Data and Methods

These analyses are conducted with the sample of 2880 LSAC Birth Cohort participants selected through the selection procedure outlined in Chapter 3. At Wave 1 children were aged from 3 months to 1 year; at Wave 2, children were aged from 2 to 3 years; and at Wave 3, children were aged from 4 to 5 years.

4.2.1 Measures used in the analyses

Variables of interest were selected a priori from measures in the parent interviews across three waves of data collection. Relevant scales from the mother - reported temperament data collected at each wave were selected to represent the

domains of emotional and cognitive regulation. These scales were drawn from the Short Temperament Scale for Infants (Wave 1), Short Temperament Scale for Toddlers (Wave 2) and Short Temperament Scale for Children (Wave 3; Prior, Sanson, & Oberklaid, 1989).

Reactivity items from temperament scales were selected at each wave to tap emotional regulation. Persistence items were selected at Waves 2 and 3 to tap cognitive regulation. There were no items measuring cognitive regulation at Wave 1 (infancy). Different item sets at each wave reflect the developmental stages of children the measures are designed for. Mothers responded to items on a 6-point scale: 1 = almost never to, 6 = almost always. For the current study, items were reverse coded where required in order for higher scores to reflect lower reactivity and higher persistence, and therefore potentially higher regulatory skills.

Variables measuring sleep regulation were selected at each wave to tap

99 from The Infant Sleep Study (Bayer et al., 2007), each with a yes/no response.

Responses were reverse scored in order for higher scores to reflect a greater capacity to regulate sleep, demonstrated through lower levels of sleeping problems.

4.2.2 Approach to the analyses

Descriptive statistics including frequencies and correlations were used to screen variables prior to further analysis. CFAs for the latent variables of sleep regulation, reactivity and persistence were conducted using Mplus Version 7 software at each wave. This was done to examine the extent to which these items worked well together as indices of self-regulation. The longitudinal relationships among the latent variables for sleep regulation, reactivity and persistence were then explored using longitudinal SEM. All variables were treated in the analyses as ordinal categorical as a maximum of six-point response scales were used and so were not considered continuous. The

estimator used was the WLSMV estimator, which provides “weighted least square parameter estimates using a diagonal weight matrix with standard errors and mean- and variance-adjusted chi-square test statistic that use a full weight matrix” (Muthén & Muthén, 1998 - 2012, p. 533). This estimator has been recommended where CFA analyses use data that are categorical or ordinal in nature (Brown, 2006).

The extent to which each model fit the data was assessed using the RMSEA, CFI, TLI and WRMR fit indices as described in Chapter 3. A model was assessed as having ‘excellent’ fit if it met the criteria for all four fit indices, ‘good’ if it met the criteria for three indices and was close to meeting criteria for the fourth, ‘adequate’ if it met criteria for two out of the four fit indices and ‘poor’ if it met only one or none of the criteria across the four indices.

When the hypothesised measurement model at baseline showed poor fit to the data, the model estimates and modification indices were examined and re-specification undertaken as required. The model estimates included the path coefficients and r- squares for the items. The path coefficients in this case represent tobit regression coefficients because the variables were indicated in the model as categorical. These coefficients represent the factor loadings of the indicator variables onto their underlying latent construct. R-square values represent the proportion of variance in each dependent variable accounted for by its related factor. These are shown in italics in the figures below.

100 Modification indices were examined to identify parameter constraints which, if freely estimated, would contribute to a significant drop in chi-square, hence, potentially improving overall model fit (Byrne, 2012). These issues were used along with current self-regulation theory to guide decisions regarding model re-specification. Any re- specified models were then compared to the baseline model using the DIFFTEST option in Mplus. This option is required to obtain a correct chi-square difference test when the WLSMV estimator is used because the difference in chi-square values for two nested models using this estimator is not distributed as chi-square (Muthén & Muthén, 1998 - 2012). Significant chi-square difference values indicate that the nested model is a significantly better fit than the baseline model.

Due to the innovative nature of this work and the complexity of the

developmental phenomenon under investigation, perfectly fitting models were not anticipated. Goffin (2007) and MacCallum (2003) have noted that SEMs that involve complex psychological and developmental phenomena may not meet tests for perfect fit and therefore it cannot be assumed that they contain the whole truth. Rather, such models that describe a close approximation to reality may guide further theoretical and research developments. Model interpretation and the results reported throughout this chapter were undertaken with reference to a range of recent literature pertaining to the topic of SEM and reporting of measurement models (Bentler, 2007; Jackson et al., 2009; Kline, 2011; McDonald & Ho, 2002; Schreiber et al., 2006).

Prior to conducting the analyses presented in this chapter, a different approach to modelling the relationships among the self-regulation constructs was explored. This involved developing measurement models for a second-order factor of broad self- regulation at each time point. At each wave this second-order factor was indicated by first-order factors of sleep regulation, reactivity and persistence. A single item of eating problems was also used at Wave 1. These analyses were useful in order to learn the theory and procedures for conducting CFAs within a SEM framework, but were ultimately of no substantive use in the ongoing development of this program of

research. This is because the second-order models did not fit the data well and various estimation problems prevented them from being used longitudinally. The results of these initial CFA analyses are presented in Appendix E in the interest of space in this chapter.

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