Estimation for structural equation models with missing data

A direct method in handling incomplete data in general covariance structural models is investigated. Asymptotic statistical properties of the generalized least squares method are developed. It is shown that this approach has very close relationships with the maximum likelihood approach. Iterative procedures for obtaining the generalized least squares estimates, the maximum likelihood estimates, as well as their standard error estimates are derived. Computer programs for the confirmatory factor analysis model are implemented. A longitudinal type data set is used as an example to illustrate the results.This research was supported in part by Research Grant DAD1070 from the U.S. Public Health Service. The author is indebted to anonymous reviewers for some very valuable suggestions. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.     

A bayesian approach to confirmatory factor analysis

Confirmatory factor analysis is considered from a Bayesian viewpoint, in which prior information on parameter is incorporated in the analysis. An iterative algorithm is developed to obtain the Bayes estimates. A numerical example based on longitudinal data is presented. A simulation study is designed to compare the Bayesian approach with the maximum likelihood method.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong.     

Covariance structure analysis in several populations

This paper is concerned with the study of covariance structural models in several populations. Estimation theory of the parameters that are subject to general functional restraints is developed based on the generalized least squares approach. Asymptotic properties of the constrained estimator are studied; and asymptotic chi-square tests are presented to evaluate appropriate model comparisons. The method of multipliers and the standard reparametrization technique are discussed in obtaining the estimates. The methodology is demonstrated by a set of real data.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong. The authors are indebted to several anonymous reviewers for suggestions for improvement of this paper.     

A comparison of the key-peck and treadle-press operants in the pigeon: differential-reinforcement-of-low-rate schedule of reinforcement

Key pecking and treadle pressing in pigeons were compared under concurrent (key-treadle) and single-operant differential-reinforcement-of-low-rate schedules of food reinforcement ranging from 5 to 60 sec (concurrent procedure) or 5 to 120 sec (single-operant procedure). Under both procedures, the two operants followed the same general law: decreasing response rate and reinforcement rate and increasing number of responses per reinforcement as a function of increasing schedule interval. High correlations were found between key pecking and treadle pressing for the measures of response rate, reinforcement rate, and responses per reinforcement. Regression equations allowed the prediction of treadle pressing from key pecking. More bursting occurred in responding to the key, and key pecking showed a more precise temporal discrimination than treadle pressing. A test for sequential dependencies between key and treadle responses showed significant dependencies not only under the concurrent procedure but also in data created artificially by merging key and treadle sequences from different pigeons under the concurrent procedure and from the same pigeon under the single-operant procedure. It seems likely that the sequential dependencies found were due to the independent action of the schedule on each operant and that behavioral dependencies did not occur with the concurrent training procedure. The key-peck operant does not appear to have any special qualities that preclude its use in discovering general laws of behavior, at least under the differential-reinforcement-of-low-rate schedule. The usefulness of the key peck in other situations requires direct experimental study.     

Structural constraints in the perception of English stop-sonorant clusters

Native-language phonemes combined in a non-native way can be misperceived so as to conform to native phonotactics, e.g. English listeners are biased to hear syllable-initial [tr] rather than the illegal [tl] (Perception and Psychophysics 34 (1983) 338; Perception and Psychophysics 60 (1998) 941). What sort of linguistic knowledge causes phonotactic perceptual bias? Two classes of models were compared: unit models, which attribute bias to the listener's differing experience of each cluster (such as their different frequencies), and structure models, which use abstract phonological generalizations (such as a ban on [coronal][coronal] sequences). Listeners (N=16 in each experiment) judged synthetic 6 x 6 arrays of stop-sonorant clusters in which both consonants were ambiguous. The effect of the stop judgment on the log odds ratio of the sonorant judgment was assessed separately for each stimulus token to provide a stimulus-independent measure of bias. Experiment 1 compared perceptual bias against the onsets [bw] and [dl], which violate different structural constraints but are both of zero frequency. Experiment 2 compared bias against [dl] in CCV and VCCV contexts, to investigate the interaction of syllabification with segmentism and to rule out a compensation-for-coarticulation account of Experiment 1. Results of both experiments favor the structure models (supported by NSF).     

Molecular analyses of the principal components of response strength

Killeen and Hall (2001) showed that a common factor called strength underlies the key dependent variables of response probability, latency, and rate, and that overall response rate is a good predictor of strength. In a search for the mechanisms that underlie those correlations, this article shows that (a) the probability of responding on a trial is a two-state Markov process; (b) latency and rate of responding can be described in terms of the probability and period of stochastic machines called clocked Bernoulli modules, and (c) one such machine, the refractory Poisson process, provides a functional relation between the probability of observing a response during any epoch and the rate of responding. This relation is one of proportionality at low rates and curvilinearity at higher rates.     

Variability of the MAX and MIN Statistic: A Theory of the Quantile Spread as a Function of Sample Size

The maximum and minimum of a sample from a probability distribution are extremely important random variables in many areas of psychological theory, methodology, and statistics. For instance, the behavior of the mean of the maximum or minimum processing time, as a function of the number of component random processing times (n), has been studied extensively in an effort to identify the underlying processing architecture (e.g., Townsend & Ashby, 1983; Colonius & Vorberg, 1994). Little is known concerning how measures of variability of the maximum or minimum change with n. Here, a new measure of random variability, the quantile spread, is introduced, which possesses sufficient strength to define distributional orderings and derive a number of results concerning variability of the maximum and the minimum statistics. The quantile spread ordering may be useful in many venues. Several interesting open problems are pointed out. This work was supported by an NIH Grant R01 MH57717 to the first author. Some of the collaboration took place during the year 2000 while J.T. Townsend was a Fellow at the Hanse Institute for Advanced Study (HWK), sponsored by H. Colonius at Oldenburg University.     

Speech and non-speech processing in people with specific language impairment: a behavioural and electrophysiological study

McArthur and Bishop (2004) found that people with specific language impairment (SLI) up to 14 years of age have poor behavioural frequency discrimination (FD) thresholds for 25-ms pure tones, while people with SLI upto 20 years of age have abnormal auditory N1--P2--N2 event-related potential (ERP) responses to the same tones. In the present study, we extended these findings to more complex non-speech and speech sounds by comparing younger (around 13 years) and older (around 17 years) teenagers with SLI and controls for their behavioural FD thresholds and N1-P2 ERPs to 25 and 250-ms pure tones, vowels, and non-harmonic complex tones. We found that a subgroup of people with SLI had abnormal responses to tones and vowels at the level of behaviour and the brain, and that poor processing was associated with the spectral complexity of auditory stimuli rather than their phonetic significance. We suggest that both the age of listeners and the sensitivity of psychoacoustic tasks to age-related changes in auditory skills may be crucial factors in studies of sound processing in SLI.     

Neighbourhood effects on error rates in speech production

Models of speech production differ on whether phonological neighbourhoods should affect processing, and on whether effects should be facilitatory or inhibitory. Inhibitory effects of large neighbourhoods have been argued to underlie apparent anti-frequency effects, whereby high-frequency default features are more prone to mispronunciation errors than low-frequency nondefault features. Data from the original SLIPs experiments that found apparent anti-frequency effects are analysed for neighbourhood effects. Effects are facilitatory: errors are significantly less likely for words with large numbers of neighbours that share the characteristic that is being primed for error ("friends"). Words in the neighbourhood that do not share the target characteristic ("enemies") have little effect on error rates. Neighbourhood effects do not underlie the apparent anti-frequency effects. Implications for models of speech production are discussed.     

The Bursts and Lulls of Multimodal Interaction: Temporal Distributions of Behavior Reveal Differences Between Verbal and Non‐Verbal Communication

Recent studies of naturalistic face‐to‐face communication have demonstrated coordination patterns such as the temporal matching of verbal and non‐verbal behavior, which provides evidence for the proposal that verbal and non‐verbal communicative control derives from one system. In this study, we argue that the observed relationship between verbal and non‐verbal behaviors depends on the level of analysis. In a reanalysis of a corpus of naturalistic multimodal communication (Louwerse, Dale, Bard, & Jeuniaux, 2012 ), we focus on measuring the temporal patterns of specific communicative behaviors in terms of their burstiness. We examined burstiness estimates across different roles of the speaker and different communicative modalities. We observed more burstiness for verbal versus non‐verbal channels, and for more versus less informative language subchannels. Using this new method for analyzing temporal patterns in communicative behaviors, we show that there is a complex relationship between verbal and non‐verbal channels. We propose a “temporal heterogeneity” hypothesis to explain how the language system adapts to the demands of dialog.