An overview of applied robust methods

Data in social sciences are typically non-normally distributed and characterized by heavy tails. However, most widely used methods in social sciences are still based on the analyses of sample means and sample covariances. While these conventional methods continue to be used to address new substantive issues, conclusions reached can be inaccurate or misleading. Although there is no ‘best method’ in practice, robust methods that consider the distribution of the data can perform substantially better than the conventional methods. This article gives an overview of robust procedures, emphasizing a few that have been repeatedly shown to work well for models that are widely used in social and behavioural sciences. Real data examples show how to use the robust methods for latent variable models and for moderated mediation analysis when a regression model contains categorical covariates and product terms. Results and logical analyses indicate that robust methods yield more efficient parameter estimates, more reliable model evaluation, more reliable model/data diagnostics, and more trustworthy conclusions when conducting replication studies. R and SAS programs are provided for routine applications of the recommended robust method.     

Heart-rate deceleration and smiling in 3-month-old infants

The relation between heart-rate deceleration and the expression of positive affect in infancy is examined by testing the hypothesis that intensity of orienting (as indexed by heart-rate deceleration) is predictive of intensity of positive affect (smile size and duration). A social-stimulation procedure was utilized to elicit smiles in 41 3-month-old infants. The first smile elicited was coded for smile size and duration, and the preceding heart-rate deceleration was coded for magnitude, duration, and slope of deceleration. Slope and duration of heart-rate deceleration proved to be reliable predictors of smile size, but none of the heart-rate measures correlated with smile duration. Results suggest that the steeper and more rapid the deceleration, the larger the ensuing smile. Possible mechanisms for this finding are discussed.     

A pharmacological examination of the resistance-to-change hypothesis of response strength.

The effects of d-amphetamine sulfate, sodium pentobarbital, haloperidol, and cholecystokinin-octapeptide were examined within the context of Nevin's (1974, 1979) resistance-to-change hypothesis of response strength. In three experiments, rats' responding was reinforced by delivery of food under chained random-interval 30-s random-interval 30-s, multiple fixed-interval 30-s fixed-interval 120-s, or multiple random-interval 30-s random-interval 120-s schedules. Each rat received several doses of each drug and changes in response rate were measured. The resistance-to-change hypothesis predicts greater disruption of response rate relative to baseline in the initial component of the chained schedule and in the 120-s component of the multiple schedules. In the chained schedule cholecystokinin-octapeptide produced greater reductions in response rate relative to baseline in the initial component. However, no differences between components were observed with haloperidol or sodium pentobarbital, and high doses of d-amphetamine reduced response rate in the terminal component relatively more than in the initial component. In the multiple schedules either no differences were observed between components or response rate was reduced more relative to baseline in the 30-s component. The data fail to support the notion that drugs may be viewed within the same context as other response disruptors such as extinction, satiation, and the presentation of alternative reinforcement.     

On the measurement of time allocation on multiple variable-interval schedules

Six pigeons were trained on a modified multiple-schedule procedure. In a three-key chamber, the center key was lighted red or green, depending upon which component schedule was in effect. A response on this key transferred this color to each of two side keys, and responses on one of those keys produced reinforcers according to the component schedule. After 2 s, the side-key lights were extinguished, the center key was reilluminated, and a further center-key response was required to give access, as before, to the component schedules. Components alternated every 3 min. This limited-access procedure allowed both times spent switched into the side keys and time spent not switched in to be measured in the two components. Component reinforcer rates were varied over eight experimental conditions. Both component response rate and component time allocation were increasing functions of relative component reinforcer rate, and these functions were not significantly different. This finding implies that local response rates (responses divided by time switched in) were unaffected by changing component reinforcer rates on multiple schedules. Because a similar result was recently obtained for concurrent schedules, models of multiple and concurrent-schedule performance may need to consider only the time allocation of behavior emitted at equal tempo in the component schedules.     

On scaling models applied to data from several groups

Statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups. These methods can be used to (a) compare the corresponding estimated latent distributions obtained using the scaling model applied to the different groups, (b) compare the corresponding estimated item reliabilities (or item response error rates) for the different groups, and (c) test whether the scaling model applied to the several groups can be replaced by a more parsimonious scaling model that includes various homogeneity constraints (i.e., constraints that describe which parameters in the model are the same for the several groups). Various kinds of scaling models are considered here in the multiple-group context.Support for this research was provided in part by the National Science Foundation, to Clogg by Grant No. SES-7823759 and to Goodman by Grant No. SES-8303838. Clogg and Goodman were Fellows at the Center for Advanced Study in the Behavioral Sciences when part of the research was done, with financial support provided in part by National Science Foundation grant BNS-8011494 to the Center. The authors are indebted to Mark P. Becker and James W. Shockey for helpful comments.     

Conjunctive item response theory kernels

Conjunctive item response models are introduced such that (a) sufficient statistics for latent traits are not necessarily additive in item scores; (b) items are not necessarily locally independent; and (c) existing compensatory (additive) item response models including the binomial, Rasch, logistic, and general locally independent model are special cases. Simple estimates and hypothesis tests for conjunctive models are introduced and evaluated as well. Conjunctive models are also identified with cognitive models that assume the existence of several individually necessary component processes for a global ability. It is concluded that conjunctive models and methods may show promise for constructing improved tests and uncovering conjunctive cognitive structure. It is also concluded that conjunctive item response theory may help to clarify the relationships between local dependence, multidimensionality, and item response function form.I appreciate the many helpful suggestions that were given by the reviewers and Ivo Molenaar.