Hierarchical structured data cause problems in analysis, because the usual assumptions of independently and identically distributed variables are violated. Muthén (1989) described an estimation method for multilevel factor and path analysis with hierarchical data. This article assesses the robustness of the method with unequal groups, small sample sizes at both the individual and the group level, in the presence of a low or a high intraclass correlation (ICC). The within-groups part of the model poses no problems. The most important problem in the between-groups part of the model is the occurrence of inadmissible estimates, especially when group level sample size is small (50) while the intracluster correlation is low. This is partly compensated by using large group sizes. When an admissible solution is reached, the factor loadings are generally accurate. However, the residual variances are underestimated, and the standard errors are generally too small. Having more or larger groups or a higher ICC does not effectively compensate for this. Therefore, although the nominal alpha level is 5%, the operating alpha level is about 8% in all simulated conditions with unbalanced groups. The strongest factor is an inadequate sample size at the group level. Imbalance is only a problem for the overall fit test. For balanced data, the chi-square fit test is accurate. The size of the biases is comparable to the effect of moderate nonnormality in ordinary modeling, and in our view, the approximate solution remains a useful analysis tool, provided the group level sample size is at least 100.
To examine the effectiveness of a theory-driven self-management course in reducing cardiovascular risk in patients with screen-detected type 2 diabetes, taking ongoing medical treatment into account.A total of 196 screen-detected patients, receiving either intensive pharmacological or usual-care treatment since diagnosis (3-33 months previously), were subsequently randomized to a control or intervention condition (self-management course). A 2 x 2 factorial design evaluated the behavioral intervention (self-management course versus control) nested within the medical treatment (intensive versus usual-care), using multilevel regression modeling to analyze changes in patients' BMI, A1C, blood pressure (BP), and lipid profiles over 12 months, from the start of the 3-month course to 9-month follow-up.The self-management course significantly reduced BMI (-0.77 kg/m2) and systolic BP (-6.2 mmHg) up until the 9-month follow-up, regardless of medical treatment. However, intensive medical treatment was also independently associated with lower BP, A1C, total cholesterol, and LDL before the course and further improvements in systolic BP (-4.7 mmHg). Patients receiving both intensive medical treatment and the self-management course therefore had the best outcomes.This self-management course was effective in achieving sustained reductions in weight and BP, independent of medical treatment. A combination of behavioral and medical interventions is particularly effective in reducing cardiovascular risk in newly diagnosed patients.
The classical multitrait-multimethod (MTMM) matrix can be viewed as a two-dimensional cross-classification of traits and methods. Beside commonly used analysis methods such as structural equation modeling and generalizability theory, multilevel analysis offers attractive possibilities. If the focus is only on analyzing classical MTMM data, the multilevel approach has no surplus value, because the resulting model is equivalent to a confirmatory factor model with additional restrictions imposed by the multilevel parameterization. However, if the data contain further complexities, such as additional information on the traits or persons, multilevel analysis of MTMM data offers a flexible analysis tool with more possibilities than the other approaches.
The authors' goal was to examine the course and predictors of posttraumatic stress symptoms among persons hospitalized for burns. A total of 301 participants completed self-report measures assessing peritraumatic mental state, anxiety related to pain, and posttraumatic stress symptoms. Twenty-six percent of the participants were suffering from posttraumatic stress symptoms at 2-3 weeks postburn and 15% of them at 12 months postburns. In general, a decrease in symptoms was observed over time, although a substantial part of the participants with acute stress symptoms suffers from chronic posttraumatic stress symptoms 1-year postburn. Symptoms were predicted by anxiety measures and objective factors, such as female gender, locus, and severity of injury.
Achievements of students in primary education have been the object of study over a long period. Both individual and contextual characteristics have proved their value for the prediction of these achievements. In this paper a theoretical model of the time and attention division of the teacher is elaborated. From this model, hypotheses are deduced about the labeling of a student as a problem student, and the possible referral of problem students to special education. Relative student characteristics are predicted to be of more importance than absolute characteristics. Hypotheses testing is based on data about 2,340 students in the Netherlands. The hypotheses are confirmed. Labeling of problem students is based on the relative achievements and relative behavior of students, while the referral to special education also can be predicted on the basis of relative achievements.
Background and Purpose— The purpose of this research was to describe the clinical course of children’s functioning (depression, behavioral problems, and health status) during the first year after parental stroke and to determine which patient-, spouse-, or child-related factors at the start of inpatient rehabilitation can predict children’s functioning after parental stroke at 1-year poststroke. Methods— Interviews with 82 children (4 to 18 years of age) and their parents (n=55) shortly after admission to a rehabilitation center, 2 months after discharge from inpatient rehabilitation, and 1 year after stroke. Depression was assessed using the Children Depression Inventory, behavioral problems with the Child Behavior Check List, and health status with the Functional Status II. Potential predictors were gender and age (child), activities of daily living disability and communication ability (patient), and spouse’s depression and perception of the marital relationship. Results— At the start of the stroke patient’s rehabilitation, 54% of the children had ≥1 subclinical or clinical problems, which improved to 29% 1 year after stroke. Children’s functioning 1 year after stroke could best be predicted by their functioning at the start of rehabilitation. Spouse depression and perception of marital relationship were also significant predictors. A total of 28% to 58% of the variance in children’s functioning could be explained. Conclusions— Children’s functioning after parental stroke improved during the first year after stroke. Identifying children at risk for problems 1 year after stroke requires assessment of children’s functioning and the healthy spouse’s depressive symptoms and perception of the marital relationship at the start of rehabilitation. This demonstrates the need for a family-centered approach in stroke rehabilitation.
A multilevel problem concerns a population with a hierarchical structure. A sample from such a population can be described as a multistage sample. First, a sample of higher level units is drawn (e.g. schools or organizations), and next a sample of the sub‐units from the available units (e.g. pupils in schools or employees in organizations). In such samples, the individual observations are in general not completely independent. Multilevel analysis software accounts for this dependence and in recent years these programs have been widely accepted. Two problems that occur in the practice of multilevel modeling will be discussed. The first problem is the choice of the sample sizes at the different levels. What are sufficient sample sizes for accurate estimation? The second problem is the normality assumption of the level‐2 error distribution. When one wants to conduct tests of significance, the errors need to be normally distributed. What happens when this is not the case? In this paper, simulation studies are used to answer both questions. With respect to the first question, the results show that a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second‐level standard errors. The answer to the second question is that only the standard errors for the random effects at the second level are highly inaccurate if the distributional assumptions concerning the level‐2 errors are not fulfilled. Robust standard errors turn out to be more reliable than the asymptotic standard errors based on maximum likelihood.
