Analysis of Longitudinal Data: Introduction

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Analysis of Longitudinal Data Introduction
Psychometrics workshop August 27-31 Friday Harbor
- San Juan Islands, WA
Elena A. Erosheva Department of Statistics,
School of Social Work, and the Center for
Statistics and the Social Sciences, University of
Washington
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Outline

• Longitudinal data features.

• Basic question How change occurs?

• Exploring longitudinal data
• Individual growth plots,
• Smoothing,
• Differences in change across people.

• Framing questions about change.

• Analytic challenges.

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Longitudinal data features

• Three or more waves of data on each unit/person.

• Outcome values.
• Preferably continuous (although categorical
  outcomes are possible)
• Systematically change over time
• Metric, validity and precision of the outcome
  must be preserved across time.

• Sensible metric for clocking time.
• Automobile study months since purchase, miles,
  or number of oil changes?

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Data format

• Person-level (multivariate format)
• One line/record per each person which contains
  the data for all measurement occasions.

• Person-period (univariate format)
• One line/record per each measurement occasion per
  each person.

• Person-period data format is usually preferable
• Contains time and predictors at each occasion
• More efficient format for unbalanced data.

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Question How change occurs?

• How does the outcome change over time?
• Individual growth trajectories.
• Within-individual changes over time.

• Can we predict differences in these changes?
• Associations between predictors and the patterns
  of change.
• Inter-individual difference in change.

• These two types of questions refer to different
  levels of data hierarchy.

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Exploring longitudinal data

• Empirical growth plots.
• If too many, select a random sample.
• Reveal how each person changes over time.

• Smoothing techniques for trends
• Nonparametric moving averages, splines, lowess
  and kernel smoothers.
• Examine intra- and inter-individual differences
  in the outcome.
• Gather ideas about functional form of change.

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Exploring longitudinal data (cont.)

• More formally use OLS regression methods.
• Estimate within-person regressions.
• Record summary statistics (OLS parameter
  estimates, their standard errors, R2).
• Evaluate the fit for each person.
• Examine summary statistics across individuals
  (obtain their sample means and variances).

• Known biases sample variance of estimated
  slopes gt population variance in the rate of
  change.

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Exploring longitudinal data (cont.)

• To explore effects of categorical predictors
• Group individual plots.
• Examine smoothed individual growth trajectories
  for groups.
• Examine relationship between OLS parameter
  estimates and categorical predictors.

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Framing questions about change

• Inferences from longitudinal data
• Population mean
• Individual variation about the population mean
• The effects of covariates on
• The population mean,
• The individual variation
• Prediction of new observations.

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Examples of questions

• Is the average response equal in the two groups
  at all times?

• If not, is the average response pattern over
  time the same in the two groups, apart from a
  constant level shift?

• If not, are the differences increasing or
  decreasing over time?

• If differences are not monotone, how do they
  change over time?

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Examples of questions (cont.)

• Another type of questions for longitudinal data
  (wont be our focus at this workshop)
• Whether and when does a certain event occur?

• Time as an outcome (as opposed to time as a
  predictor).

• Different set of statistical approaches
  survival analysis, event history analysis,
  failure time analysis, and hazard modeling.

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Analytic challenges

• Longitudinal data are not i.i.d.!

• Parametric modeling of the mean response.

• Model selection.

• Missing data.

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Selected References

• Singer, J. D., Willet, J. B. (2003) Applied
  Longitudinal Data Analysis, Oxford University
  Press.
• Diggle,P. J., Heagerty, P., Liang, Kung-Yee,
  Zeger, S. L. (2002). Analysis of Longitudinal
  Data, Oxford University Press.
• Weiss, R. (2005) Modeling Longitudinal Data,
  Springer.