Correspondence analysis and association models constrained by a conditional independence graph

The manner in which the conditional independence graph of a multiway contingency table effects the fitting and interpretation of the Goodman association model (RC) and of correspondence analysis (CA) is considered.Estimation of the row and column scores is presented in this context by developing a unified framework that includes both models. Incorporation of the conditional independence constraints inherent in the graph may lead to equal or additive scores for the corresponding marginal tables, depending on the topology of the graph. An example of doubly additive scores in the analysis of a Burt subtable is given.Thanks are due to anonymous referees who substantially improved the original draft of this paper.     

Relations between baseline contingencies and equivalence probe performances

Following the emergence of two three-member equivalence classes (A1B1C1 and A2B2C2), 5 college students were exposed to one or more changes in the reinforcement contingencies controlling baseline conditional discriminations. AC relations were either reversed (i.e., C2 was reinforced and C1 punished when A1 was the sample; C1 was reinforced and C2 punished when A2 was the sample) or arranged randomly (i.e., C2 and C1 were reinforced and punished equally often in the presence of A1 and A2). In a third condition, the original AB and AC relations were reversed. Results showed that although baseline conditional discrimination performances were under the control of reinforcement contingencies, and performances on symmetry trials varied with baseline responding for 3 of 4 subjects when contingencies were reversed, performances on transitivity probes remained consistent with the initial equivalence class. These inconsistencies between probe and baseline performances were striking because conditional discriminations are thought to be the determinants of equivalence class performance. Similarly, the contrast between performances on symmetry and transitivity probes was of theoretical interest because equivalence classes are defined by congruent patterns of responding on probe trials.     

Conditional discrimination in mentally retarded adults: the development of generalized skills.

The development of generalized conditional discrimination skills was examined in adults with retardation. Two subjects with histories of failure to acquire arbitrary matching under trial-and-error procedures were successful under procedures that trained one or more prerequisite skills. The successive discrimination between the sample stimuli was established by training the subjects to name the stimuli. The simultaneous discrimination between the comparison stimuli was established using either (a) standard simple discrimination training with reversals or (b) a procedure in which each of the two sample-comparison relations in the conditional discrimination was presented in blocks of trials, with the size of the blocks decreasing gradually until sample presentation was randomized. The amount of prerequisite training required varied across subjects and across successive conditional discriminations. After acquiring either two or three conditional discriminations with component training, both subjects learned new conditional discriminations under trial-and-error procedures. In general, each successive conditional discrimination was acquired more rapidly. Tests showed that conditional responding had become a generalized skill. Symmetry was shown for almost all trained relations. Symmetry trial samples were ultimately named the same as the stimuli to which they were related in training.     

Conditioned reinforcement by conditional discriminative stimuli.

A concurrent-chains schedule was used to examine how a delay to conditional discriminative stimuli affects conditioned reinforcement strength. Pigeons' key-peck responses in the initial link produced either of two terminal links according to independent variable-interval 30-s schedules. Each terminal link involved an identical successive conditional discrimination and was segmented into three links: a delay interval (green), a color conditional discriminative stimulus (blue or red), and a line conditional discriminative stimulus (vertical or horizontal lines). Food delivery occurred 45 s after entering the terminal link with a probability of .5, but its conditional probability (1.0 or 0) depended on the combination of the color and the line stimuli. One of the color stimuli occurred independently of further responding, 5 s after entry into the right terminal link, but it occurred 35 s after entry into the left terminal link. One of the line stimuli occurred independently of responding 40 s after entry into either terminal link, synchronized with the offset of the color stimulus. The initial-link relative response rate for the right was consistently higher in comparison with a control condition in which the color stimuli occurred 20 s after entry into either terminal link. The preference for the short delay to the color conditional discriminative stimuli suggests the possibility of conditioned reinforcement by information about the relation between the line conditional discriminative stimuli and the outcomes.     

Control of behavior by an establishing stimulus

Seventeen pigeons were exposed to a three-key discrete-trial procedure in which a peck on the lit center key produced food if, and only if, the left keylight was lit. The center key was illuminated by a peck on the lit right key. Of interest was whether subjects pecked the right key before or after the response-independent onset of the left keylight. Pecks on the right key after left-keylight onset suggest control of behavior by the left keylight—an establishing stimulus. In three experiments, the strength of center-keylight onset as conditioned reinforcer for a response on the right key was manipulated by altering the size of the reduction in time to food delivery correlated with its onset. Control of pigeons' key pecks by onset of the left keylight occurred on more trials per session when the center keylight was a relatively weak conditioned reinforcer and on fewer trials per session when the center keylight was a relatively strong condtioned reinforcer. Differences across conditions in the degree of control by onset of the establishing stimulus were greatest when changes in conditioned reinforcer strength occurred relatively frequently and were signaled. The results provide evidence of the function of an establishing stimulus.     

Trend in correlated proportions

A random effects probit model is developed for the case in which the same units are sampled repeatedly at each level of an independent variable. Because the observed proportions may be correlated under these conditions, estimating their trend with respect to the independent variable is no longer a standard problem for probit, logit or loglinear analysis. Using a qualitative analogue of a random regressions model, we employ instead marginal maximum likelihood to estimate the average latent trend line. Likelihood ratio tests of the hypothesis of no trend in the average line, and the hypothesis of no differences in average trend lines between experimental treatments, are proposed. We illustrate the model both with simulated data and with observed data from a clinical experiment in which psychiatric patients on two drug therapies are rated on five occasions for the presence or absence of symptoms.Supported by a grant from the MacArthur Foundation and National Science Foundation Grant BNS85-11774.The authors are indebted to James Heckman for calling our attention to the Clark algorithm.     

DOES CONDITIONAL DISCRIMINATION LEARNING BY PIGEONS NECESSARILY INVOLVE HIERARCHICAL RELATIONSHIPS?

Four experiments demonstrate that when putative conditional and discriminative cues are presented simultaneously in the single reversal procedure, it is not possible to ascribe a uniquely conditional or uniquely discriminative function to either of the cues. In Experiment 1, pigeons were trained to respond to a blue key and not to a red key while the houselight was on; then in a different session they learned the reversal of this discrimination with the houselight off (single reversal). Separate groups were tested for color generalization with houselight conditions alternating in blocks of trials or for houselight intensity generalization with blue and red key colors alternating in blocks of trials. Both test procedures revealed a conditional relationship between houselight and key color conditions. Experiment 2 produced the same result following training in which the key colors were held constant across training sessions while the houselight and no houselight conditions varied within sessions. In Experiment 3, separate groups were trained with the two procedures but were tested with randomly ordered combinations of key colors and houselight intensities. The two groups yielded indistinguishable bidimensional generalization gradients with peaks at both previously reinforced stimulus combinations. In Experiment 4 the subjects were switched from one of these training procedures to the other with no decrement in their discriminative performance. We conclude that for successive discriminations between conditional- and discriminative-stimulus combinations, the notion of a hierarchical relation between conditional and discriminative stimuli must be extended to include a symmetrical relationship or the notion should be abandoned altogether.     

A comparison of analysis methods to estimate contingency strength

To date, several data analysis methods have been used to estimate contingency strength, yet few studies have compared these methods directly. To compare the relative precision and sensitivity of four analysis methods (i.e., exhaustive event‐based, nonexhaustive event‐based, concurrent interval, concurrent+lag interval), we applied all methods to a simulated data set in which several response‐dependent and response‐independent schedules of reinforcement were programmed. We evaluated the degree to which contingency strength estimates produced from each method (a) corresponded with expected values for response‐dependent schedules and (b) showed sensitivity to parametric manipulations of response‐independent reinforcement. Results indicated both event‐based methods produced contingency strength estimates that aligned with expected values for response‐dependent schedules, but differed in sensitivity to response‐independent reinforcement. The precision of interval‐based methods varied by analysis method (concurrent vs. concurrent+lag) and schedule type (continuous vs. partial), and showed similar sensitivities to response‐independent reinforcement. Recommendations and considerations for measuring contingencies are identified.     

基于语料库统计的“音-形”激活概率及加工机制

为了了解心理词典中语音与汉字的联结情况以及从音到形的加工机制,研究首先计算出了基于语料库统计的“音-形”激活概率(某个音节激活其对应汉字的概率),并通过一个听写实验来验证这种激活概率是否反映实际加工中的激活情况。结果证明基于语料统计得到的“音-形”激活概率基本可以预测实际的“音-形”激活情况,表现为:“音-形”激活概率越高的汉字被激活的概率和强度越高,并且有明显的优势字效应; 该统计概率具有可独立于其他影响因素的预测功能。