Understanding the effects of weighting on parameter estimation for multilevel models

Ismail, Olusegun Afis and Neal, Peter (2022) Understanding the effects of weighting on parameter estimation for multilevel models. PhD thesis, Lancaster University.

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Abstract

Creating a model from hierarchical data with missing data without addressing the missingness in the data may lead to poor parameter estimates. Hence the overall aim of this thesis is to investigate the effects of weighting adjustment methods on parameter estimates of weighted multilevel linear model to address unequal sampling selection and non -response in the continuous response variable. The significance of this thesis is that it seeks to fill the gaps in the existing body of work on complex survey data analysis on the identification of best weighting adjustment and conditions suitable to achieve reliable estimates from a weighted multilevel linear model. To achieve the aim of this thesis, the Jamaica Survey of Living Conditions 2007 was used in a simulation study on a weighted multilevel linear model of the annual household expenditure of meals purchased away from home to investigate four weighting adjustments methods using two scenarios: Missing at Random (MAR) and Missing not at Random (MNAR) at 20%, 40% & 60% rate of missing respectively in the outcome variable. In order to fully investigate the effects of the weighting adjustments, the missingness in the outcome variable were tested as a function of a continuous, categorical and combination of both continuous and categorical variables. The simulation study was also extended to the scaling of the weights to identify changes in the effects on the parameter estimates. The weighting adjustment with the most reliable estimates were applied to the modelling of reported income from the China Health and Nutrition Survey (CHNS 1989 & 2011) data as well as the household expenditure of meals purchased away from home in the Jamaica Survey of Living Conditions 2007 respectively. In the application of the weighting adjustments, different scenarios on different multilevel models were investigated to identify any changes in the parameter estimates. The findings from the simulation study on the random effect multilevel model revealed that sampling weight adjusted for missing data using item non-response weight produced the most reliable estimates of the fixed component of the linear multilevel models at the 20% rate of missing.