Appraisal-coping goodness of fit: a daily internet study

Using an Internet daily diary methodology, this study tested the goodness of fit hypothesis, which highlights the importance of the match between controllability appraisals and coping efforts in adjustment to stressful events. For 28 days, 190 undergraduates described their most stressful event and its controllability, how they coped, and their daily positive and negative mood. Individuals demonstrated fit across situations, with control appraisals associated positively with problem-focused coping and negatively with emotional approach coping and avoidance coping. A pooled within-person interaction indicated that problem-focused coping had a stronger positive association with positive mood when dealing with high versus low control stressors. Significant variation also was found in several other within-person interactions between control appraisals and coping, and some evidence was found for the notion that individual differences in the degree of matching coping to control appraisals were associated with person-level adjustment.     

A goodness of fit test for the rasch model

The Rasch model is an item analysis model with logistic item characteristic curves of equal slope,i.e. with constant item discriminating powers. The proposed goodness of fit test is based on a comparison between difficulties estimated from different scoregroups and over-all estimates. Based on the within scoregroup estimates and the over-all estimates of item difficulties a conditional likelihood ratio is formed. It is shown that—2 times the logarithm of this ratio isx ²-distributed when the Rasch model is true. The power of the proposed goodness of fit test is discussed for alternative models with logistic item characteristic curves, but unequal discriminating items from a scholastic aptitude test.     

Testing the concept of goodness of fit in early intervention

While the conceptual and clinical utility of the goodness of fit concept has been documented extensively, the number of specific empirical tests of the concept has been limited. In this study, the concept was applied in the conceptualization and analysis of early intervention efforts. The major question examined was the extent to which the goodness of fit of child, maternal, and support variables discriminated good and poor adaptation of the mother as measured by the quality and appropriateness of care giving involvement with her handicapped child. Findings indicated that an index of maternal and child characteristics and measures of maternal locus of control, child temperament, and social support collectively contributed to the correct classification of 77% of mothers in high vs. low involvement groups. Locus of control and the maternal/child index accounted for 25% of the variance in caregiver involvement. The findings illustrate the applicability of the goodness of fit concept and provide support for efforts focused on maximizing the fit of the child, family, and variables in early intervention.     

Psychometric network models from time-series and panel data

Researchers in the field of network psychometrics often focus on the estimation of Gaussian graphical models (GGMs)—an undirected network model of partial correlations—between observed variables of cross-sectional data or single-subject time-series data. This assumes that all variables are measured without measurement error, which may be implausible. In addition, cross-sectional data cannot distinguish between within-subject and between-subject effects. This paper provides a general framework that extends GGM modeling with latent variables, including relationships over time. These relationships can be estimated from time-series data or panel data featuring at least three waves of measurement. The model takes the form of a graphical vector-autoregression model between latent variables and is termed the ts-lvgvar when estimated from time-series data and the panel-lvgvar when estimated from panel data. These methods have been implemented in the software package psychonetrics, which is exemplified in two empirical examples, one using time-series data and one using panel data, and evaluated in two large-scale simulation studies. The paper concludes with a discussion on ergodicity and generalizability. Although within-subject effects may in principle be separated from between-subject effects, the interpretation of these results rests on the intensity and the time interval of measurement and on the plausibility of the assumption of stationarity.

     

Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis

Multidimensional scaling is the problem of representingn objects geometrically byn points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically incomplete. Our fundamental hypothesis is that dissimilarities and distances are monotonically related. We define a quantitative, intuitively satisfying measure of goodness of fit to this hypothesis. Our technique of multidimensional scaling is to compute that configuration of points which optimizes the goodness of fit. A practical computer program for doing the calculations is described in a companion paper.     

The psychometric function: I. Fitting, sampling, and goodness of fit.

The psychometric function relates an observer's performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. This paper, together with its companion paper (Wichmann & Hill, 2001), describes an integrated approach to (1) fitting psychometric functions, (2) assessing the goodness of fit, and (3) providing confidence intervals for the function's parameters and other estimates derived from them, for the purposes of hypothesis testing. The present paper deals with the first two topics, describing a constrained maximum-likelihood method of parameter estimation and developing several goodness-of-fit tests. Using Monte Carlo simulations, we deal with two specific difficulties that arise when fitting functions to psychophysical data. First, we note that human observers are prone to stimulus-independent errors (or lapses). We show that failure to account for this can lead to serious biases in estimates of the psychometric function's parameters and illustrate how the problem may be overcome. Second, we note that psychophysical data sets are usually rather small by the standards required by most of the commonly applied statistical tests. We demonstrate the potential errors of applying traditional chi2 methods to psychophysical data and advocate use of Monte Carlo resampling techniques that do not rely on asymptotic theory. We have made available the software to implement our methods.     

An objective test of goodness of fit of the continuous strength model in STM

The continuous strength model of recognition memory was evaluated in a task where Ss were tested for recognition of 10-number lists using a rating procedure. Maximum likelihood estimates of the parameters of the model were obtained by an iterative method on a high-speed computer, and a chi-square goodness-of-fit test was performed for individual Ss. For 15 of 20 Ss, the chi-square values were nonsignificant, p < .05, indicating that the model provided a good fit to the data. Although the model gave a good fit to the data, the Δm measure of sensitivity was highly correlated with a true recognition score computed by subtracting false alarmsfrom correct recognitions.     

Model complexity: The fit to random data reconsidered

A recent controversy in the field of depth perception has highlighted an important aspect of model testing concerning a model's complexity, defined as the prior propensity of the model to fit arbitrary data sets. The present article introduces an index of complexity, called the mean minimum distance, defined as the average squared distance between an arbitrary data point and the prediction range of the model. It may also be expressed as a dimensionless quantity called the scaled mean minimum distance. For linear models, theoretical values for the scaled mean minimum distance and the variance of the scaled minimum distance can be readily obtained and compared against empirical estimates obtained from fits to random data. The approach is applied to resolving the question of the relative complexity of the Linear Integration model and the Fuzzy Logic of Perception model, both of which have been the subject of controversy in the field of depth perception. It is concluded that the two models are equally complex. Received: 10 October 1998 / Accepted: 22 December 1998     

Estimating the π* goodness of fit index for finite mixtures of item response models

Testing the fit of finite mixture models is a difficult task, since asymptotic results on the distribution of likelihood ratio statistics do not hold; for this reason, alternative statistics are needed. This paper applies the π* goodness of fit statistic to finite mixture item response models. The π* statistic assumes that the population is composed of two subpopulations – those that follow a parametric model and a residual group outside the model; π* is defined as the proportion of population in the residual group. The population was divided into two or more groups, or classes. Several groups followed an item response model and there was also a residual group. The paper presents maximum likelihood algorithms for estimating item parameters, the probabilities of the groups and π*. The paper also includes a simulation study on goodness of recovery for the two‐ and three‐parameter logistic models and an example with real data from a multiple choice test.     

Statistical analysis of binary relational data: Parameter estimation

Binary interaction data, measuring the presence or absence of a relation between pairs of actors in a “dyadic interaction situation,” are commonly gathered to study the social structure of the group of actors. Recent developments have made the statistical analysis of such data statistically easier and more substantively sophisticated. These developments allow researchers to simultaneously study several sociometric structural properties, such as reciprocity, differential popularity, and equivalence of actors. Building on this research, we review the stochastic models responsible for this breakthrough, and discuss methods for estimating expected values and model parameters. Throughout, we also highlight recent advances designed to incorporate nodal or actor attribute data into the relational data analysis. We conclude with an example illustrating these ideas based on conversational activities among actors in a group of eight people.     

Welfare policies and very young children: experimental data on stage-environment fit

The authors examined the effects of welfare programs that increased maternal employment and family income on the development of very young children using data from 5 random-assignment experiments. The children were 6 months to 3 years old when their mothers entered the programs; cognitive and behavioral outcomes were measured 2-5 years later. While there were no overall program impacts, positive or negative, on the development of children in this age group, there was a pair of domain- and age-specific effects: The programs decreased positive social behavior among 1-year-olds and increased school achievement among 2-year-olds. After exploring several explanations for these results, the authors suggest that the contextual changes engendered by the programs, including children's exposure to center-based child care, interacted differentially with specific developmental transitions.     

Statistical evaluation of measures of fit in the Lingoes-Borg procrustean individual differences scaling

PINDIS, as recently presented by Lingoes and Borg [1978] not only marks the latest development within the scope of individual differences scaling, but, may be of benefit in some closely related topics, such as target analysis. Decisions on whether the various models available from PINDIS fit fallible data are relatively arbitrary, however, since a statistical theory of the fit measures is lacking. Using Monte Carlo simulation, expected fit measures as well as some related statistics were therefore obtained by scaling sets of 4(4)24 random configurations of 5(5)30 objects in 2, 3, and 4 dimensions (individual differences case) and by fitting one random configuration to a fixed random target for 5(5)30 objects in 2, 3, and 4 dimensions (target analysis case). Applications are presented.     

Method of constant stimuli: Recalculations show that response-frequency equalization cannot fit the data

The bias found in the method of constant stimuli has been attributed either to an adaptation-level effect or to a response bias. Restle and Levison presented data purported to show that the result could not be explained by response frequency equalization, the best available response-bias theory. Erlebacher and Sekuler elaborated their theory and calculated a version of the model that would fit the main experimental result, but chose an erroneously large value for the standard deviation of their model. Their model does not produce an acceptable fit to the data, and therefore does not successfully compete with the adaptation-level model.     

Integrating the levels of person-environment fit: The roles of vocational fit and group fit

Previous research on fit has largely focused on person-organization (P-O) fit and person-job (P-J) fit. However, little research has examined the interplay of person-vocation (P-V) fit and person-group (P-G) fit with P-O fit and P-J fit in the same study. This article advances the fit literature by examining these relationships with data collected from 167 employees and their respective supervisors. As predicted, P-V fit related positively to both P-O and P-J fit, while P-O and P-J fit together fully mediated relations between P-V fit and outcome variables. Also as predicted, P-G fit moderated several relations of P-O and P-J fit with such outcome variables as in-role and extra-role performance. The article concludes with directions for future research on relations among these four different types of fit and implications for management practice.     

Dynamic analysis of multivariate panel data with non-linear transformations

Many models for multivariate data analysis can be seen as special cases of the linear dynamic or state space model. Contrary to the classical approach to linear dynamic systems analysis, in which high-dimensional exact solutions are sought, the model presented here is developed from a social science framework where low-dimensional approximate solutions are preferred. Borrowing concepts from the theory on mixture distributions, the linear dynamic model can be viewed as a multi-layered regression model, in which the output variables are imprecise manifestations of an unobserved continuous process. An additional layer of mixing makes it possible to incorporate non-normal as well as ordinal variables.Using the EM-algorithm, we find estimates of the unknown model parameters, simultaneously providing stability estimates. The model is very general and cannot be well estimated by other estimation methods. We illustrate the applicability of the obtained procedure through an example with generated data.