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UBC Theses and Dissertations

Temporal adjusted prediction for predicting Indian reserve populations in Canada Cho, Derek


In order to predict the population of Indian reserves in Canada for the 2016 Census, we can construct a suitable model using data from the Indian Register and past censuses. Linear mixed effects models are a popular method for predicting values of responses on longitudinal data. However, linear mixed effects models require repeated measures in order to fit a model. Alternative methods such as linear regression only require data from a single time point in order to fit a model, but it does not directly account for within-individual correlation when predicting. Since we are predicting the responses of the same set of individuals, we can expect responses at the next time point to be strongly correlated with past responses for an individual. We introduce a new method of prediction, temporal adjusted prediction (TAP), that addresses the issue of within-individual correlation in predictions and only requires data from a single time point to estimate model parameters. Predictions are based on the last recorded response of an individual and adjusted based on changes to the values of their covariates and estimated regression coefficients that relate the response and the covariates. Predictions are made using a random intercept model rather than a linear regression model. It is shown that if the random intercept accounts for a larger proportion of the random variation in the data than the random error term, then temporal adjusted prediction achieves a lower mean squared prediction error than linear regression. TAP performs better than linear regression when predicting on the same set of individuals at different time points. It also shows similar prediction performance compared to linear mixed effects models estimated with maximum likelihood estimation despite only requiring data from one time point in order to fit a model.

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