The Multilevel Approach to Repeated Measures for Complete and Incomplete Data

Repeated measurements often are analyzed by multivariate analysis of variance (MANOVA). An alternative approach is provided by multilevel analysis, also called the hierarchical linear model (HLM), which makes use of random coefficient models. This paper is a tutorial which indicates that the HLM can be specified in many different ways, corresponding to different sets of assumptions about the covariance matrix of the repeated measurements. The possible assumptions range from the very restrictive compound symmetry model to the unrestricted multivariate model. Thus, the HLM can be used to steer a useful middle road between the two traditional methods for analyzing repeated measurements. Another important advantage of the multilevel approach to analyzing repeated measures is the fact that it can be easily used also if the data are incomplete. Thus it provides a way to achieve a fully multivariate analysis of repeated measures with incomplete data. This revised version was published online in June 2006 with corrections to the Cover Date.     

Robustness issues in multilevel regression analysis

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.     

A model of the Dutch labour market (AMO-K)

Summary So far, the labour market has not received any special attention from macro-econometric model builders. In this article an attempt has been made to describe the labour market in detail, paying attention to such important phenomena as the friction between labour supply and demand, the heterogeneity of labour, the dependence of labour supply on the labour-market situation, the Phillips mechanism and the impact of real wages on labour demand. To make it suitable for policy simulations, the model has been extended to a complete macro-econometric model, taking account of the fact that both labour and capital limit the production possibilities.This paper summarises an extensive Dutch report on the construction of a model for the Netherlands labour market. The title of the original report is AMO-K: Een arbeidsmarktmodel met twee categorieën arbeid; (AMO-K, A labour-market model with two categories of labour) ; it was published by the Netherlands Economic Institute (NEI) in Rotterdam in the so-called Olive Series, 1982-2, pp. 403ff. Some details of the model presented in that report were changed after its publication; see G. den Broeder, AMO-K 81-12, Tussenrapport betreffende de verdere ontwikkeling van het arbeidsmarktmodel (Interim report on the further development of the labourmarket model), Rotterdam, September 1983. Since then, only minor changes have been carried through. The model reproduced in this paper is the modified version. The model was developed within the National Programme of Labour-Market Research (NPAO) (now defunct), the NPAO organisation having granted a commission to the NEI in Rotterdam.     

What is being exchanged? Framing the logic of value creation in financial services

Financial service providers are facing a major paradigm shift. The understanding of what eventually constitutes customer value is being extended; economic value as the sole core of exchange is a far too limited perspective in contemporary competition. To address this emerging shift, the purpose of this study is to reframe the logic of value creation in financial services. As a result, a tentative framework for value creation logic in financial services is developed and discussed. On the basis of the framework, financial service providers should not limit their attention and resources to the exchange process, but identify innovative value-creating mechanisms through which they could contribute to the customer value actualization process. Our tentative framework (i) offers financial service providers guidance on which innovative value-creating mechanisms would enable them to participate in their customers’ value actualization process; (ii) shows how a product becomes a channel for a service, specifically a solution possessing value in the customer’s routine processes; (iii) illustrates that researchers and service providers should develop their understanding of customers beyond the traditional loan, insurance and/or investment product orientation.     

Longitudinal Meta-analysis

The goal of meta-analysis is to integrate the research results of a number of studies on a specific topic. Characteristic for meta-analysis is that in general only the summary statistics of the studies are used and not the original data. When the published research results to be integrated are longitudinal, multilevel analysis can be used for the meta-analysis. We will demonstrate this with an example of longitudinal data on the mental development of infants. We distinguish four levels in the data. The highest level (4) is the publication, in which the results of one or more studies are published. The third level consists of the separate studies. At this level we have knowledge about the degree of prematurity of the group of infants in the specific study. The second level are the repeated measures. We have data about the test age, the mental development, the corresponding standard deviations, and the sample sizes. The lowest level is needed for the specification of the meta-analysis model. Both the way in which the multilevel model has to be specified (the Mln-program is used) as the results will be presented and interpreted.