Thomas R. Ten Have

New Evidence for the effectiveness of the early screening inventory

This article presents data concerning the psychometric properties of the Early Screening Inventory (ESI; Meisels & Wiske, 1983 ), a developmental screening instrument designed to identify 4- to 6-year-old children at high risk for school failure. Presented in this article are normative data based on a national sample of 2,746 children, item analyses, interrater and test-retest reliability data, predictive validity data based on a subsample of 179 children, and preliminary data concerning an innovative method for enhancing ESI predictions by combining the ESI with its accompanying Parent Questionnaire. Results indicate that the ESI is a developmental screening instrument that distinguishes clearly between children who are referred and not referred. It is highly reliable and valid, and it may be possible to increase its accuracy by combining it with the Parent Questionnaire. The article concludes with a discussion of the importance of incorporating multiple sources of information into the screening process.

A GAUSS program for computing an index of tracking from longitudinal observations

Tracking can be defined as the tendency of individuals or collections of individuals to stay within a particular course of growth over time relative to other individuals. Thus, tracking describes stability in growth patterns. This paper outlines a statistical procedure for examining tracking in a single sample of measurements made on humans or other animals. This nonparametric procedure, based on Cohens (1960) kappa statistic, is suitable for equally or unequally spaced serial data that is complete and is appropriate for questions concerning growth as well as other time‐dependent phenomena. It is a conceptually simple longitudinal method that affords insight regarding the predictability of growth within a population. For example, by tracking, one can ask if young children who are in the lowest height for age category are likely to end up in that category at an older age. A user‐friendly GAUSS program is provided that generates overall as well as individual and track‐specific statistics. High‐resolution graphic representations of the data are also generated by the program. Examples are presented, including a tracking analysis of Guatemalan Indian children using quartiles.

PC program for analyzing one-sample longitudinal data sets which satisfy the two-stage polynomial growth curve model

The two‐stage polynomial growth curve model is described and a GAUSS program to perform the associated computations is documented and made available to interested readers. The two‐stage model is similar to that considered by us earlier (Schneiderman and Kowalski: American Journal of Physical Anthropology 67:323–333, 1985; American Journal of Human Biology 1:31–42, 1989), i.e., it is appropriate for the analysis of one‐sample longitudinal data collected at either equal or unequal time intervals. Here, however, the covariance matrix, Σ, instead of being considered arbitrary, is now assumed to have the special structure Σ = W A W′ + σ2I. We show the conditions under which this special structure may be expected to arise and how it may be exploited to produce sharper results in certain situations. The method and the program are illustrated and the results are contrasted to those obtained when Σ is arbitrary. It is suggested that the two‐stage model is more efficient when the same degree polynomial is adequate to model the data in the two situations, but that, should a higher degree be necessary for the two‐stage model, confidence intervals and/or bands may be wider than those corresponding to Σ arbitrary.

A PC program for performing multigroup longitudinal comparisons using the Potthoff-Roy analysis and orthogonal polynomials

A PC-program performing the Potthoff-Roy (PR) multigroup (G-sample) analysis of longtidinal data is described and illustrated. This program and the underlying statistical model are useful in the comparison of several longitudinal samples. Applications include the study of growth, development, adaptation, aging, and treatment effects (in short, any phenomenon in which the passage of time is important) for which serial data are available. Specifically, this method fits polynomials to the average growth curves in the samples, and tests hypotheses concerning the curves themselves and the individual coefficients of the polynomials. The program features the utilization of orthogonal polynomial regression coefficients (OPRCs) and is written in GAUSS, a relatively inexpensive yet comprehensive matrix programming language. It is documented that using OPRCs to comprise the within-individual or time design matrix has several advantages over the more usual choice of the successive-powers-of-t form of this matrix and an example of one important such advantage is provided. GAUSS was employed to make the program readily-accessible (i.e., executable code) to biomedical investigators. The GAUSS compiler is not required to run this program. Information regarding the availability of the program is provided in the Appendix.

Computation of Foulkes and Davis' nonparametric tracking index using GAUSS

Foulkes and Davis (1981) define tracking as the maintenance of relative rank over a given time span. This paper outlines the development of their statistic, based on a set of individual growth profiles, which estimates the degree of tracking observed in a one‐sample longitudinal data set and shows how confidence intervals for the corresponding population parameter may be constructed. An example using a measure of skeletal growth is given and a GAUSS program to do the computations is provided. (Information on obtaining the GAUSS program is provided in the Appendix.) Properties of this statistical approach to tracking are contrasted with another non‐parametric method based on Cohens kappa statistic.

PC program for comparing tracking indices in several independent groups

A method for computing a measure of tracking based on Cohens kappa statistic for one‐sample longitudinal data sets was previously described and implemented. This paper shows how one may test the equality of several kappas, each computed from an independent longitudinal sample. Thus, it is possible to formally compare groups of individuals with regard to stability in growth (or adaptive) patterns. Relative assessments of predictability in growth outcomes in different populations can be made with this approach. Also, when a common value of kappa is not contradicted by the data, a method to estimate this value and obtain a confidence interval for it is shown. A menu‐driven GAUSS program for carrying out the procedure is described and made available. The method and program are illustrated with three samples of Guatemalan children.

Rao's polynomial growth curve model for unequal-time intervals: A menu-driven gauss program

For lack of alternatives, longitudinal data are often analyzed with cross-sectional statistical methods, for instance, t-tests, ANOVA and ordinary least-squares regression. Appropriate statistical software has been generally unavailable to investigators using serial records to study growth and development or treatment effects. In an earlier paper (Schneiderman and Kowalski, Am. J. Phys. Anthropol., 67 (1985) 323-333.) we described a suitable method, Raos polynomial growth curve model (Rao, Biometrika, 46 (1959) 49-58), and provided an SAS computer program for the analysis of a single sample of complete longitudinal data. This method included the computation of an average polynomial growth curve, its 95% confidence band, its coefficients and corresponding confidence intervals. The present paper extends this method to accommodate a sample with observations made at unequal time-intervals. Significant improvements in the accessibility, operation and user-friendliness of the program have been made, facilitated by recent advances in microcomputer technology. This stand-alone GAUSS program (no compiler necessary) runs on PC-compatibles and is available at a nominal cost. In this report we provide an overview of the statistical model, the general structure of the program, and give an example in which a developmental variable (human upper incisor angulation) is analyzed. Ease of installation and use, speed of execution and color graphic displays of growth curves and confidence bands, and most importantly, suitability to longitudinal data, make this method/program a potentially valuable tool for those interested in growth, development, and treatment effects in humans and other species. Some areas in which this method will have immediate applications are orthodontics, maxillofacial surgery and pediatrics.

A GAUSS program for computing the Foulkes-Davis tracking index for polynomial growth curves

We have previously published a GAUSS program for computing the Foulkes-Davis tracking index, gamma, from a one-sample longitudinal data set when no assumptions were made concerning the structure of the individual growth curves (Schneiderman et al., Am J Hum Biol, 4 (1992) 417-420). In this paper we consider the computation of the Foulkes-Davis index assuming that each individual growth curve may be adequately represented by a polynomial function in time and a GAUSS program performing these computations is made available. As with the two other tracking indices we have described, gamma and kappa (Schneiderman et al., Am J Hum Biol, 2 (1990) 475-490), this one can be used to evaluate regularity in patterns of growth or adaptation. An example is presented where statural growth in the same three groups considered in the earlier papers are analyzed. The small disparities between these and the earlier results are discussed in view of the different assumptions of the models and the differences in how they operationalize the concept of tracking.

PC program extending the two-stage polynomial growth curve model to allow missing data

A stand-alone, menu-driven PC program, written in GAUSS386i, extending the analysis of one-sample longitudinal data sets satisfying the two-stage polynomial growth curve model (Ten Have et al., Am J Hum Biol, 3 (1991) 269-279) to allow missing data is described, illustrated and made available to interested readers. The method and the program are illustrated using data previously analyzed by the authors (Schneiderman and Kowalski, Am J Phys Anthropol, 67 (1985) 323-333) but with several randomly chosen data points discarded and treated as missing.