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All You Need to Know About Longitudinal Data Analysis:

All You Need to Know About Longitudinal Data Analysis:. A Ninety Minute Dash. Major Themes of This Talk. Despite the plethora of models, methods, terminology and software, most longitudinal analysis falls in a few basic categories.

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All You Need to Know About Longitudinal Data Analysis:

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  1. All You Need to Know AboutLongitudinal Data Analysis: A Ninety Minute Dash

  2. Major Themes of This Talk • Despite the plethora of models, methods, terminology and software, most longitudinal analysis falls in a few basic categories. • Basically, its all regression analysis of one kind or another, linked closely to traditional ANOVA-based methods. • But the jump from ANOVA to regression is confusing for many investigators and the flexbility regression makes available is not understood.

  3. Two Generic Issues in Longitudinal Data Analysis • Conceptual: How to we represent the role of time? • Statistical: How do we deal with the fact that we have repeated measures on the same persons or entities, thereby violating the classical statistical assumptions?

  4. What Questions Can We Ask? • End point analysis. • Trajectory/growth analysis. • Survival analysis. • Each of the above can be adapted to deal with mediators and moderators. • In what follows I will concentrate on trajectory/growth analysis.

  5. A Little Review • Thinking of longitudinal data for some continuous outcome, we generally consider “factors” (experimental conditions, categorical settings) and covariates, both continuous and categorical. • Traditional ANOVA uses this terminology which is expressed in software like SPSS. • For most of us, this is the way we were trained and it’s a natural way of thinking.

  6. Setup For a Generic Example • Three Experimental Conditions • Control, Minimal Exercise, Intense Exercise • Major interest in Gender • Control for age and arthritis status • Output examples using SPSS • Measures at three points in time

  7. Classic Layout for the data

  8. But Its all Regression • All ANOVA type-models can be written as a regression equation. • To a degree, this matters only to statisticians, but most modern software, such as HLM, assumes users are comfortable with this and require them to specify models in regression terms.

  9. In fact, its more general than that • Most of were trained to deal with normally distributed, continuous outcomes. • But the regression model extends to all kinds of other outcomes including: • Simple dichotomies (logistic) • Ordered categories (ordered logistic) • Nominal categories (multinomial) • Waiting times (survival) • Counts (Poisson and generalizations thereof).

  10. Why make things more complicated? • Traditional ANOVA-type models require: • Equal number of observations in the various cells of the design (so attrition is a real problem) • Equal spacing between measurement intervals over person (so the logistics of getting everyone measured at exactly the same time are daunting • Assumptions regarding error structures are inflexible.

  11. What more modern methods permit • Unequal numbers of observations per cell • Varying times of measurement • A wide variety of error structures • Both time-fixed and time-varying covariates • etc

  12. Layouts for Longitudinal Data • Time-fixed and time-varying covariates. • Classic “wide” or “multivariate” format – what we are used to. • “Long” or “univariate” format and why modern programs want to see data this way. • Moving back and forth.

  13. End Point Analysis • Strictly speaking, not a longitudinal method, in effect, its cross-sectional. • We are modeling some outcome at the end of the study, using data on independent variables collected over the course of the study. • Example:

  14. Trajectory or Growth Curve Analysis • We can plot each person’s trajectory on some outcome variable over time. • We then want to explain the variability in the intercepts and slopes of these trajectories as a function of one or more other variables. • We can think of the dependent variable as the rate of change with respect to time.

  15. But the Basic Question is Simple • Does the average rate of change (slope) vary as a function of experimental group? • Does the rate of change vary as a function of other time-fixed and time-varying covariates? • This method easy generalizes to non-continuous outcomes. • Example

  16. Survival Analysis • We are interested primarily in the timing of transitions, hence the term “event history analysis” in some literatures. • The dependent variable is not directly observed; it is the “hazard rate” defined, loosely, as the probability of a transition at time t given that it has not occurred to that point. • We regress this variable on the usual stuff.

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