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LONGITUDINAL ANALYSIS
An introductory graduate level text on longitudinal analysis using SPSS, SAS, and Stata.
Longitudinal analysis is an umbrella term for a variety of statistical procedures which deal with any type of data which is measured over time. Sections of this volume group longitudinal analysis methods under the following categories:
Time series analysis, often used for projecting economic or other time series, with or without additional independent variables.
Linear regression models, which incorporate time as an independent variable.
Panel data regression models,
Repeated measures GLM, used to implement analysis of variance and regression models.
General estimating equations analysis (GEE), used to implement nonlinear forms of regression modeling, including logistic and probit regression for repeated measures data.
Linear mixed modeling (LMM), used for multilevel analysis where multiple time periods are treated as a data level.
Generalized linear mixed models for longitudinal data (GLMM), used to implement nonlinear forms of linear mixed modeling
Structural equation modeling (SEM), used for growth curve analysis and modeling change in structural relationships across a limited number of time periods.
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Below is the unformatted table of contents.
LONGITUDINAL ANALYSIS Table of Contents Overview 13 Comparing time series procedures 13 GLM (OLS regression or ANOVA) with time as a variable 13 Time series analysis (ex., ARIMA 14 Repeated measures GLM 14 Generalized estimating equations (GEE) 14 Population-averaged panel data regression 14 Random effects panel data regression 15 Linear mixed models (LMM) 15 Generalized linear mixed models (GLMM) 15 Structural equation modeling 15 GLMM-SEM 15 Key concepts and terms 16 Types of time-related data 16 Statistical procedures for different types of data collected over time 18 Time series analysis 19 Overview 19 Key Terms and Concepts 19 Simple time series design 20 Time series effects 20 Serial dependence 20 Stationarity 20 Differencing 21 Specification 21 Autocorrelation 21 Decomposition 22 Model order 22 Exponential Smoothing 23 Overview 23 Weighting 23 Example 24 Sequence charts 24 Requesting exponential smoothing in SPSS 26 Exponential smoothing model types: Simple 27 Exponential smoothing model types: Holt's linear trend 30 Exponential smoothing model types: Brown's linear trend 31 Exponential smoothing model types: Damped trend 32 Exponential smoothing model types: Seasonal effects 32 Transformation of the dependent variable 33 Statistical output for time series analysis in SPSS 33 Residual and partial residual autocorrelation 36 Displaying forecast values 37 Saving exponential smoothing values in SPSS 38 ARIMA Models 40 Overview 40 Example 40 Constants and predictors 41 Stationarity 41 ARIMA p, d, and q parameters 46 Types of ARIMA models 50 Unit roots 52 ARIMA for the example data 52 Forecasts 54 Residual Analysis 55 Seasonal ARIMA 61 ARIMA Modeling: Intervention and transfer function analysis 62 The SPSS "Expert Modeler" 68 Overview 68 The "Expert Modeler" interface 68 Leading indicator (CCF) analysis 71 Overview 71 SPSS set-up 71 CCF output 72 Creating a leading indicator variable 74 Assumptions of time series analysis 75 Stationarity 75 Normally distributed independent residuals with homogenous variance 76 Inconsequential outliers 76 Frequently asked questions about time series analysis 76 How many time periods are needed? 76 What should the researcher do about missing data? 76 When I try to specify p, d, and q for an ARIMA model, should non-significant spikes be treated as zero? 77 I suspect there is not a single trend line but rather the trend is different for different subgroups in my population. How do I handle this? 77 How does one go about disentangling age, period, and cohort time series effects? 79 Is there an acceptable ARIMA model for all data? 79 What is an ARFIMA model? 80 Regression time series models 80 Curve fitting 80 Curve Estimation dialog in SPSS 80 Comparative fit plots 81 Statistical output 82 Saved variables 84 Nonlinear regression 84 Overview 84 Nonlinear regression models related to time series analysis 85 Ordinary regression with time as a variable 86 Overview 86 Ordinary regression without time as a variable 87 Ordinary regression with time as a control variable 89 Panel data regression 91 Overview 91 Panel data 91 Cross-sectional time series data 91 How a panel regression dataset is structured 92 Example 93 Panel data regression in Stata 94 Stata 94 Stata data setup 94 Types of panel data regression 96 Overview 96 " Population-averaged and pooled regression models. 97 The Hausman test 102 Fixed effects panel data regression 106 Declaring data to be panel data 106 Examining the data 107 Pooled regression and population-averaged models as points of comparison 110 The default fixed effects model 111 Random effects panel data regression 114 Overview 114 Statistical output 115 Population-averaged panel data regression 118 Overview 118 Statistical output 119 Panel data regression: Frequently asked questions 121 How do I compare groups in panel data regression in Stata? 121 In the various models that STATA supports, what are the "vcetype" options? 121 Repeated measures GLM for longitudinal data 122 Overview 122 Example 123 SPSS interface for GLM repeated measures 123 The initial repeated measures dialog 123 The model button dialog 125 The contrasts button dialog 126 The plots button dialog 127 The post hoc button dialog 128 The save button dialog 129 The (statistical) options button dialog 130 SPSS statistical output for GLM repeated measures 131 The within- and between-subjects factors tables 131 Descriptive statistics 132 The multivariate tests table 134 The tests of within-subjects effects table 135 The tests of within-subjects contrasts table 136 The tests of between-subjects effects table 137 The parameter estimates table 137 The univariate tests of lack of fit table 138 The multivariate tests of lack of fit table 139 The within-subjects, between-subjects and residual SSCP matrices 140 The contrast results table 142 Estimated marginal means tables 142 The post-hoc multiple comparisons table 144 Observed by predicted by residual plots 146 Profile plots 147 Assumptions for repeated measures 148 ANOVA assumptions 148 Balanced vs. unbalanced models 149 Homogeneity assumption: Box's M test 149 Homogeniety assumption: Levene's test 150 Homogeneity assumption: Spread vs. level plots 151 Sphericity 152 Generalized estimating equations for longitudinal data (GEE) 154 Overview 154 Example 155 Data structure 156 Unbalanced designs 158 The SPSS user interface for GEE 159 The SPSS GEE dialog, Repeated tab 159 The "Type of Model" tab 164 The "Response" tab 167 The "Predictors" tab 168 The "Model" tab 169 The "Estimation" tab 171 The "Statistics" tab 173 The "EM Means" tab 175 The "Save" tab 177 The "Export" tab 178 SPSS statistical output for GEE 180 Case processing summary 180 Descriptive statistics 180 Correlated data summary 180 Model information table 181 Goodness of fit table 181 Tests of model effects table 182 Parameter estimates table 183 Other tables 183 The Lagrange multiplier test 187 Assumptions of GEE models 188 Dependence and independence 188 Data level 188 Data distribution 188 Multicollinearity 188 Missing data 189 Correct specification of the covariance structure 189 Ordinal models 189 Homogeneity of variance 189 Linearity 189 Correlated error 189 Linear mixed models for longitudinal data (LMM) 190 Overview 190 A simple longitudinal example using SPSS LMM 191 Example 191 The SPSS LMM user interface 191 LMM statistical output in SPSS 204 Likelihood ratio tests of model differences 213 Longitudinal, Growth, and Repeated Measures LMM Models 214 Overview 214 A random intercepts longitudinal model using SPSS 215 SPSS LMM user interface 216 LMM statistical output for the random intercepts longitudinal model in SPSS 219 A revised model compared to OLS regression 221 A random coefficients growth model with time as a random effect, using SPSS. 224 Modeling time as a random effect 224 LMM statistical output for the random coefficients model in SPSS 225 A repeated measures random coefficients model using SPSS LMM 228 Modeling time as a repeated measure 228 LMM statistical output for the repeated measures random coefficients model 231 A repeated measures model with additional covariates using SPSS. 234 SPSS setup 234 Statistical output 237 A three-level longitudinal null model using HLM software 242 Example 242 The HLM7 user interface 245 Statistical Output for the intercept-only model 250 A three-level unconditional linear growth model using HLM software 254 Example 254 Statistical output for the unconditional linear growth model 256 A three-level conditional linear growth model 261 Example 261 Statistical output for the conditional linear growth model 262 Likelihood ratio test 266 Assumptions of linear mixed models 266 Measurement level 266 Linearity 266 Normality 266 Independence 267 Properly specified covariance structures 267 Convergence 267 Proper model specification 267 Random sampling 267 Adequate sample size 267 Missing values 269 Centered data 269 Multicollinearity 270 Outliers 270 Normal distribution of residuals 270 What is modeled 270 Generalized linear mixed models for longitudinal data (GLMM) 270 Overview 270 Example 271 SPSS GLMM user interface 272 The main GLMM interface in SPSS 272 The "Fields & Effects" tab 273 The "Build Options" tab 278 The "Model Options" tab 280 SPSS syntax for the GLMM example 283 Statistical output for the GLMM model in SPSS 285 The SPSS Model Viewer 285 The "Model Summary" table 286 The "Data Structure" table 286 The "Predicted by Observed" plot 287 The "Fixed Effects" diagram and table 288 The "Fixed Coefficients" diagram and table 289 The "Random Effect Covariances" table 290 The "Covariance Parameters" tables: Residuals 291 The "Covariance Parameters" tables: Block 1 292 The "Estimated Means" table 294 The "Information" table 295 Absolute mean error 295 Frequently Asked Questions about GLMM 296 Can AIC, BIC, and other information theory measures assess goodness of fit across models with different link functions? 296 Can AIC, BIC, and other information theory measures be negative? 296 Assumptions of GLMM 297 Distribution of the dependent variable 297 Linearity in the link 297 Independence 297 Structural equation modeling for longitudinal data (SEM) 297 Overview 297 Latent Growth Curve Modeling 298 Overview 298 Example 298 Data setup 298 Creating and running the LGC model in AMOS 299 Interpretation 308 Standardized estimates 308 Testing the predictor for no effect 311 Create the constrained model 311 Model comparison 313 Regression weights 313 Summary 314 Model fit 315 Multiple growth models 315 Output for multiple growth models 315 Multiple group analysis 316 Appendix: Covariance Structure Types 316 Variance components structure type 317 Diagonal structure type 317 Unstructured covariance structure type 318 Autoregressive covariance structure types 318 Compound symmetry 319 Other covariance structure types 319 Selecting among covariance structure assumptions 320 Bibliography 320 Pagecount: 328