Sequential COHORT DESIGN, Exams of Design

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SEQUENTIAL COHORT DESIGN

Mixing cross-sectional and longitudinal designs

Expanding the number of time points

• Repeated measurements are expensive
• Basic simultaneous cross-sectional studies can also provide information on age-related effects - Just treat age as time! - The key assumption is that there are no cohort effects
• No intra-individual change can be assessed, only group effects
• Useful in educational research Age group Sample Occasion Variables Implied occasion A1 S1 T1 X1, X2,…Xm T A2 S2 T1 X1, X2,…Xm T … … Ag Sg T1 X1, X2,…Xm Tg

Sequential cohort design

• Latent Growth Cohort-Sequential (or accelerated) design links adjacent segments of repeated data from different age cohorts to estimate a common developmental trend or growth curve - Each cohort has a different pattern of “missingness” - It is possible to build the complete curve using information from all

cohorts simultaneously

Study of drinking habits in young

people

• Research question: Development of alcohol use from age 16 to 29
• Sample: community sample of Swiss urban adolescents and young adults aged 16 to 24 (N=2840)
• Occasions: baseline 2003; 2-year follow up, 5- year follow up
• Measure: Frequency of alcohol use during the month prior to the interviews using 5 response categories: 0=never, 1=1–3 times a month, 2=1– 2 times a week, 3=3–6 times a week, 4=daily.

Age as time

• Cohort Age >>
  • 1987 t1 t2 t
  • 1986 t1 t2 t
  • 1985 t1 t2 t
  • 1984 t1 t2 t
  • 1983 t1 t2 t
  • 1982 t1 t2 t
  • 1981 t1 t2 t
  • 1980 t1 t2 t
  • 1979 t1 t2 t
• Time score

Data mapping approach

• DATA COHORT syntax option in Mplus – works out the

time score based on birth year and measurement year

• Only works with continuous variables!

• Let’s pretend that our “alcohol use” variables are

continuous and check out this option

• The idea is to re-map our cohort and occasion variables

as new time score

• Then specify a growth model for the whole time span

(14 years)

• Let’s hypothesise a quadratic growth curve
• Drinking will steadily increase, reach a pick in mid 20th, and then decrease

Accelerated cohort syntax

VARIABLE: !some other commands here DATA COHORT: COHORT IS BirthY (1987 1986 1985 1984 1983 1982 1981 1980 1979); TIMEMEASURES= t1alk (2003) t2alk (2005) t3alk (2008); TNAMES = alk; MODEL: int slope qu | [email protected] [email protected] [email protected] [email protected] alk20@-. [email protected] [email protected] alk23@0 alk24@. [email protected] [email protected] [email protected] [email protected] [email protected]; alk16-alk29* (1); !assume residual variances the same across time Centring on the middle time point is often better for quadratic curves

Results with continuous data: fit

• Model fit is not great but not too bad either

Chi-Square Test of Model Fit Value 100. Degrees of Freedom 45 P-Value 0. CFI 0. TLI 0. RMSEA (Root Mean Square Error Of Approximation) Estimate 0. 90 Percent C.I. 0.015 0.

Discussion of the DATA COHORT

approach

• Even if no data is missing due to nonresponse, there is plenty of missing data by design - Each individual only has 3 non-missing responses, and 11 missing responses - can be considered MCAR because these responses were never collected
• However, this approach assumes that we actually had 14 data collection occasions - Which we did not - Are the degrees of freedom correct?

Multi-group approach

• The idea is to specify a growth model for each of the

cohorts (using the new time score)

• And then test if the same model holds for all cohorts

• Different cohorts will have different occasions present

• Missing by design (MCAR)

• Treat cohorts as multiple groups with their own

measurement occasions

• Importantly, to maintain common growth model, its

parameters have to be constrained equal across

cohorts

Sequential cohort multi-group syntax:

common model

MODEL:

! This is the common model, and also model for the 1987 cohort INT SLP QU | [email protected] [email protected] [email protected]; !These constraints mean that the samples are drawn from the same population INT (1); !variance of the intercept is the same across samples SLP (2); !variance of the slope is the same QU (3); !variance of the quadratic term is the same [INT] (4); !mean of the intercept is the same [SLP] (5); !mean of the slope is the same [QU] (6); !mean of the quadratic term is the same INT WITH SLP0 (7); !and all covariances are the same INT WITH QU0 (8); SLP WITH QU0 (9); t1alk-t3alk (10); !residuals are assumed equal across time Same middle- point centring as before

Sequential cohort multi-group syntax:

cohort-specific models

MODEL 1986: INT SLP QU| [email protected] [email protected] [email protected]; MODEL 1985: INT SLP QU| [email protected] [email protected] t3alk@0; MODEL 1984: INT SLP QU| [email protected] [email protected] [email protected]; MODEL 1983: INT SLP QU| [email protected] [email protected] [email protected]; MODEL 1982: INT SLP QU| [email protected] t2alk@0 [email protected]; MODEL 1981: INT SLP QU| [email protected] [email protected] [email protected]; MODEL 1980: INT SLP QU| t1alk@0 [email protected] [email protected]; MODEL 1979: INT SLP QU| [email protected] [email protected] [email protected];

Model results: approximate fit

• Fit indices are a little worse than in the DATA

COHORT approach

RMSEA (Root Mean Square Error Of Approximation) Estimate 0. 90 Percent C.I. 0.043 0. Probability RMSEA <= .05 0. CFI 0. TLI 0.

Model results: means

• Means Estimate S.E. Est./S.E. P-Value
• INT 1.493 0.015 97.160 0.
• SLP 0.374 0.031 12.161 0.
• QU -0.575 0.065 -8.866 0.
• Observed and estimated means plotted Means are exactly the same as in the DATA COHORT model (slide 12)