Godfried van den Wittenboer

On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints.

The authors show how the use of inequality constraints on parameters in structural equation models may affect the distribution of the likelihood ratio test. Inequality constraints are implicitly used in the testing of commonly applied structural equation models, such as the common factor model, the autoregressive model, and the latent growth curve model, although this is not commonly acknowledged. Such constraints are the result of the null hypothesis in which the parameter value or values are placed on the boundary of the parameter space. For instance, this occurs in testing whether the variance of a growth parameter is significantly different from 0. It is shown that in these cases, the asymptotic distribution of the chi-square difference cannot be treated as that of a central chi-square-distributed random variable with degrees of freedom equal to the number of constraints. The correct distribution for testing 1 or a few parameters at a time is inferred for the 3 structural equation models mentioned above. Subsequently, the authors describe and illustrate the steps that one should take to obtain this distribution. An important message is that using the correct distribution may lead to appreciably greater statistical power.

Longitudinal relations between sleep quality, time in bed and adolescent problem behaviour

Poor sleep appears to be related to behaviour problems in adolescence (Fallone, Owens, & Deane, 2002; Wolfson & Carskadon, 2003). Poor sleep is generally related to bad sleep quality or shortness of sleep. However, most studies do not make a distinction between the effects of sleep quality and sleep duration on problem behaviour. This is remarkable considering the differential effects of sleep quality or insomnia complaints and sleep duration onmeasures of health (Pilcher, Ginter, & Sadowsky, 1997) and problem behaviour (Liu & Zhou, 2002; Meijer, Habekothe, & Van Den Wittenboer, 2000). In addition to components such as difficulty falling asleep or staying asleep, sleep quality includes subjective indices of sleep, such as how well rested one feels upon awakening and satisfactionwith sleep (Pilcher et al., 1997). In this respect, sleep quality corresponds to insomnia, as defined by the American Psychiatric Association (APA, 2000). In most studies sleep duration is generally operationalized as self-reported sleep time or time in bed (see, for example, Fredriksen, Rhodes, Reddy, & Way, 2004; Liu & Zhou, 2002; Meijer et al., 2000). Because time in bed is considered to be the time that one goes to bed to the time that one gets out of the bed in the morning, it is usually longer than sleep duration, which is defined as the amount of time one spends asleep during the night. Reported correlations between adolescents’ time in bed and sleep quality are not significant (Meijer et al., 2000; Totterdell, Reynolds, Parkinson, & Briner, 1994). Reported prevalence of sleep problems (initiating and maintaining sleep) for (pre)adolescents varies from 10% to 33% (Fricke-Oerkermann et al., 2007; Ipsiroglu, Fatemi, Werner, Paditz, & Schwarz, 2002; Liu & Zhou, 2002; Manni et al., 1997; Meijer et al., 2000). Based on the DSM-IV criteria for insomnia, a prevalence of 11% among 13–16-year-old adolescents was found (Johnson, Roth, Schultz, & Breslau, 2006). Based on the more stringent Youth-Reported DSM-IV symptom criteria for a diagnosis of insomnia (APA, 2000), Roberts, Roberts, and Duong (2008) reported a point prevalence of one or more symptoms of insomnia for 27% of 11–17-year-old adolescents. In this group 5% met diagnostic criteria for insomnia. Sleep quality or insomnia seems in particular to be related to internalising problem behaviour (Paavonen, Solantaus, Almqvist, & Aronen, 2003), neuroticism and neuro-somaticism (Meijer et al., 2000), psychosomatic symptoms and perceived health (Roberts, Roberts, & Chen, 2001; Roberts, Roberts, & Duong, 2008). It is also related to disturbed mood, anxiety and depression (Forbes et al., 2008; Johnson, Roth, & Breslau, 2006; Manni et al., 1997; Morrison, McGee, & Stanton, 1992; Roberts et al., 2001; Roberts et al., 2008) and stress (Kataria, Swanson, & Trevathan, 1987; Wolfson, Tzschinsky, Darley, Acebo, & Carskadon, 1995); although, in a few studies, relations of sleep quality with externalising problem behaviour, especially with aggressive and hostile behaviour, have also been found (Dahl, 2006; Ireland & Culpin, 2006; Meijer et al., 2000). One of the most remarkable facts concerning adolescents’ sleep is the decline of sleep duration (Steinberg & Morris, 2001). Associations of sleep duration or time in bed with oppositional behaviour, inattentive behaviour, and impaired mood are reported (Fallone et al., 2002; Liu & Zhou, 2002). Sixth grade students who obtained less sleep over time exhibited higher levels of depression and lower levels of self-esteem in the eighth grade (Fredriksen et al., 2004) and sleep problems at age 4, as rated by parents, were related to increasing levels of depression/anxiety and aggression, rated also by parents, in mid-adolescence (Gregory & O’Connor, 2002). Longitudinal studies concerning the influence of sleep on (pre)adolescents’ problem behaviour are scarce. Because they are mostly part of a larger epidemiological study, they are restricted to the study of sleep loss (Fredriksen et al., 2004), insomnia (Roberts et al., 2008), a single question concerning ‘sleeping difficulties’ (Paavonen et al., 2003) or a general sleep estimate (Gregory & O’Connor, 2002). Generally, sleep measures in these studies are associated with a broad range of problem behaviour. In order to study the differential effects of both sleep quality and sleep duration on adolescent problem behaviour, we focused on the unique and combined influence of sleep quality, time in bed, chronological age and gender on various types of adolescent problem behaviour. A longitudinal design of three measurements at one-year time intervalswas used to take developmental aspects into account. We expected that worse sleep quality and a decline in time in bed wouldbe related tomoreproblembehaviourover time. Conflict of interest statement: No conflicts declared. Journal of Child Psychology and Psychiatry 51:11 (2010), pp 1278–1286 doi:10.1111/j.1469-7610.2010.02261.x

Mental health, parental rules and sleep in pre‐adolescents

A health‐sleep model concerning the relationship of mental health and parental rules with time in bed and sleep quality has been developed on the basis of survey data collected from 448 children in the first trimester of the regular school year. The children had a mean age of about 11 years and were attending last two grades of primary school. The relations between mental health characteristics, parental rules concerning sleep, sleep environment, sleep quality and time in bed are analysed using a structural equation model. In addition to a latent variable for ‘mental health’, two uncorrelated latent variables had to be introduced for sleep to achieve a satisfactory fit. One latent variable is related to sleep quality (restorative sleep), and the other relates to lying awake in bed prior to sleep (awake in bed). Restorative sleep shows a strong relationship with mental health, and awake in bed is related to having an own bedroom.

Including Time-Invariant Covariates in the Latent Growth Curve Model

Within the latent growth curve model, time-invariant covariates are generally modeled on the subject level, thereby estimating the effect of the covariate on the latent growth parameters. Incorporating the time-invariant covariate in this manner may have some advantages regarding the interpretation of the effect but may also be incorrect in certain instances. In this article we discuss a more general approach for modeling time-invariant covariates in latent growth curve models in which the covariate is directly regressed on the observed indicators. The approach can be used on its own to get estimates of the growth curves corrected for the influence of a 3rd variable, or it can be used to test the appropriateness of the standard way of modeling the time-invariant covariates. It thus provides a test of the assumption of full mediation, which states that the relation between the covariate and the observed indicators is fully mediated by the latent growth parameters.

Unbalanced 2 x 2 Factorial Designs and the Interaction Effect: A Troublesome Combination

In this power study, ANOVAs of unbalanced and balanced 2 x 2 datasets are compared (N = 120). Datasets are created under the assumption that H1 of the effects is true. The effects are constructed in two ways, assuming: 1. contributions to the effects solely in the treatment groups; 2. contrasting contributions in treatment and control groups. The main question is whether the two ANOVA correction methods for imbalance (applying Sums of Squares Type II or III; SS II or SS III) offer satisfactory power in the presence of an interaction. Overall, SS II showed higher power, but results varied strongly. When compared to a balanced dataset, for some unbalanced datasets the rejection rate of H0 of main effects was undesirably higher. SS III showed consistently somewhat lower power. When the effects were constructed with equal contributions from control and treatment groups, the interaction could be re-estimated satisfactorily. When an interaction was present, SS III led consistently to somewhat lower rejection rates of H0 of main effects, compared to the rejection rates found in equivalent balanced datasets, while SS II produced strongly varying results. In data constructed with only effects in the treatment groups and no effects in the control groups, the H0 of moderate and strong interaction effects was often not rejected and SS II seemed applicable. Even then, SS III provided slightly better results when a true interaction was present. ANOVA allowed not always for a satisfactory re-estimation of the unique interaction effect. Yet, SS II worked better only when an interaction effect could be excluded, whereas SS III results were just marginally worse in that case. Overall, SS III provided consistently 1 to 5% lower rejection rates of H0 in comparison with analyses of balanced datasets, while results of SS II varied too widely for general application.

Respiratory Variability and Psychological Well-Being in Schoolchildren

Among the relations between respiration and psychological state, associations with respiratory variability have been contradictory. In this study, respiration was measured noninvasively in 162 children with a mean age of 11 years (from 9 to 13). They completed a battery of psychological tests. Structural Equation Modeling (SEM or LISREL) revealed a model that fit the data well (χ 2 = 88.201, df = 79, p = .224). In this model, respiratory variability was positively related to anger-in and negatively to negative fear of failure and neurotic complaints. Respiration rate was positively related to positive fear of failure, and duty cycle was positively related to the latent variable of negative affect. Variability in resting time components of respiration was higher among children with less fear of failure and fewer complaints. Therefore, respiratory variability need not necessarily be a sign of psychological dysfunctions, and interventions should not always impose a fixed breathing pattern.Among the relations between respiration and psychological state, associations with respiratory variability have been contradictory. In this study, respiration was measured noninvasively in 162 children with a mean age of 11 years (from 9 to 13). They completed a battery of psychological tests. Structural Equation Modeling (SEM or LISREL) revealed a model that fit the data well (X2 = 88.201, df = 79, p = .224). In this model, respiratory variability was positively related to anger-in and negatively to negative fear of failure and neurotic complaints. Respiration rate was positively related to positive fear of failure, and duty cycle was positively related to the latent variable of negative affect. Variability in resting time components of respiration was higher among children with less fear of failure and fewer complaints. Therefore, respiratory variability need not necessarily be a sign of psychological dysfunctions, and interventions should not always impose a fixed breathing pattern.

Fractional designs: a simulation study of usefulness in the social sciences

Fractional designs can be extremely useful in social science research, especially when a large number of factors is involved. Reluctance for the use of fractional designs seems to be warranted for two reasons: (1) In the social sciences, the amount of measurement error is often large, which may decrease the power, and (2) higher order interactions are assumed to be nonsignificant, which is difficult to guarantee without sufficient research. This simulation study shows the effects of measurement error and assumption violations under various conditions. It is concluded that fractional designs handle measurement error gracefully and that they are as powerful as a full design when equal degrees of freedom are available. Significant interaction effects can cause serious problems, especially in situations with low or intermediate measurement error, and can lead to erroneous conclusions. Only when estimated confounded effects are clearly not significant, the chance of a wrong decision is reasonably small. Therefore, fractional designs are especially warranted for the exclusion of irrelevant factors. However, we note pitfalls in the use of Version 1.0 of the program Trail Run from SPSS, Inc., to implement the procedures.

On the Structure of Measurements in Facet Theory

The mapping sentence in facet theory suggestsconstructing items according to a factorial design of facets. Analyzing the structure ofthe responses by multidimensional scaling, theorists usually expect the solution toreflect the constituting facets, so that it can be partitioned by levels of the facets. In the paperwe elucidate that each dimension relates to the response function of a specific subgroup, ratherthan to one or more separate facets. Partitioning by levels of a facet may lead toneglecting the real structure of the response function to be analyzed.The mapping sentence in facet theory suggestsconstructing items according to a factorial design of facets. Analyzing the structure ofthe responses by multidimensional scaling, theorists usually expect the solution toreflect the constituting facets, so that it can be partitioned by levels of the facets. In the paperwe elucidate that each dimension relates to the response function of a specific subgroup, ratherthan to one or more separate facets. Partitioning by levels of a facet may lead toneglecting the real structure of the response function to be analyzed.

Fractional Design Wizard: A computer program for cost-effective experimental research design

The computer program Fractional Design Wizard creates fractional factorial designs that are cost-effective and especially useful for discarding irrelevant factors from a large number of possible candidates. The program is intended for researchers who are relativelynew to the field of fractional design and who want to acquaint themselves with the use of fractions for the reduction of large experimental designs. Fractional designs allow estimation of main effects, and sometimes two-way interactions, without one’s having to examine all treatment conditions. The program needs Microsoft Windows 95 or better and 32 MB of memory. In a step-by-step fashion, the user can specify the required properties of the fractional design. When there are more valid designs, the user can generate these successively If necessary the user can go back to diminish the requirements. The output can be copied, printed, and saved. The program generates all the information that is needed for the use and interpretation of fractional designs. A help file explains the use of the program and also the purpose, the analysis, and the interpretation of fractional designs. The program, which is written in Object Pascal, is available as freeware on www.fss.uu.nl/ms/hl/fracdes.htm.

Conflicting Strategies in Dual Control Problems with Different Goals

Dual control problems are defined as dynamic games in which two players control the same dynamic system. If these players pursue different goals, interesting strategic problems arise when the two players make their moves sequentially. Distinct optimal strategies can be derived from a number of conceivable interpretations of the quadratic individual loss function in that case. Five such strategies are discussed, and the quite common assumption that the two players involved use the same strategy is dropped. Further results show how the different strategies perform against a linear optimal strategy and against each other.