Modelling Synergy using Manifest Categorical Variables

This paper discusses methods to model the concept of synergy at the level of manifest categorical variables. First, a classification of concepts of synergy is presented. A dditive and nonadditive concepts of synergy are distinguished. Most prominent among the nonadditive concepts is superadditive synergy. Examples are given from the natural sciences and the social sciences. M delling focuses on the relationship between the agents involved in a synergetic process. These relationships are expressed in form of contrasts, expressed in effect coding vectors in design matrices for nonstandard log-linear models. A method by Schuster is used to transform design matrices such that parameters reflect the proposed relationships. A n example reanalyses data presented by Bishop, Fienberg, and Holland (1975) that describe the development of thromboembolisms in women who differ in their patterns of contraceptive use and smoking. Alternative methods of analysis are com pared. Implications for developmental research are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66523/2/10.1080_016502598384261.pd

Directional Dependence in the Analysis of Single Subjects

Many statistical methods applied in person-oriented research make use of theoretical principles originally derived in a variable-oriented context. From this perspective, it naturally follows that advances originated in variable-oriented methodology may potentially contribute to the development of methods suitable for person-oriented perspectives. Direction Dependence Analysis (DDA) constitutes one of these recent advances and provides a framework to statistically evaluate asymmetric properties of observed variable relations. These asymmetric properties enable researchers to make statements whether a model of the form x ! y or a model assuming y ! x is more likely to approximate the underlying data-generating process in non-experimental settings. The present article introduces DDA to the context of person-oriented research and extends the DDA principle to (linear) vector autoregressive models (VAR) which can be used to describe individual development. We show that DDA can be used to empirically evaluate directional theories of (potentially multivariate) intraindividual development (e.g., which of two longitudinally observed variables is more likely to be the explanatory variable and which one is more likely to reflect the outcome). An illustrative example is provided from a study on the development of experienced mood and alcohol consumption behavior. It is demonstrated that VAR-DDA resolves the issue of identifying the direction of contemporaneous effects in longitudinal data. Temporality issues of directional theories used to explain intraindividual development, guidelines to achieve acceptable power, methodological requirements, and potential further extensions of DDA for person-oriented research are discussed

Strengthening arguments based on scale levels?

No abstract available

Local Associations in Latent Class Analysis: Using Configural Frequency Analysis for Model Evaluation

It is proposed to enrich the arsenal of methods for the evaluation of local independence within latent classes by methods from Configural Frequency Analysis (CFA). CFA provides researchers with two additional options. The first involves identifying those patterns of categories of manifest variables that contradict the assumption of local independence within a given class. If such patterns exist, local independence is viewed as violated not (only) at the level of relations among variables, but at the level of individual patterns that occur at rates significantly different than expected under the assumption of variable inde-pendence. The second option involves comparing classes at the level of individual patterns. The results of such a comparison of classes can be that outlying patterns are identified as class-specific. Second, it is possible that classes differ in the occur-rence rates of individual patterns (i.e., specific response patterns may be more likely to occur in certain classes). This can occur even when these patterns do not contradict the assumption of local independence. An empirical example is given using data on alcohol consumption behavior among college students. Extensions and applications of the proposed methods are discussed

General linear models for the analysis of single subject data and for the comparison of individuals

In longitudinal person-oriented and idiographic research, individual-specific parameter estimation is strongly preferred over estimation that is based on aggregated raw data. In this article, we ask whether methods of the General Linear Model, that is, repeated measures ANOVA and regression, can be used to estimate individual-specific parameters. Scenarios and corresponding design matrices are presented in which the shape of temporal trajectories of individuals is parameterized. Real world data examples and simulation results suggest that, for series of sufficient length, trajectories can be well described for individuals. In addition, scenarios are presented for the comparison of two individuals. Here again, trajectories can be well described and the statistical comparison of individuals is possible. However, in contrast to the power for the description of individual series, which is satisfactory, the power for the comparison of individuals is low (except when effect sizes are large). In all simulated scenarios, the power of tests increases only up to a certain number of observation points, and reaches a ceiling at this number. The fact that all parameters cannot always be estimated is also discussed, and options are presented that go beyond what standard general purpose software packages offer

The individual as moderator of variable relations – A configural approach

Moderators are variables that change the relations among other variables. Moderators are variables that are substantive just as the variables whose relations are moderated. In the present article, we propose using individuals as moderators. Specifically, we propose using Configural Frequency Analysis, that is, investigating moderators from a person-oriented perspective. The question asked is whether variable relations vary across individuals. Base models are specified for Configural Frequency Analysis that allow one to identify individuals that differ in variable relations. In a data example, it is shown that not a single individual in a sample of alcoholics shows the pattern of association between subjective stress and beer consumption that was found for the entire sample. Extensions of the configural moderator model are discussed

A Configural Perspective of Interindividual Differences in Intraindividual Change

Lag analysis can be used to inspect stability and change of behavior over a pre-determined time interval, the lag. In the analysis of metric variables, lag analysis is well known and used to identify such temporal effects as seasonal trends. In the analysis of categorical variables, the same can be done. Either approach can be employed in the analysis of both aggregated and individual data. In the domain of studying individual cells of contingency tables, that is, in configural analysis, only two sources exist in which lag analysis is discussed (von Eye, Mair, & Mun, 2010; von Eye & Mun, 2012). In this paper, we place the method of configural lag analysis in a person-oriented context and propose new variants for the comparison of individuals. Three approaches are considered. The first involves searching for configural types and antitypes separately for the comparison individuals. The second approach can be viewed parallel to two- or multiple group Configural Frequency Analysis. Both approaches are presented within a log-linear framework. Configural base models are specified for the original configural lag method as well as the extended comparative methods, and questions are defined that can be answered using configural lag analysis. The third approach allows researchers to test hypotheses concerning groups of cells. In an empirical example, data are analyzed from a study on the development of drinking behavior in alcoholics. Further extensions and alternative methods of analysis are discussed

Direction of effects in categorical variables: Looking inside the table

In the variable-oriented domain, direction of dependence analysis of metric variables is defined in terms of changes that the independent (or causal) variable has on the univariate distribution of the dependent variable. In this article, we take a person-oriented perspective and extend this approach in two aspects, for categorical variables. First, instead of looking at univariate frequency distributions, direction dependence is defined in terms of special interactions. That is, direction dependence is defined as a process that can be detected “inside the table” instead of in its marginals. Second, the present approach takes an event-based perspective. That is, direction of effect is defined for individual categories of variables instead of the entire range of possible scores (or categories). Log-linear models are presented that allow researchers to test the corresponding hypotheses. Simulation studies illustrate characteristics and performance of these models. An empirical ex-ample investigates whether there is truth to the adage that money does not buy happiness. Extensions and limitations are discussed