The relationship between external variables and common factors

A theorem is presented which gives the range of possible correlations between a common factor and an external variable (i.e., a variable not included in the test battery factor analyzed). Analogous expressions for component (and regression component) theory are also derived. Some situations involving external correlations are then discussed which dramatize the theoretical differences between components and common factors.Support by the National Research Council of Canada (NRC Grant No. A4640) and the University of British Columbia (UBC Humanities and Social Sciences Grant 26-9718) is gratefully acknowledged.This paper is based in part on the author's Ph.D. dissertation. I am particularly grateful to my dissertation advisor, Dr. Peter H. Schönemann. Thanks also to the editor and the anonymous reviewers, who contributed many helpful comments and suggestions.     

Best univocal estimates of orthogonal common factors

A general formulation is presented for obtaining conditionally unbiased, univocal common-factor score estimates that have maximum validity for the true orthogonal factor scores. We note that although this expression is formally different from both Bartlett's formulation and Heermann's approximate expression, all three, while developed from very different rationales, yield identical results given that the common-factor model holds for the data. Although the true factor score validities can be raised by a different non-orthogonal transformation of orthogonalized regression estimates—as described by Mulaik—the resulting estimates lose their univocality.     

Conditions for factor (in)determinacy in factor analysis

The subject of factor indeterminacy has a vast history in factor analysis (Guttman, 1955; Lederman, 1938; Wilson, 1928). It has lead to strong differences in opinion (Steiger, 1979). The current paper gives necessary and sufficient conditions for observability of factors in terms of the parameter matrices and a finite number of variables. Five conditions are given which rigorously define indeterminacy. It is shown that (un)observable factors are (in)determinate. Specifically, the indeterminacy proof by Guttman is extended to Heywood cases. The results are illustrated by two examples and implications for indeterminacy are discussed.     

First- and Second-Order Logic of Mass Terms

Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation.     

Gender-based differential item functioning in common measures of body dissatisfaction

Many widely used measures of body image were developed using all-female samples and thus may not adequately capture the male experience of body dissatisfaction. The current study examined differential item functioning (DIF) in three commonly-used measures of body image: The Body Shape Questionnaire (N = 590, 39.7% male), the Body Dissatisfaction subscale of the Eating Disorders Inventory (N = 529, 44.6% male), and the Shape and Weight Concern subscales of the Eating Disorders Examination Questionnaire (N = 1116, 43.5% male). Participants completed a series of measures evaluating body image and eating pathology. Results evidenced statistically significant DIF in several of the items; one item met criteria for clinically significant DIF. While most items did not evidence clinically elevated levels of DIF, additional evaluation is necessary in order to determine overall quality of the measures in terms of capturing the experience of male body image concerns.     

The common factors in fifty-two mental tests

An analysis by Thurstone's centroid method of the intercorrelations of fifty-two tests was carried to ten factors. Included were tests of social intelligence, Philip's attention tests, and Seashore's tests of musical ability. After rotation of axes, the most important factors appeared to pertain to operations conventionally alluded to by the following terms: verbal facility; spatial ability; numerical ability; attention; musical ability; and memory (or memory span). The social intelligence tests proved to be mainly tests of the verbal factor. A factorial sex difference was indicated by the superiority of men in tests of spatial ability.     

The unique correspondence of the item response function and item category response functions in polytomously scored item response models

The item response function (IRF) for a polytomously scored item is defined as a weighted sum of the item category response functions (ICRF, the probability of getting a particular score for a randomly sampled examinee of ability ). This paper establishes the correspondence between an IRF and a unique set of ICRFs for two of the most commonly used polytomous IRT models (the partial credit models and the graded response model). Specifically, a proof of the following assertion is provided for these models: If two items have the same IRF, then they must have the same number of categories; moreover, they must consist of the same ICRFs. As a corollary, for the Rasch dichotomous model, if two tests have the same test characteristic function (TCF), then they must have the same number of items. Moreover, for each item in one of the tests, an item in the other test with an identical IRF must exist. Theoretical as well as practical implications of these results are discussed.This research was supported by Educational Testing Service Allocation Projects No. 79409 and No. 79413. The authors wish to thank John Donoghue, Ming-Mei Wang, Rebecca Zwick, and Zhiliang Ying for their useful comments and discussions. The authors also wish to thank three anonymous reviewers for their comments.     

Adjusting for information inflation due to local dependency in moderately large item clusters

When multiple items are clustered around a reading passage, the local independence assumption in item response theory is often violated. The amount of information contained in an item cluster is usually overestimated if violation of local independence is ignored and items are treated as locally independent when in fact they are not. In this article we provide a general method that adjusts for the inflation of information associated with a test containing item clusters. A computational scheme was presented for the evaluation of the factor of adjustment for clusters in the restrictive case of two items per cluster, and the general case of more than two items per cluster. The methodology was motivated by a study of the NAEP Reading Assessment. We present a simulated study along with an analysis of a NAEP data set.The research was supported under the National Assessment of Educational Progress (Grant No. R999G30002) as administered by the Office of Educational Research and Improvement, U.S. Department of Education. This work was started when the author was at the Division of Statistics and Psychometrics at the Educational Testing Service. The author thanks Juliet Shaffer, Bob Mislevy, Eric Bradlow, three reviewers and an associate editor for their helpful comments on the paper.     

Analysis of residuals for the multionmial item response model

Using the item response model as developed on the multinomial distribution, asymptotic variances are obtained for residuals associated with response patterns and first-, and second-order marginal frequencies of manifest variables. When the model does not fit well, an examination of these residuals may reveal the source of the poor fit. Finally, a limited-information test of fit for the model is developed by using residuals defined for the first-, and second-order marginals. Model evaluation based on residuals for these marginals is particularly useful when the response pattern frequencies are sparse.The author would like to thank Yasuo Amemiya and Joseph Lucke for helpful suggestions. This research was supported by a Research Incentive Grant from Arizona State University.     

The role of item extremity in the emergence of keying-related factors: an exploration with the life orientation test

Keying-related factors in psychological scales are variously interpreted substantively or as products of violations of the assumptions underlying item keying. The present study investigated whether the extremity of the wording of items may contribute to the emergence of item-keying factors in a commonly used psychological scale. Respondents (N = 277) completed the Life Orientation Test (M. F. Scheier & C. S. Carver, 1985) in either its original or modified, more moderately worded form. Results indicate that the interaction of item extremity and item keying significantly affected subscale means and, more important, that the more moderately worded scale was substantially more unidimensional. Results are explained partially through the association of lesser and greater extremity with the tendency for some respondents to agree or disagree with items irrespective of keying direction. These results, although demonstrated in only 1 scale, have potential relevance to any scale comprising positive and negative items.     

The Relatively Infinite Value of the Environment

Some environmental ethicists and economists argue that attributing infinite value to the environment is a good way to represent an absolute obligation to protect it. Others argue against modelling the value of the environment in this way: the assignment of infinite value leads to immense technical and philosophical difficulties that undermine the environmentalist project. First, there is a problem of discrimination: saving a large region of habitat is better than saving a small region; yet if both outcomes have infinite value, then decision theory prescribes indifference. Second, there is a problem of swamping probabilities: an act with a small but positive probability of saving an endangered species appears to be on par with an act that has a high probability of achieving this outcome, since both have infinite expected value. Our paper shows that a relative (rather than absolute) concept of infinite value can be meaningfully defined, and provides a good model for securing the priority of the natural environment while avoiding the failures noted by sceptics about infinite value. Our claim is not that the relative infinity utility model gets every detail correct, but rather that it provides a rigorous philosophical framework for thinking about decisions affecting the environment.     

The nonconvergence of factals: A nonmetric common factor analysis

FACTALS is a nonmetric common factor analysis model for multivariate data whose variables may be nominal, ordinal or interval. In FACTALS an Alternating Least Squares algorithm is utilized which is claimed to be monotonically convergent.In this paper it is shown that this algorithm is based upon an erroneous assumption, namely that the least squares loss function (which is in this case a nonscale free loss function) can be transformed into a scalefree loss function. A consequence of this is that monotonical convergence of the algorithm can not be guaranteed.     

The effect of additional variables on factor indeterminacy in models with a single common factor

Determinate solutions for the indeterminate common factor ofp variables satisfying the single common factor model are not unique. Therefore an infinite sequence of additional variables that conform jointly with the originalp variables to the original single common factor model does not determine a unique solution for the indeterminate factor of thep variables (although the solution is unique for the factor of the infinite sequence). Other infinite sequences may be found to determine different solutions for the factor of the originalp variables. The paper discusses a number of theorems about the effects of additional variables on factor indeterminacy in a model with a single common factor and draws conclusions from them for factor theory in general.     

Spoken-word processing in aphasia: effects of item overlap and item repetition

Two studies were carried out to investigate the effects of presentation of primes showing partial (word-initial) or full overlap on processing of spoken target words. The first study investigated whether time compression would interfere with lexical processing so as to elicit aphasic-like performance in non-brain-damaged subjects. The second study was designed to compare effects of item overlap and item repetition in aphasic patients of different diagnostic types. Time compression did not interfere with lexical deactivation for the non-brain-damaged subjects. Furthermore, all aphasic patients showed immediate inhibition of co-activated candidates. These combined results show that deactivation is a fast process. Repetition effects, however, seem to arise only at the longer term in aphasic patients. Importantly, poor performance on diagnostic verbal STM tasks was shown to be related to lexical decision performance in both overlap and repetition conditions, which suggests a common underlying deficit.     

影响大学生身体活动参与心理因素研究

采用自编的《大学生身体活动心理影响因素调查问卷》和《国际身体活动问卷》对湖北省9所高校的395名大学生进行调查,采用验证性因子分析对不同锻炼行为理论模型对闲暇时间身体活动的影响进行比较得出,影响大学生闲暇时间身体活动水平的主要心理影响因素是行为习惯、目标态度、结果评价、情感体验、社会支持、自我认同、行为态度、行为意向这8个因素;并从性别、年级、专业、生源地以及学校类型几个方面对湖北省大学生身体活动心理因素进行了比较。     

The impact of social desirability bias on the EPQ-R item scores: An item response theory analysis

This study assessed the potential influence of social desirability (SD) response bias on the E, N, and P EPQ-R scores at the level of individual items. The study was based on a bidimensional IRT model which was fitted in a large sample. This allowed a detailed analysis of both the internal validities of the items and the content of the items which were most affected by SD. The E items were least affected by SD, but the direction of the impact depended on the type of item. As expected, in the N and P cases the relations obtained were consistently negative, but the strength of the SD impact also depended considerably on the type of item. The P scale was the most problematic in terms of convergent and discriminant validity.     

A note on sufficient conditions that a common factor will be determinate in an infinite domain of variables

It is proved for the common factor model withr common factors that under certain condition s which maintain the distinctiveness of each common factor a given common factor will be determinate if there exists an unlimited number of variables in the model each having an absolute correlation with the factor greater than some arbitrarily small positive quantity.The author is indebted to R. P. McDonald for suggesting the proof of Guttman's determinantal equation for the squared multiple correlation in predicting a factor from the observed variables used in the parenthetical note.     

The role of item distinctiveness in short-term recall of order information

In two experiments, we examined short-term recall of order information using a partial-report distractor task. We manipulated the characteristics of a single letter in one of two four-letter segments. Participants knew in advance the identity of the letters in each segment. We made a single letter distinctive at presentation either by printing it in red or by replacing it with a red dash. Presenting the letter in red did not affect overall recall of the positions of the letters in the segment but did facilitate specific recall of the position of the distinct letter. Replacing the letter with a red dash inhibited overall recall as well as specific recall of the distinct letter. Participants were also less likely to respond in the regular output order when there was a dash replacing a letter in the segment. These effects of distinctiveness are explained in terms of output order processes in recent versions of the perturbation model.     

The relationship between intelligence and multiple domains of religious belief: Evidence from a large adult US sample

High levels of religiosity have been linked to lower levels of intelligence in a number of recent studies. These results have generated both controversy and theoretical interest. Here in a large sample of US adults we address several issues that restricted the generalizability of these previous results. We measured six dimensions of religiosity (rather than just one or two), along with a multi-scale instrument to assess general intelligence. We also controlled for the influence of the personality trait openness on facets of religious belief and practice. The results indicated that lower intelligence is most strongly associated with higher levels of fundamentalism, but also modestly predicts central components of religiosity such as a sense of religious identification and private religious practice. Secondly, we found that a higher level of openness - often assumed to lead to lower religiosity - is weakly associated with reduced fundamentalism but with increased religious mindfulness, private religious practice, religious support, and spirituality. These new results provide a framework for understanding the links between reasoning and faith.     

The role of collateral information about examinees in item parameter estimation

Standard procedures for estimating item parameters in item response theory (IRT) ignore collateral information that may be available about examinees, such as their standing on demographic and educational variables. This paper describes circumstances under which collateral information about examineesmay be used to make inferences about item parameters more precise, and circumstances under which itmust be used to obtain correct inferences.This work was supported by Contract No. N00014-85-K-0683, project designation NR 150-539, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the United States Government. We are indebted to Tim Davey, Eugene Johnson, and three anonymous referees for their comments on earlier versions of the paper.