Mixture Distribution Analysis Research Articles

Finite mixture distribution models of simple discrimination learning.

Through the application of finite mixture distribution models, we investigated the existence of distinct modes of behavior in learning a simple discrimination. The data were obtained in a repeated measures study in which subjects aged 6 to 10 years carried out a simple discrimination learning task. In contrast to distribution models of exclusively rational learners or exclusively incremental learners, a mixture distribution model of rational learners and slow learners was found to fit the data of all measurement occasions and all age groups. Hence, the finite mixture distribution analysis provides strong support for the existence of distinct modes of learning behavior. The results of a second experiment support this conclusion by crossvalidation of the models that fit the data of the first experiment. The effect of verbally labeling the values on the relevant stimulus dimension and the consistency of behavior over measurement occasions are related to the mixture model estimates.

Cohorts in space:geostatistical mapping of the age structure of the squat lobster Pleuroncodes monodon population off central Chile

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 196:239-251 (2000) - doi:10.3354/meps196239 Cohorts in space: geostatistical mapping of the age structure of the squat lobster Pleuroncodes monodon population off central Chile Rubén Roa*, Fabián Tapia** Departamento de Oceanografía, Universidad de Concepción, Casilla 160-C, Concepción, Chile *E-mail: rroa@udec.cl **Present address: Biology Department, MS#34, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA ABSTRACT: Animal populations are spatial objects in the sense that their structure and functioning depend on the spatial context they inhabit. However, most population dynamics models ignore the spatial context and set populations Œin the air¹. This paper is focused on the squat lobster Pleuroncodes monodon population inhabiting the narrow continental shelf off central Chile, and encompassing 3 degrees of latitude. We tested the hypothesis that the spatial functioning of this population is driven by annual cohorts that enter the population through a nursery ground, and then radiate away from the nursery to the north and south by individual dispersal, thus creating a spatial pattern where age and distance from the nursery are correlated. To test the hypothesis we performed an extensive survey from 34 to 37°S along the continental shelf, collecting data on individual mean size by sex and spatial location. The data gathered was analysed using a combination of mixture distribution analysis on size frequency data and geostatistical mapping on size and location data. Isotropic and anisotropic variogram models were fitted to size data for both sexes. Selection of the appropriate models and kriging parameters was done by cross validation. The hypothesis posed was fully corroborated by the data and the analysis, with 6 adult cohorts identified for both sexes radiating away from the nursery ground in waves at an average distance of one fifth the latitudinal range of the population. Geostatistical mapping of size data for juveniles in the nursery ground, collected with a higher resolution in previous years, showed that recruitment can occur as several relatively small patches interspersed through the nursery area or as a large patch in the middle of the nursery. The corroborated model of spatial population functioning explains the history of commercial over-exploitation and recolonisation of this population. It also suggest that this 350 km long population is renewed by recruits from nearby cohorts, both to the south and north of the nursery area, while cohorts farther north can be exporting recruits to prime nursery habitat. These insights into the functioning of this large population could only be gained by a fully spatially explicit analysis. KEY WORDS: Population dynamics · Cohort dispersal · Geostatistical mapping · Spatially explicit · Habitat features · Crustacean biology · Chile Full text in pdf format PreviousNextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 196. Publication date: April 18, 2000 Print ISSN:0171-8630; Online ISSN:1616-1599 Copyright © 2000 Inter-Research.

Mixture distribution analysis of length of hospital stay for efficient funding

This paper aims to demonstrate the importance of mixture distribution modelling in analysing the characteristics of inpatient length of stay (LOS), which has direct implications on health planning and formation of payment policy. It is found that mixture distribution analysis can confirm the homogeneity of certain Diagnosis Related Groups (DRGs). It can also reveal the heterogeneous patterns of other DRGs. For those DRGs exhibiting heterogeneity in LOS, related socio-economic factors influencing LOS are compared and contrasted between components by Poisson mixture regressions. Such an analysis provides an integrated framework to link funding with relevant influencing factors of LOS. A Poisson mixture regression model can give useful insights for state health institutions to initiate efficient casemix payments. It also benefits hospital managers and clinicians to manage LOS more effectively.

Prevalence estimation under heterogeneity in the example of bovine trypanosomosis in Uganda

We examine variance estimators of a binomial parameter established under cluster sampling using data from a cross-sectional study of bovine trypanosomosis in Mukono County, Uganda. Fifty farms (referred to as clusters), were sampled with a total sample size of 487 cattle. Trypanosomes were found in 17.9% (87/487) of the total sample. The cluster-level (CL) prevalences were not homogeneously distributed. According to maximum-likelihood parameters established by mixture-distribution analysis, 18% of the cluster had 0% prevalence whereas 48% and 34% of the clusters could be allocated to subpopulations of clusters with mean prevalences 11.6% and 31.9%, respectively. We show that this form of heterogeneity invalidates the applicability of the Beta distribution as a model for the distribution of CL prevalences. Furthermore, we provide empirical evidence for a variance inflation due to heterogeneity (inflation factor 2.07) that exceeds the design-based variance inflation due to clustering alone (inflation factor 1.82). The variance inflation due to heterogeneity is given in a closed form so that the approach can be conveniently applied to survey data that involve cluster sampling under heterogeneity.

Recent Developments in Computer-Assisted Analysis of Mixtures

This paper reviews recent developments in the area of computer-assisted analysis of mixture distributions (C.A.MAN). Given a biometric situation of interest in which, under homogeneity assumptions, a certain parametric density occurs, such as the Poisson, the binomial, the geometric, the normal, and so forth, then it is argued that this situation can easily be enlarged to allow a variation of the scalar parameter in the population. This situation is called unobserved heterogeneity. This naturally leads to a specific form of nonparametric mixture distribution that can then be assumed to be the standard model in the biometric application of interest (since it also incorporates the homogeneous situations as a special case). Besides developments in theory and algorithms, the work focuses on developments in biometric applications such as meta-analysis, fertility studies, estimation of prevalence under clustering, and estimation of the distribution function of survival time under interval censoring. The approach is nonparametric for the mixing distribution, including leaving the number of components (subpopulations) of the mixing distribution unknown.

Evaluation and comparison of antibody ELISAs for serodiagnosis of bovine trypanosomosis

A total of 457 serum samples from cattle kept under moderate tsetse challenge in Mukono County, Uganda, (79 of them with confirmed trypanosomosis) and 86 sera from cattle in Germany were tested for Trypanosoma antibodies using enzyme-linked immunosorbent assay (ELISA) with antigen obtained from blood stream form (BSF) and in vitro cultivated procyclic (PRO) trypanosomes. The BSF and PRO ELISA showed a moderate quantitative correlation. A difference plot revealed a slightly non-linear relation between the two methods. Cut-off values were established using (A) non-exposed controls, (B) exposed negative controls and (C) by mixture distribution analysis of the quantitative ELISA results for the sample from the endemic target population. The diagnostic agreement between both assays was significant (κ, p<0.05). The diagnostic accuracy of the two tests relative to standard parasitological detection methods was not markedly different as shown by the areas under the receiver operating characteristics (ROC) plots. In out study, neither non-exposed controls (cut-off A) nor exposed negative controls (cut-off B) were suitable for establishing cut-off values. Based on the cut-off value C, derived from mixture distribution analysis, the proportion of animals with elevated antibody levls in the study population was estimated by both assays at 45% (41–50% binomial 95% confidence interval). This can be regarded as an unbiased estimate of the proportion of ‘sero-responders’ and not necessarily as a proxy for infection prevalence in the target population. We recommend the PRO ELISA to be used for seroepidemiological surveys, since in vitro cultivation of procyclic trypanosomes allows a continuous and standardised preparation of test antigen.

Impact of biological factors on the interpretation of bovine trypanosomosis serology

A total of 457 cattle from dairy farms in Mukono County, Uganda, were investigated for Trypanosoma antibodies by ELISA. The objective of the study was to identify explanatory covariate factors for seropositivity among nine farm-specific and four animal-specific variables. We used logistic regression models for parasitological and serological outcome variables and then compared the adjusted odds ratios for explanatory factors between the models. Age is positively correlated with seropositivity but not with the detection of the parasite. Therefore, age group-specific cut-off values were established using mixture-distribution analysis. This procedure, as well as a mixture-distribution-derived cut-off value for the total sample, resulted in a greater relative efficiency of the ELISA as compared to conventional interpretation (cut-off value defined using non-exposed negative controls). The relevance of age and other biological factors for the serological status is briefly discussed.

Mixture distribution and receiver operating characteristic analysis of bedside chest imaging with screen-film and computed radiography.

The authors demonstrated the use of mixture distribution analysis as an alternative to receiver operating characteristic (ROC) analysis in a clinical study, where independent verification of the imaging diagnosis is not always feasible. ROC and mixture distribution analyses were applied to the blind readings of four radiologists on a stratified, random sample of 95 screen-film radiographs and 95 computed radiographs of the chest obtained from a medical intensive care unit. The imaging diagnosis established by an expert panel was used as the truth for the ROC analysis, and agreement of ratings was used for the mixture distribution analysis. Both methods yielded similar values for the proportion of correct diagnoses. Mixture distribution analysis may be useful for comparing imaging techniques in situations where the true imaging diagnosis cannot be established with a method independent of that being evaluated.

Normal ageing, impaired cognitive functioning and senile dementia--a mixture distribution analysis.

Dementia scores in the population of very old subjects (70 to > 95) do not demonstrate an obviously bimodal distribution. Heterogeneity analysis shows that the assumption of two distributions explains the data significantly better than a one-distribution model. The first distribution component can be regarded as representing the normal range of scores and the second the pathological range. An additional finding shows the normal range distribution shifting to the pathological range with increasing age.

Interval censored data: A note on the nonparametric maximum likelihood estimator of the distribution function

Gentleman & Geyer (1994) discuss the analysis of interval censored data and present results based on standard convex optimisation theory. Here, this problem is viewed from the perspective of a mixing problem of indicator functions. Using an analogy with the problem of mixture distributions a variety of results are easily derived, including a characterisation theorem for the maximum likelihood estimator and various reliably convergent algorithms. Software for the analysis of mixture distributions can be used to find the nonparametric estimate of the distribution function of the interval-censored survival time. Examples are provided to demonstrate the theory

An Application of the Laplace Method to Finite Mixture Distributions

Abstract An exact Bayesian analysis of finite mixture distributions is often computationally infeasible, because the number of terms in the posterior density grows exponentially with the sample size. A modification of the Laplace method is presented and applied to estimation of posterior functions in a Bayesian analysis of finite mixture distributions. The procedure, which involves computations similar to those required in maximum likelihood estimation, is shown to have high asymptotic accuracy for finite mixtures of certain exponential-family densities. For these mixture densities, the posterior density is also shown to be asymptotically normal. An approximation of the posterior density of the number of components is presented. The method is applied to Duncan's barley data and to a distribution of lake chemistry data for north-central Wisconsin.

Cerebrospinal-fluid neuropeptides: a biochemical subgrouping approach.

Cerebrospinal-fluid (CSF) corticotropin-releasing hormone, somatostatin, and thyrotropin-releasing hormone were measured by specific radioimmunoassays in 257 hospitalized psychiatry patients suffering from dementia disorders (n = 85), schizophrenia (n = 104), and mood and anxiety disorders (n = 39). Neurological controls (n = 29) were also investigated. Since there were large overlaps of the peptide levels across the nosological groups we subjected the dataset to a three-dimensional normal mixture distribution analysis. We obtained four biochemically separable clusters. Dementia disorders, but not the others, were heterogeneously distributed in these clusters but after eliminating the effects of age and illness duration this difference disappeared. No single clinical, psychological, or background variable emerged as a prominent correlate of the neuropeptide clusters. It is concluded that although CSF neuropeptide concentrations in psychiatric patient populations appear to be separable into distinct, normally distributed subgroups this distinction does not coincide with present nosological classifications.

Some recent research in the analysis of mixture distributions

(1990). Some recent research in the analysis of mixture distributions. Statistics: Vol. 21, No. 4, pp. 619-641.

Temporal properties of human information processing: Tests of discrete versus continuous models

Cognitive psychologists have characterized the temporal properties of human information processing in terms of discrete and continuous models. Discrete models postulate that component mental processes transmit a finite number of intermittent outputs (quanta) of information over time, whereas continuous models postulate that information is transmitted in a gradual fashion. These postulates may be tested by using an adaptive response-priming procedure and analysis of reaction-time mixture distributions. Three experiments based on this procedure and analysis are reported. The experiments involved varying the temporal interval between the onsets of a prime stimulus and a subsequent test stimulus to which a response had to be made. Reaction time was measured as a function of the duration of the priming interval and the type of prime stimulus. Discrete models predict that manipulations of the priming interval should yield a family of reaction-time mixture distributions formed from a finite number of underlying basis distributions, corresponding to distinct preparatory states. Continuous models make a different prediction. Goodness-of-fit tests between these predictions and the data supported either the discrete or the continuous models, depending on the nature of the stimuli and responses being used. When there were only two alternative responses and the stimulus-response mapping was a compatible one, discrete models with two or three states of preparation fit the results best. For larger response sets with an incompatible stimulus-response mapping, a continuous model fit some of the data better. These results are relevant to the interpretation of reaction-time data in a variety of contexts and to the analysis of speed-accuracy trade-offs in mental processes.