, defined as the product of the sample size and the deviance of empirical proportions from population proportions. The intended outcome is to predict the optimal timing for harvesting crops at desired development stages when coupled with the phenology model, for which variability of the maximum likelihood estimates of the phenology model depends on sample size.