The bias function of the maximum likelihood estimate of ability for the dichotomous response level

Samejima has recently given an approximation for the bias function for the maximum likelihood estimate of the latent trait in the general case where item responses are discrete, generalizing Lord's bias function in the three-parameter logistic model for the dichotomous response level. In the present paper, observations are made about the behavior of this bias function for the dichotomous response level in general, and also with respect to several widely used mathematical models. Some empirical examples are given.     

An approximation for the bias function of the maximum likelihood estimate of a latent variable for the general case where the item responses are discrete

Lord developed an approximation for the bias function for the maximum likelihood estimate in the context of the three-parameter logistic model. Using Taylor's expansion of the likelihood equation, he obtained an equation that includes the conditional expectation, given true ability, of the discrepancy between the maximum likelihood estimate and true ability. All terms of orders higher thann ^?1 are ignored wheren indicates the number of items. Lord assumed that all item and individual parameters are bounded, all item parameters are known or well-estimated, and the number of items is reasonably large. In the present paper, an approximation for the bias function of the maximum likelihood estimate of the latent trait, or ability, will be developed using the same assumptions for the more general case where item responses are discrete. This will include the dichotomous response level, for which the three-parameter logistic model has been discussed, the graded response level and the nominal response level. Some observations will be made for both dichotomous and graded response levels.     

Logistic positive exponent family of models: Virtue of asymmetric item characteristic curves

The paper addresses and discusses whether the tradition of accepting point-symmetric item characteristic curves is justified by uncovering the inconsistent relationship between the difficulties of items and the order of maximum likelihood estimates of ability. This inconsistency is intrinsic in models that provide point-symmetric item characteristic curves, and in this paper focus is put on the normal ogive model for observation. It is also questioned if in the logistic model the sufficient statistic has forfeited the rationale that is appropriate to the psychological reality. It is observed that the logistic model can be interpreted as the case in which the inconsistency in ordering the maximum likelihood estimates is degenerated.The paper proposes a family of models, called the logistic positive exponent family, which provides asymmetric item chacteristic curves. A model in this family has a consistent principle in ordering the maximum likelihood estimates of ability. The family is divided into two subsets each of which has its own principle, and includes the logistic model as a transition from one principle to the other. Rationale and some illustrative examples are given.     

Effects of generalized self-efficacy and negative social comparison feedback on specific self-efficacy and performance

The effects of social comparison feedback on specific self-efficacy and performance of high generalized self-efficacy participants and low generalized self-efficacy participants were examined with the help of 20 participants with high generalized self-efficacy and 20 participants with low generalized self-efficacy. Half of the participants in each generalized self-efficacy group received negative social comparison feedback after each of four trials of an experimental task while the other half received no feedback. Two kinds of specific self-efficacy-performance-based and normative-based--were measured once before the task and four times after the trials of the task. After the task, the High generalized self-efficacy/Feedback group rated performance-based specific self-efficacy higher and performed better than the Low generalized self-efficacy/Feedback group. No significant difference was observed between the High generalized self-efficacy/No feedback group and Low generalized self-efficacy/No feedback group. There were no significant effects with regard to normative-based specific self-efficacy.     

Knowledge and strategies used by adolescents to compare duration of movement by two objects

This study investigated the knowledge and strategies used by senior high school students to compare durations of movement by two objects. The developmental process during adolescence was also examined by comparing the results with those published for Grade 7 to Grade 9 students and university undergraduates. A cathode-ray tube monitor was used to present images of two cars traveling in the same direction for various durations and distances. 30 Grade 12 students were asked to identify which of the cars had traveled for a longer duration and why. Analysis suggested that the strategies develop during adolescence in a sequence. Initially, comparison of durations was based on the relative distance traveled by the two cars. Then the comparison was based exclusively on knowledge that "duration = temporal starting point- temporal stopping point." Finally, the two types of knowledge were used appropriately according to the characteristics of the specific task.     

Normal ogive model on the continuous response level in the multidimensional latent space

The homogeneous case of the continuous response model is expanded to the multi-dimensional latent space, and the normal ogive model is presented. The operating density characteristic of the continuous item response and the vector of basic functions are developed. It is found out that there is a vector of sufficient statistics for estimating the subject's vector of latent traits, given the item parameter vectors. The relationship between the model and the linear factor analysis is observed. The matrix of item response information functions is introduced. Some additional observations are also made.The work described in this paper was partly carried out while the author was at Bowling Green State University with the support of its Research Associateship in the summer, 1972.     

A method of estimating item characteristic functions using the maximum likelihood estimate of ability

A method of estimating item characteristic functions is proposed, in which a set of test items, whose operating characteristics are known and which give a constant test information function for a substantially wide range of ability, are used. The method is based on the maximum likelihood estimates of ability for a group of several hundred examinees. Throughout the present study the Monte Carlo method is used.