This dissertation investigates the interactive or joint influence of autocorrelative processes (autoregressive-AR, moving average-MA, and autoregressive moving average-ARMA) and sample weights present in a longitudinal panel data set. Specifically, to what extent are the sample estimates influenced when autocorrelation (which is usually present in a panel data having correlated observations and errors) and sample weights (complex sample design feature used in longitudinal data having multi-stage sampling design) are modeled versus when they are not modeled or either one of them is taken into account. The current study utilized a Monte Carlo simulation design to vary the type and magnitude of autocorrelative processes and sample weights as factors incorporated in growth or latent curve models to evaluate the effect on sample latent curve estimates (mean intercept, mean slope, intercept variance, slope variance, and intercept slope correlation). Various latent curve models with weights or without weights were specified with an autocorrelative process and then fitted to data sets having either the AR, MA or ARMA process. The relevance and practical importance of the simulation results were ascertained by testing the joint influence of autocorrelation and weights on the Early Childhood Longitudinal Study for Kindergartens (ECLS-K) data set which is a panel data set having complex sample design features. The results indicate that autocorrelative processes and weights interact with each other as sources of error to a statistically significant degree. Accounting for just the autocorrelative process without weights or utilizing weights while ignoring the autocorrelative process may lead to bias in the sample estimates particularly in large-scale datasets in which these two sources of error are inherently embedded. The mean intercept and mean slope of latent curve models without weights was consistently underestimated when fitted to data sets having AR, MA or ARMA process. On the other hand, the intercept variance, intercept slope, and intercept slope correlation were overestimated for latent curve models with weights. However, these three estimates were not accurate as the standard errors associated with them were high. In addition, fit indices, AR and MA estimates, parsimony of the model, behavior of sample latent curve estimates, and interaction effects between autocorrelative processes and sample weights should be assessed for all the models before a particular model is deemed as most appropriate. If the AR estimate is high and MA estimate is low for a LCAR model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an AR process between the observations. If the MA estimate is high and AR estimate is low for a LCMA model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an MA process between the observations. If both AR and MA estimates are high for a LCARMA model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an ARMA process between the observations. The results from the current study recommends that biases from both autocorrelation and sample weights needs to be simultaneously modeled to obtain accurate estimates. The type of autocorrelation (AR, MA or ARMA), magnitude of autocorrelation, and sample weights influences the behavior of estimates and all the three facets should be carefully considered to correctly interpret the estimates especially in the context of measuring growth or change in the variable(s) of interest over time in large-scale longitudinal panel data sets.

Although previous studies on structural equation modeling (SEM) have indicated that the second-order latent growth model (SOLGM) is a more appropriate approach to longitudinal intervention effects, its application still requires researchers to collect at least three-wave data (e.g. randomized pretest, posttest, and follow-up design). However, in some circumstances, researchers can only collect two-wave data for resource limitations. With only two-wave data, the SOLGM can not be identified and researchers often choose alternative SEM models to fit two-wave data. Recent studies show that the two-wave longitudinal common factor model (2W-LCFM) and latent change score model (2W-LCSM) can perform well for comparing latent change between groups. However, there still lacks empirical evidence about how accurately these two-wave models can estimate the group effects of latent change obtained by three-wave SOLGM (3W-SOLGM). The main purpose of this dissertation, therefore, is trying to examine to what extent the fixed effects of the tree-wave SOLGM can be recovered from the parameter estimates of the two-wave LCFM and LCSM given different simulation conditions. Fundamentally, the supplementary study (study 2) using three-wave LCFM was established to help justify the logistics of different model comparisons in our main study (study 1). The data generating model in both studies is 3W-SOLGM and there are in total 5 simulation factors (sample size, group differences in intercept and slope, the covariance between the slope and intercept, size of time-specific residual, change the pattern of time-specific residual). Three main types of evaluation indices were used to assess the quality of estimation (bias/relative bias, standard error, and power/type I error rate). The results in the supplementary study show that the performance of 3W-LCFM and 3W-LCSM are equivalent, which further justifies the different models' comparison in the main study. The point estimates for the fixed effect parameters obtained from the two-wave models are unbiased or identical to the ones from the three-wave model. However, using two-wave models could reduce the estimation precision and statistical power when the time-specific residual variance is large and changing pattern is heteroscedastic (non-constant). Finally, two real datasets were used to illustrate the simulation results. / Doctor of Philosophy / To collect and analyze the longitudinal data is a very important approach to understand the phenomenon of development in the real world. Ideally, researchers who are interested in using a longitudinal framework would prefer collecting data at more than two points in time because it can provide a deeper understanding of the developmental processes. However, in real scenarios, data may only be collected at two-time points. With only two-wave data, the second-order latent growth model (SOLGM) could not be used. The current dissertation compared the performance of two-wave models (longitudinal common factor model and latent change score model) with the three-wave SOLGM in order to better understand how the estimation quality of two-wave models could be comparable to the tree-wave model. The results show that on average, the estimation from two-wave models is identical to the ones from the three-wave model. So in real data analysis with only one sample, the point estimate by two-wave models should be very closed to that of the three-wave model. But this estimation may not be as accurate as it is obtained by the three-wave model when the latent variable has large variability in the first or last time point. This latent variable is more likely to exist as a statelike construct in the real world. Therefore, the current study could provide a reference framework for substantial researchers who could only have access to two-wave data but are still interested in estimating the growth effect that supposed to obtain by three-wave SOLGM.

Educational researchers are often interested in phenomena that unfold over time within a person and at the same time, relationships between their characteristics that are stable over time. Since variables in a longitudinal study reflect both within- and between-person effects, researchers need to disaggregate them to understand the phenomenon of interest correctly. Although the person-mean centering technique has been believed as the gold standard of the disaggregation method, recent studies found that the centering did not work when there was a trend in the predictor. Hence, they proposed some detrending techniques to remove the systematic change; however, they were only applicable to multilevel models. Therefore, this dissertation develops novel detrending methods based on structural equation modeling (SEM). It also establishes the links between centering and detrending by reviewing a broad range of literature. The proposed SEM-based detrending methods are compared to the existing centering and detrending methods through a series of Monte Carlo simulations. The results indicate that (a) model misspecification for the time-varying predictors or outcomes leads to large bias of and standard error, (b) statistical properties of estimates of the within- and between-person effects are mostly determined by the type of between-person predictors (i.e., observed or latent), and (c) for unbiased estimation of the effects, models with latent between-person predictors require nonzero growth factor variances, while those with observed predictors at the between level need either nonzero or zero variance, depending on the parameter. As concluding remarks, some practical recommendations are provided based on the findings of the present study. / Doctor of Philosophy / Educational researchers are often interested in longitudinal phenomena within a person and relations between the person's characteristics. Since repeatedly measured variables reflect their within- and between-person aspects, researchers need to disaggregate them statistically to understand the phenomenon of interest. Recent studies found that the traditional centering method, where the individual's average of a predictor was subtracted from the original predictor value, could not correctly disentangle the within- and between-person effects when the predictor showed a systematic change over time (i.e., trend). They proposed some techniques to remove the trend; however, the detrending methods were only applicable to multilevel models. Therefore, the present study develops novel detrending methods using structural equation modeling. The proposed models are compared to the existing methods through a series of Monte Carlo simulations, where we can manipulate a data-generating model and its parameter values. The results indicate that (a) model misspecification for the time-varying predictor or outcome leads to systematic deviation of the estimates from their true values, (b) statistical properties of estimates of the effects are mostly determined by the type of between-person predictors (i.e., observed or latent), and (c) the latent predictor models require nonzero growth factor variances for unbiased estimation, while the observed predictor models need either nonzero or zero variance, depending on the parameter. As concluding remarks, some recommendations for the practitioners are provided.

This thesis investigates the relationship between labour market statuses and well-being in the UK working age population, and the moderating role of the Great Recession. Research on the relationship between labour market statuses and well-being outcomes identifies negative associations with unemployment and economic inactivity. These findings are typically presented as independent of macroeconomic conditions, but to what extent does this assumption hold? The central proposition of this thesis, is that economic crises moderate the way in which labour market statuses affect well-being, thereby changing the value of statuses, not just their prevalence. The main research question addressed is ‘for the UK working age population, to what extent did labour market and employment statuses contribute to the greater or lesser effects of the economic crisis (2007/8–2011) on well-being, compared to the pre-recession ‘boom’ period (2003/4–2006/7)?’I make use of a national panel data series from the British Household Panel Survey and Understanding Society. Firstly, after critiquing the reliance on subjective well-being (SWB) measures, confirmatory factor analysis is used to develop a measure of positive psychological health, representing a single dimension of well-being. This is then compared to a measure of SWB in a series of latent growth models to investigate individual trajectories over the study period. Secondly, multilevel models are used to estimate the relationship between five labour market and employment statuses and positive psychological health, comparing the pre-recession and recession periods. Finally, a dynamic structural equation modelling approach is used to investigate selection and causation in the relationship between labour market status and positive psychological health. Aggregate positive psychological health was associated with a recession period decline, in contrast to SWB which remained stable. Labour market statuses were found to moderate the impact of recession. People who were economically inactive were associated with the largest declines in positive psychological health during the recession period, compared to the pre-recession period, followed by those in standard employment. In contrast, the relationship between non-standard employment and unemployment and positive psychological health remained constant over time. Finally, despite evidence of selection into labour market statuses, the findings show a strong causal impact of statuses on positive psychological health. The findings provide a different take on those hardest hit by recession, showing that some of the most vulnerable to low psychological health were most exposed to the impact of recession by virtue of their labour market status. The protective value of standard employment was also diminished relatively. Evidence in favour of a causal interpretation suggests policy makers should use employment and welfare policy to prevent an accumulation of welfare issues.