1 / 18

# Longitudinal data analysis in HLM - PowerPoint PPT Presentation

Longitudinal data analysis in HLM. Longitudinal vs cross-sectional HLM. Similar things: Fixed effects Random effects Difference: Cross-sectional HLM: individual, school,… Longitudinal HLM: observations over time, individual,…. Characteristics in longitudinal data.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Longitudinal data analysis in HLM ' - larissa-sherman

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Longitudinal data analysis in HLM

Longitudinal vs cross-sectional HLM

• Similar things:

• Fixed effects

• Random effects

• Difference:

• Cross-sectional HLM: individual, school,…

• Longitudinal HLM: observations over time, individual,…

• Source of variations

• Within-subject variation (intra-individual variation)

• Between-subject variation (inter-individual variation)

• Often incomplete data or unbalanced data

• OLS regression is not suitable to analyze longitudinal data because its assumptions are violated by the data.

Limitations of traditional approach for modeling longitudinal data

• Univariate repeated measure ANOVA

• Person effects are random, time effects and other factor effects are fixed – it reduces residual variance by considering the person effects.

• Fixed time point (evenly or unevenly spaced)

• It assumes a unique residual variance-covariance structure (compound symmetry), which assume equal variance over time among observations from the same person and a constant covariance.

Limitations of traditional approach for modeling longitudinal data

• Univariate repeated measure ANOVA

• An alternative assumption, sphericity: it assumes equal variance difference between any two time points.

Limitations of traditional approach for modeling longitudinal data

• Univariate repeated measure ANOVA

• The assumptions could not be held for longitudinal data

• People change at varied rates, so that variances often change over time

• Covariances close in time usually greater than covariances distil in time

• Test of variance-covariance structure is necessary to validate significance tests

Limitations of traditional approach for modeling longitudinal data

• Multivariate repeated measure ANOVA

• Use generalized method – no specific assumptions about variances and covariances (unstructured).

• It does not allow any other structure, so when the repeated measures increase, it causes over-parameterization.

• Subjects with missing data on any time point will be deleted from analysis.

Limitations of traditional approach for modeling longitudinal data

• In addition, none of them allow time-varying predictors

Advantage of longitudinal data analysis in HLM longitudinal data

• Ability to deal with missing data (missing at random, MAR)

• No assumptions about compound symmetry

• More flexible:

• Unequal numbers of measurement or unequal measurement intervals

• Includes time-varying covariate

Research questions longitudinal data

• Is there any effect of time on average (fixed effect of time significant)?

• Does the average effect of time vary across persons (random effect of time significant)?

A Linear Growth Model longitudinal data

• Level 1 (within subject model)

Yti is the measurement of ith subject at tthtime point

• Level 2 (between subject model)

An example longitudinal data

covariance

Residual

Sample

Intercept

(Grand Mean)

Sample

slope

(Grand Mean)

Individual

Intercept

Deviation

Individual

slope

Deviation

In the model longitudinal data

• Six Parameters:

• Fixed Effects: β00and β10, level 2

• Random Effects:

• Variances of r0iand r1i(τ002, τ112), level 2

• Covariance of r0iand r1i(τ01), level 2

• Residual Variance of eti (σe2), level 1

Average growth trend longitudinal data

Growth rate, average English increase at one unit of time increment is 1.50

Initial status, average English score at time 0 is 235.62

Final estimation of fixed effects:

----------------------------------------------------------------------------

Standard Approx.

Fixed Effect Coefficient Error T-ratio d.f. P-value

----------------------------------------------------------------------------

For INTRCPT1, P0

INTRCPT2, B00 235.619409 0.344737 683.476 6822 0.000

For TIME slope, P1

INTRCPT2, B10 1.500423 0.033980 44.156 6822 0.000

Random intercept-slope longitudinal data

Growth rates are different among different students, various slopes. A student whose growth is 1 SD above average is expected to grow at the rate of 1.50+0.93=2.43 per time unit

Initial status, students vary significantly in English score at time 0.

Final estimation of variance components:

-----------------------------------------------------------------------------

Random Effect Standard Variance df Chi-square P-value

Deviation Component

-----------------------------------------------------------------------------

INTRCPT1, R0 19.99410 399.76396 6703 11430.55547 0.000

TIME slope, R1 0.930350.86556 6703 9568.06880 0.000

level-1, E 24.81882 615.97397

Reliability longitudinal data

• Ratio of the “true” parameter variance to the “total” observed variance. Close to zero means observed score variance must be due to error.

• Without knowledge of the reliability of the estimated growth parameter, we might falsely draw a conclusion due to incapability of detecting relations.

----------------------------------------------------

Random level-1 coefficient Reliability estimate

----------------------------------------------------

INTRCPT1, B0 0.423

TIME, B1 0.108

----------------------------------------------------

Correlation of change with initial longitudinal datastatus

• Choose “print variance-covariance matrices” under output settings.

• Students who have higher English score at initial point tend to have a faster growth rate.

Tau (as correlations)

INTRCPT1,B0 1.000 0.413

TIME,B1 0.413 1.000

We could make it more complicated longitudinal data

• An intercepts- and Slopes-as-outcomes model

• Level 1 (within subject model)

Yti is the measurement of ith subject at tthtime point

• Level 2 (between subject model)