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Garson, G. D. (2013). Longitudinal Analysis. Asheboro, NC: Statistical Associates Publishers.

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Table of Contents
ISBN: 978-1-62638-002-8
@c 2013 by G. David Garson and Statistical Associates Publishers. worldwide rights reserved in all languages and on all media. Permission is not granted to copy, distribute, or post e-books or passwords.


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.

Pagecount: 328

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Below is the unformatted table of contents.

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
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