On component analyses

Principal components analysis can be redefined in terms of the regression of observed variables upon component variables. Two criteria for the adequacy of a component representation in this context are developed and are shown to lead to different component solutions. Both criteria are generalized to allow weighting, the choice of weights determining the scale invariance properties of the resulting solution. A theorem is presented giving necessary and sufficient conditions for equivalent component solutions under different choices of weighting. Applications of the theorem are discussed that involve the components analysis of linearly derived variables and of external variables.Preparation of this article was supported in part by National Institute of Aging Grant NIA-AG03164-03 to William Meredith.     

The linear regression line as a judgmental aid in visual analysis of serially dependent A-B time-series data

The purpose of this study was to investigate the effects of different types and magnitudes of serial dependence (first-order moving average and autoregression) and of linear regression lines within experimental phases on the agreement between results of visual and results of statistical data analyses. The stimulus material consisted of computer-simulated A-B-design data graphs. The time series were generated with a constant variance, varying degrees of treatment effects (changes in level), five conditions of serial dependency, and with or without linear regression lines. The material was presented to three groups of student raters (n₁=52, n₂=14, n₃=17) who rated the treatment effect in the graphs on a five-point scale. These ratings were compared with statistical results (time-series analyses). Each group had to interpret 70 graphs, 35 of which had regression lines. Data were analyzed by means of two three-factor and one four-factor ANOVA and by graphic display. The linear regression lines generally enhanced the agreement between the raters' estimations and the statistical results. Serial dependency also increased the agreement between the two analysis methods. However, with strong autoregression processes in the data, the raters tended to overestimate treatment effects relative to time-series analysis.Parts of this study were presented at the World Congress on Behavior Therapy, Washington, DC, December 11, 1983. The authors wish to express their appreciation to Christoph Bonk and Willi Ecker for their extensive collaboration in data analysis and for their assistance in carrying out the study.     

Model modification

An analysis of empirical data often leads to a rejection of a hypothesized model, even if the researcher has spent considerable efforts in including all available information in the formulation of the model. Thus, the researcher must reformulate the model in some way, but in most instances there is, at least theoretically, an overwhelming number of possible actions that could be taken. In this paper a modification index will be discussed which should serve as a guide in the search for a better model. In statistical terms, the index measures how much we will be able to reduce the discrepancy between model and data, as defined by a general fit function, when one parameter is added or freed or when one equality constraint is relaxed. The modification index discussed in this paper is an improvement of the one incorporated in the LISREL V computer program in that it takes into account changes in all the parameters of the model when one particular parameter is freed.The research reported in this paper has been supported by The Swedish Council for Research in the Humanities and Social Sciences under Research Program Multivariate Statistical Analysis, Project Director Karl G Jöreskog.     

Joint consistency of nonparametric item characteristic curve and ability estimation

The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. The asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation are investigated under very general assumptions on the underlying item response theory model as both the test length and the sample size increase. A large deviation probability inequality is stated for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one.     

A new procedure for detection of crossing DIF

The purpose of this paper is to present a hypothesis testing and estimation procedure, Crossing SIBTEST, for detecting crossing DIF. Crossing DIF exists when the difference in the probabilities of a correct answer for the two examinee groups changes signs as ability level is varied. In item response theory terms, crossing DIF is indicated by two crossing item characteristic curves. Our new procedure, denoted as Crossing SIBTEST, first estimates the matching subtest score at which crossing occurs using least squares regression analysis. A Crossing SIBTEST statistic then is used to test the hypothesis of crossing DIF. The performance of Crossing SIBTEST is evaluated in this study.This research was partially supported by a grant from the Law School Admission Council and by National Science Foundation Mathematics Grant NSF-DMS-94-04327. The research reported here is collaborative in every respect and the order of authorship is alphabetical. The authors thank Jeff Douglas and Louis Roussos for their useful comments and discussions.     

Improved bounds for optimal intervals in weakly constrained regression problems

The solution of weakly constrained regression problems typically requires the iterative search, in a given interval, of a point where a certain function has a zero derivative. This note deals with improved bounds for the interval to be searched.     

The stability and clinical significance of distress: A rejoinder to pepper and coyne

Past research has established that some individuals with high Beck Depression Inventory (BDI) scores at one time point have scores that are lower at a second time point. Recently, we provided evidence indicating that the temporal instability of certain BDI scores may be due partly to the regression to the mean phenomenon. Pepper and Coyne (1996) question this statistical interpretation; they argue that distress among students is unstable for substantive reasons. In the current paper, we reaffirm our view that statistical and measurement factors may account, in part, for changes in BDI scores over time. Given this possibility, inferences about distress or depression as a latent construct in student samples are not warranted if these inferences are based on the administration of a single instrument such as the BDI; any conclusions about distress as a psychological construct must be qualified by acknowledging the possible roles of error and method variance. Clearly, empirical research is needed in order to obtain a better understanding of the nature of distress as a latent variable, especially in light of evidence which indicates that subthreshold levels of depression have a high degree of clinical significance.     

A monotonically convergent algorithm for factals

Takane, Young, and de Leeuw proposed a procedure called FACTALS for the analysis of variables of mixed measurement levels (numerical, ordinal, or nominal). Mooijaart pointed out that their algorithm does not necessarily converge, and Nevels proposed a new algorithm for the case of nominal variables. In the present paper it is shown that Nevels' procedure is incorrect, and a new procedure for handling nominal variables is proposed. In addition, a procedure for handling ordinal variables is proposed. Using these results, a monotonically convergent algorithm is constructed for FACTALS of any mixture of variables.The authors are obliged to Jos ten Berge for stimulating comments on an earlier version of this paper. The research of H. A. L. Kiers has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research of Y. Takane has been supported by the Natural Sciences and Engineering Research Council of Canada, grant number A6394, and by the McGill-IBM Cooperative Grant.     

银屑病发病的心理社会因素及危险因素间关系的探讨——非条件Logistic回归分析和通径分析

本文对97例寻常型银屑病患者以及71例皮肤科对照组患者进行了成组病例对照性研究。相对危险度分析从36个研究因素中筛选出14项可疑危险因素;非条件Logistic回归分析提示其中8项因素有明显的致病意义;结合专业知识,对这8项危险因素进行通径分析。研究结果表明,银屑病发病是多因素综合作用的结果,心理社会危险因素通过直接或/和间接(联合)作用,影响致病过程。经通径图将各因素的作用大小、作用形式及协同作用关系较直观地描绘出来。     

视觉诱发电位与老年人智力和记忆力相关性研究的多因素逐步回归分析

以年龄在55—79岁的正常人(男40人,女34人,平均年龄64.34±5.67岁)为被试,做视觉诱发电位(VEP),并测试韦氏智力测验的11项分值及智力商数、临床记忆测验的5项分测验及记忆商数、测量血压和头颅CT的脑萎缩程度,根据眼底动脉硬化表现和神经体征确定脑动脉硬化的程度.将上述资料数字化输入计算机进行多因素逐步回归分析。结果表明,智力和记忆力分别与视觉诱发电位的某些指标变量有关,与脑动脉硬化程度有关,与收缩压相关性较大,与舒张压相关性不大,与生理性脑萎缩程度关系不大。还探讨了推测老年人智力和记忆力的计算公式。