Asian Journal of Probability and Statistics

This study investigated the Effect of Levels of Education on the Choice of Medical Treatment Options for three illnesses (Malaria, Mental Disorder and HIV/AIDS) in Nigeria. The study was carried out in ten randomly selected Local Government Areas (L. G. As) in Imo State using a stratified random sample of 500 individuals selected from a population of 194,932 and the data was collected using questionnaires. The Multinomial Logistic Regression Model was adopted in the analysis of the data. The result of the analysis showed that there was a significant association between Educational Level and choice of treatment of Malaria, Mental Disorder and HIV/AIDS. It was further discovered that it is only the “WAEC/GCE” level of education that is significant in the Choice of Treatment of Mental Disorder. It is therefore recommended that government should beam its searchlight on this educational level to find out the cause(s) of their Mental Disorder.

This study discusses the effects of missing observations on Buys-Ballot estimate when trend-cycle component of time series is linear. The method adopted in this study is Decomposing Without the Missing Value (DWMV) which is used to estimate missing observations in time series decomposition when data are arranged in a Buys-Ballot table. The model structure used is multiplicative. Results show that the trend parameters with and without missing observations have insignificant effect while there are significant differences in the seasonal indices only at the season points where missing observations occurred in the Buys-Ballot table.

Bayes factor is a major Bayesian tool for model comparison especially when the model priors are the same. In this paper, the Savage-Dickey Density Ratio (SDDR) is used to derive the Bayes factor to select a model from two competing models under consideration in a normal linear regression with an independent normal-gamma prior. The Gibbs sampling technique for the joint posterior distribution with equal prior precision for both the unrestricted and restricted models is used to obtain the model estimates. The result shows that the Bayes factor gave more support to the unrestricted model against the restricted and was consistent irrespective of changes in sample size.

Population increases with time through birth, and researchers have often used either Logistic regression model or Discriminant analysis to study and classify birth outcomes. In this paper, the authors sought to investigate the sensitivity of the two methods used separately to explain and classify birth outcomes under different training and test samples. Out of 5000 birth outcomes data comprising of 1250 stillbirth cases and 3750 live births and with four test samples (50%, 40%, 30% and 25%). The Discriminant Analysis averagely correctly classified 89.8% of birth outcome cases compared to 82.4% for the logistic regression. The Discriminant analysis on the average correctly predicted 94.2% of live births compared to 83.1% for the Logistic regression. On stillbirth, 75.7% and 80.9% success rates were recorded for Discriminant Analysis and Logistic regression respectively. All predictors (Maternal Age, Gestational period, fetus weight, parity and Gravida) were statistically significant (p-value < 0.01) in determining birth outcomes of pregnancies in both methods. The results showed that, both techniques are almost similar in predicting birth outcome. However, the Discriminant analysis is preferred for the 25% and 50% test samples whiles, the logistic regression performed well under the 30% and 40% test sample data.

In this study, change detection in Out-patient and In-patient malaria cases in the Northern Region of Ghana was examined using time series intervention analysis. Data on monthly Out-patient and In-patient malaria cases obtained from the Northern Regional Health Directorate were modelled using Seasonal Autoregressive Integrated Moving Average with an Independent variable (SARIMAX) and Autoregressive Integrated Moving Average with an Independent variable (ARIMAX) models. The results revealed that SARIMAX (1, 1, 1)(1, 1, 1)₁₂ was the best model for predicting Out-patient malaria cases while SARIMAX (1, 1, 1)(2, 1, 1)₁₂ emerged as the best model for predicting the In-patient cases in the region. Diagnostic checks of the two models with the Ljung-Box test and Autoregressive Conditional Heteroscedasticity Lagrange Multiplier (ARCH-LM) test revealed that both models were free from higher-order serial correlation and conditional heteroscedasticity respectively. A chi-square goodness-of-fit test also revealed that there was no significant difference between the predicted values from the models and the observed values for the year 2018. The study further revealed that the coefficients of the intervention variable for the Out-patient and In-patient cases were both negative, which suggest that the intervention policy the government of Ghana implemented brought about a decline in the number of Out-patient and In-patient cases in the region.