Statistical Modelling of Outbound Global System for Mobile Communications (Gsm) Call Counts Using Count Regession Models

This article compared Poisson and Negative Binomial Models on outbound Global System for Mobile Communications (GSM) call counts based on primary data collected from mobile telecommunications users among students of The Federal Polytechnic, Bida, Niger State, Nigeria. The data provided for 315 respondents: the outbound call count, gender, level of study, age, distance from respondent’s base to Bida and number of siblings. The Poisson regression and Negative Binomial models were utilized for data modeling where outbound call count constituted the dependent variable. Models were estimated through the maximum likelihood method. Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were the performance metrics used. The empirical distribution was right skewed with a mean of 4.324 calls and variance of 15.016 and an unconditional ratio of variance to mean of 3.473. The Pearson dispersion statistic from the Poisson regression was 3.175 and significant overdispersion was observed with the Cameron-Trivedi auxiliary test. The Negative Binomial (NB) model estimated a dispersion parameter of 0.383 (p < .001), reduced the Pearson dispersion ratio to 1.180, and produced substantially better likelihood-based fit statistics (log-likelihood = −772.562; AIC = 1,563.124; BIC = 1,596.897) than the Poisson model (log-likelihood = −891.820; AIC = 1,799.640; BIC = 1,829.660) and the Zero-inflated Poisson (log-likelihood = −889.107; AIC =1,796.213; BIC = 1,829.986). The preferred NB model found age to be statistically significant at 5% level (ß = 0.030, p = 0.015) yielding Incidence-Rate Ratio (IRR) of 1.030 and indicating that a one-year increase in age is associated with approximately 3.0% increase in the expected number of calls, holding other variables constant. The coefficient of ND2 was negative (ß = -0.246, p = 0.034) but significant. Its IRR of 0.782 indicates that, controlling for the other predictors, ND2 respondents have an expected call count approximately 21.8% lower than the ND1 reference group. Other variables were found to be not significant at 5% level. The study concludes Negative Binomial model as the appropriate for GSM calls data under consideration. The study recommends duplication of the research and extension to staff in other higher institutions of higher learning.