ACF OPRE: Early Head Start Research and Evaluation Project (EHSRE)

D.5 RESULTS FROM THE GROWTH CURVE ANALYSIS

As discussed in Chapter II, in addition to our basic point-in-time analysis, we used longitudinal statistical methods (or, more specifically, growth curve or hierarchical linear modeling) to estimate the effects of Early Head Start participation on child and family outcomes that were measured when the focus children were, on average, 15, 25, and 37 months old. These methods were used to examine impacts (program and control group differences) on the growth trajectories of child and family outcomes during the follow-up period.

In our context, the growth curve approach can be considered a two-stage process. First, a regression line is fit through the three data points for each program and control group member, and second, impacts are obtained on these estimated intercepts and slopes. For each outcome measure, the growth curve approach produces an overall regression line for the program group (defined by the mean estimated intercept and mean estimated slope across all program group members) and, similarly, an overall regression line for the control group. The difference between these overall regression lines at any given time point yields a point-in-time impact estimate.7

The sample for the growth curve analysis included only those sample members who completed interviews and assessments at every time point. The sample for the basic point-in-time analysis, however, used all available data at each time point.8

Several criteria were used to select the child and family outcomes for the growth curve analysis. First, we only selected outcomes that were measured at each birthday-related interview or assessment. Second, we selected outcomes that are continuous variables. We excluded binary and categorical variables, because it is difficult to interpret growth for these variables at the individual level. Finally, we excluded outcomes that were age-normed (for example, the Bayley MDI). Eleven outcome variables met the criteria for inclusion in the growth curve analyses.

Tables D.5A and D.5B display results from the growth curve analysis. Table D.5A displays the estimated intercepts and slopes (growth rates) for program and control group members, as well as impacts on these intercepts and slopes. The parameters of the growth curve models were scaled so that the estimated intercepts represent average outcomes when the focus children were 15 months old. Hence, the estimated slopes represent the extent to which the outcomes changed per month between the time the focus children were 15 and 37 months old.

Table D.5B displays differences between the fitted lines for the program and control groups (that is, impacts on the outcomes) evaluated at the 15-, 25-, and 37-month points. The table also displays the corresponding impact estimates obtained using the basic point-in-time approach. As expected (see Chapter II), the two sets of impacts are generally similar (and especially so for the 37-month outcomes). Thus, as discussed in Chapter V of Volume I, the two approaches yield the same policy conclusions about the effects of Early Head Start on key child and family outcomes.

In Figures D.5A through D.5K, we display the changes over time in the variables documented in the tables. In Chapter V of Volume I, we discuss these findings in the context of the other impact analyses.

TABLE D.5A

ESTIMATED INTERCEPTS AND SLOPES FOR CHILD AND FAMILY OUTCOMES FROM THE GROWTH CURVE MODELS, BY RESEARCH STATUS
Variable	Estimated Intercept: Average Outcome at 15 Months			Estimated Slope: Growth Between 15 and 37 Months
Variable	Program Group	Control Group	Impact Per Eligible Applicant	Program Group	Control Group	Impact Per Eligible Applicant
Child Engagement (Semistructured Play)	3.927	3.835	0.092	0.0399	0.0347	0.0026
Child Negativity Toward Parent (Semistructured Play)	2.089	2.115	-0.026	-0.0381	-0.0358	-0.0023
Child Sustained Attention with Objects (Semistructured Play)	5.025	4.946	0.08	-0.0016	-0.0044	0.0028
Parental Supportiveness (Semistructured Play)	4.065	3.976	0.089*	-0.0015	-0.0022	0.0007
Parent-Child Activities (HOME)	4.506	4.504	0.001	-0.0023	-0.0049	0.0027
Parent Detachment (Semistructured Play)	1.534	1.625	-0.091**	-0.0142	-0.0168	0.0026
Parent Intrusiveness (Semistructured Play)	2.365	2.43	-0.065	-0.0397	-0.0409	0.0012
Negative Regard	1.474	1.455	0.018	-0.0077	-0.0065	-0.0012
PSI: Parental Distress	26.432	27.263	-0.831*	-0.0907	-0.0865	-0.0041
PSI: Parent-Child Dysfunctional Interaction	17.165	17.466	-0.301	0.0095	0.006	0.0035
Family Conflict Scale (FES)	1.745	1.704	0.04	-0.0036	-0.0007	-0.0029*
Sample Sizee
Parent Interview	898	802	1,700	898	802	1,700
Bayley	559	485	1,044	559	485	1,044
Video	617	551	1,168	617	551	1,168

SOURCE: Parent interview and child assessments.

NOTE: All estimates were calculated using growth curve models. Generalized least squares techniques were used to estimate the regression models where the explanatory variables included a treatment status indicator variable, a variable signifying the age of the child at the interview or assessment relative to 15 months, a term formed by interacting child’s age and the treatment status indicator variable, and other explanatory variables from the HSFIS data.

aThe analysis sample for each outcome includes those with available outcome data at all three time points.

*Significantly different from zero at the .10 level, two-tailed test
**Significantly different from zero at the .05 level, two-tailed test.
***Significantly different from zero at the .01 level, two-tailed test.

TABLE D.5B

ESTIMATED IMPACTS PER ELIGIBLE APPLICANT ON KEY OUTCOMES AT 15, 25, AND 37 MONTHS USING THE POINT-IN-TIME AND GROWTH CURVE ESTIMATION METHODS
Variable	Impact at 15 Months		Impact at 24 Months		Impact at 36 Months
Variable	Point-In-Time Method	Growth Curve Method	Point-In-Time Method	Growth Curve Method	Point-In-TimeMethod	Growth Curve Method
Child Engagement (Semistructured Play)	.079	.092	.098*	.118***	.185***	.148**
Child Negativity Toward Parent (Semistructured Play)	-.110**	-0.026	-0.067	-0.049	-.073**	-0.076
Child Sustained Attention with Objects (Semistructured Play)	.095**	0.08	0.062	.108***	.138***	.142***
Parent Supportiveness (Semistructured Play)	.132***	.089*	.093*	.096**	.117***	.105*
Parent-Child Activities (HOME)	.01	.001	.079**	.028	.062	.06
Parent Detachment (Semistructured Play)	-.096**	-.091**	-.091**	-.064*	-.054*	-0.033
Parent Intrusiveness (Semistructured Play)	-0.061	-0.065	-0.044	-0.053	-0.04	-0.038
Negativity Toward Parent (Semistructured Play)	-0.029	.018	.008	.006	-0.009	-0.009
PSI: Parental Distress	-0.481	-.831*	-1.049**	-.872**	-0.67	-.922**
PSI: Parent-Child Dysfunctional Interaction	-0.216	-0.301	-.449*	-0.266	.026	-0.224
Family Conflict Scale (FES)	.006	.04	-.053**	.012	-0.022	-0.023
Sample Sizea
Parent Interview	898	802	1,700	898	802	1,700
Bayley	559	485	1,044	559	485	1,044
Video	617	551	1,168	617	551	1,168

SOURCE: Parent interview and child assessments.

aThe analysis sample for each outcome includes those with available outcome data at all three time points.(back)

FIGURE D.5A

GROWTH CURVES FOR CHILD ENGAGEMENT WITH PARENT IN
SEMISTRUCTURED PLAY
[D]
Source: Assessments of children’s behavior during parent-child interactions in semistructured play conducted when children were approximately 15, 25, and 37 months old. The variable is coded on a scale of 1 to 7 (see Box V.2 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months: Significantly different from zero at the .10 level, two-tailed test. Significantly different from zero at the .05 level, two-tailed test. **Significantly different from zero at the .01 level, two-tailed test.

FIGURE D.5B

GROWTH CURVES FOR CHILD SUSTAINED ATTENTION WITH OBJECTS IN SEMISTRUCTURED PLAY
[D]
Source: Assessments of children’s behavior during parent-child interactions in semistructured play conducted when children were approximately 15, 25, and 37 months old. The variable is coded on a scale of 1 to 7 (see Box V.3 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months: Significantly different from zero at the .10 level, two-tailed test. Significantly different from zero at the .05 level, two-tailed test. **Significantly different from zero at the .01 level, two-tailed test.

FIGURE D.5C

GROWTH CURVES FOR CHILD NEGATIVITY TOWARD PARENT IN
SEMISTRUCTURED PLAY
[D]
Source: Assessments of children’s behavior during parent-child interactions in semistructured play conducted when children were approximately 15, 25, and 37 months old. The variable is coded on a scale of 1 to 7 (see Box V.2 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months.

FIGURE D.5D

PARENT SUPPORTIVENESS DURING SEMISTRUCTURED PLAY
[D]
Source: Assessments of parents’ behavior during parent-child interactions in semistructured play conducted when children were approximately 15, 25, and 37 months old. The variable is coded on a scale of 1 to 7 (see Box V.4 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months: Significantly different from zero at the .10 level, two-tailed test. Significantly different from zero at the .05 level, two-tailed test. **Significantly different from zero at the .01 level, two-tailed test.

FIGURE D.5E

PARENT-CHILD PLAY ACTIVITIES
[D]
Source: Parent interviews conducted when children were approximately 15, 25, and 37 months old. Scores on the HOME parent-child activities scale can range from 1 to 6 (see Box V.5 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months.

FIGURE D.5F

PARENT DETACHMENT DURING SEMISTRUCTURED PLAYa
[D]
Source: Assessments of parent-child interactions in semistructured play conducted when children were approximately 15, 25, and 37 months old. The variable is coded on a scale of 1 to 7 (see Box V.6 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months: Significantly different from zero at the .10 level, two-tailed test. Significantly different from zero at the .05 level, two-tailed test. Significantly different from zero at the .01 level, two-tailed test. aImpact on the slope of the curves is statistically significant at p<.05, that is, the slope for the program group declines at a steeper rate than does the control group’s.(back**)

FIGURE D.5G

PARENT INTRUSIVENESS DURING SEMISTRUCTURED PLAY
[D]
Source: Assessments of parents’ behavior during parent-child interactions in semistructured play conducted when children were approximately 15, 25, and 37 months old. The variable is coded on a scale of 1 to 7 (see Box V.6 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months: Significantly different from zero at the .10 level, two-tailed test. Significantly different from zero at the .05 level, two-tailed test. **Significantly different from zero at the .01 level, two-tailed test.

FIGURE D.5H

PARENT NEGATIVE REGARD DURING SEMISTRUCTURED PLAY
[D]
Source: Assessments of parents’ behavior during parent-child interactions in semistructured play conducted when children were approximately 15, 25, and 37 months old. The variable is coded on a scale of 1 to 7 (see Box V.6 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months.

FIGURE D.5I

PARENT DISTRESS (PSI)a
[D]
Source: Parent interview conducted when children were approximately 15, 25, and 37 months old. The 12-item scale yields scores that can range from 12 to 60 (see Box V.8 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months: Significantly different from zero at the .10 level, two-tailed test. Significantly different from zero at the .05 level, two-tailed test. Significantly different from zero at the .01 level, two-tailed test. aImpact on the slope of the curves is statistically significant at p<.10, that is, the slope for the program group declines at a somewhat steeper rate than does the control group’s.(back**)

FIGURE D.5J

PARENT-CHILD DYSFUNCTIONAL INTERACTION (PSI)
[D]
Source: Parent interview conducted when children were approximately 15, 25, and 37 months old. The 12-item scale yields scores that can range from 12 to 60 (see Box V.8 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months.

FIGURE D.5K

FAMILY CONFLICT (FAMILY ENVIRONMENT SCALE)a
[D]
Source: Parent interview conducted when children were approximately 15, 25, and 37 months old. The 5-item scale yields an average item score ranging from 1 to 4 (see Box V.8 and Appendix C). Note: The growth curve analysis differs from the other impact analyses in several respects. The sample includes only those children and parents for whom we completed the assessments at all three ages. In addition, due to analytic complications, the growth curve analysis pooled the observations across sites rather than weighting by sites as was done for the point-in-time regression adjusted impact analyses. Appendix D.5 includes details on the sample sizes, estimated intercepts and slopes (growth rates) for each group, and the impacts on each. Hierarchical linear modeling produced the regression lines for the program and control groups. Asterisks indicate the significance of the difference between the regression lines at 15, 25, and 37 months. aImpact on the slope of the curves is statistically significant at p<.10, that is, the slope for the program group declines at a somewhat steeper rate than does the control group’s.(back)

7As discussed in Chapter II, the growth curve models were estimated in one stage rather than two, for efficiency reasons.(back)

8Another difference between the two approaches is that, because of analytic complications, sites were weighted by their sample sizes using the growth curve approach (that is, observations across sites were pooled), whereas sites were weighted equally using the basic point-in-time approach. However, as shown in the sensitivity analysis in Appendix D.4, the impact results using the basic point-in-time approach are very similar using the two weighting schemes.(back)

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