Checking Assumptions in Latent Class Regression Models via a Markov Chain Monte Carlo Estimation Approach: An Application to Depression and Socio-Economic Status

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to calculate posterior distributions and point estimates of any functions of parameters. It is this convenience that allows us to provide the diagnostic methods that we introduce. As a motivating example we present an analysis focusing on the association between depression and socioeconomic status, using data from the Epidemiologic Catchment Area study. We consider a latent class regression analysis investigating the association between depression and socioeconomic status measures, where the latent variable depression is regressed on education and income indicators, in addition to age, gender, and marital status variables. While the fitted latent class regression model yields interesting results, the model parameters are found to be invalid due to the violation of model assumptions. The violation of these assumptions is clearly identified by the presented diagnostic plots. These methods can be applied to standard latent class and latent class regression models, and the general principle can be extended to evaluate model assumptions in other types of models.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.

Quickbird satellite imagery for riparian management : characterizing riparian filter strips and detecting concentrated flow in an agricultural watershed

Riparian ecology plays an important part in the filtration of sediments from upland agricultural lands. The focus of this work makes use of multispectral high spatial resolution remote sensing imagery (Quickbird by Digital Globe) and geographic information systems (GIS) to characterize significant riparian attributes in the USDA’s experimental watershed, Goodwin Creek, located in northern Mississippi. Significant riparian filter characteristics include the width of the strip, vegetation properties, soil properties, topography, and upland land use practices. The land use and vegetation classes are extracted from the remotely sensed image with a supervised maximum likelihood classification algorithm. Accuracy assessments resulted in an acceptable overall accuracy of 84 percent. In addition to sensing riparian vegetation characteristics, this work addresses the issue of concentrated flow bypassing a riparian filter. Results indicate that Quickbird multispectral remote sensing and GIS data are capable of determining riparian impact on filtering sediment. Quickbird imagery is a practical solution for land managers to monitor the effectiveness of riparian filtration in an agricultural watershed.

Laser Thomson scattering measurements of electron temperature and density in a Hall-effect plasma

Hall-effect thrusters (HETs) are compact electric propulsion devices with high specific impulse used for a variety of space propulsion applications. HET technology is well developed but the electron properties in the discharge are not completely understood, mainly due to the difficulty involved in performing accurate measurements in the discharge. Measurements of electron temperature and density have been performed using electrostatic probes, but presence of the probes can significantly disrupt thruster operation, and thus alter the electron temperature and density. While fast-probe studies have expanded understanding of HET discharges, a non-invasive method of measuring the electron temperature and density in the plasma is highly desirable. An alternative to electrostatic probes is a non-perturbing laser diagnostic technique that measures Thomson scattering from the plasma. Thomson scattering is the process by which photons are elastically scattered from the free electrons in a plasma. Since the electrons have thermal energy their motion causes a Doppler shift in the scattered photons that is proportional to their velocity. Like electrostatic probes, laser Thomson scattering (LTS) can be used to determine the temperature and density of free electrons in the plasma. Since Thomson scattering measures the electron velocity distribution function directly no assumptions of the plasma conditions are required, allowing accurate measurements in anisotropic and non-Maxwellian plasmas. LTS requires a complicated measurement apparatus, but has the potential to provide accurate, non-perturbing measurements of electron temperature and density in HET discharges. In order to assess the feasibility of LTS diagnostics on HETs non-invasive measurements of electron temperature and density in the near-field plume of a Hall thruster were performed using a custom built laser Thomson scattering diagnostic. Laser measurements were processed using a maximum likelihood estimation method and results were compared to conventional electrostatic double probe measurements performed at the same thruster conditions. Electron temperature was found to range from approximately 1 – 40 eV and density ranged from approximately 1.0 x 1017 m-3 to 1.3 x 1018 m-3 over discharge voltages from 250 to 450 V and mass flow rates of 40 to 80 SCCM using xenon propellant.

Genotype 3 is associated with accelerated fibrosis progression in chronic hepatitis C

BACKGROUND/AIMS: While several risk factors for the histological progression of chronic hepatitis C have been identified, the contribution of HCV genotypes to liver fibrosis evolution remains controversial. The aim of this study was to assess independent predictors for fibrosis progression. METHODS: We identified 1189 patients from the Swiss Hepatitis C Cohort database with at least one biopsy prior to antiviral treatment and assessable date of infection. Stage-constant fibrosis progression rate was assessed using the ratio of fibrosis Metavir score to duration of infection. Stage-specific fibrosis progression rates were obtained using a Markov model. Risk factors were assessed by univariate and multivariate regression models. RESULTS: Independent risk factors for accelerated stage-constant fibrosis progression (>0.083 fibrosis units/year) included male sex (OR=1.60, [95% CI 1.21-2.12], P<0.001), age at infection (OR=1.08, [1.06-1.09], P<0.001), histological activity (OR=2.03, [1.54-2.68], P<0.001) and genotype 3 (OR=1.89, [1.37-2.61], P<0.001). Slower progression rates were observed in patients infected by blood transfusion (P=0.02) and invasive procedures or needle stick (P=0.03), compared to those infected by intravenous drug use. Maximum likelihood estimates (95% CI) of stage-specific progression rates (fibrosis units/year) for genotype 3 versus the other genotypes were: F0-->F1: 0.126 (0.106-0.145) versus 0.091 (0.083-0.100), F1-->F2: 0.099 (0.080-0.117) versus 0.065 (0.058-0.073), F2-->F3: 0.077 (0.058-0.096) versus 0.068 (0.057-0.080) and F3-->F4: 0.171 (0.106-0.236) versus 0.112 (0.083-0.142, overall P<0.001). CONCLUSIONS: This study shows a significant association of genotype 3 with accelerated fibrosis using both stage-constant and stage-specific estimates of fibrosis progression rates. This observation may have important consequences for the management of patients infected with this genotype.

A comparison of pixel and object-based land cover classification. A case study of the Asmara region, Eritrea

In this paper we compare the performance of two image classification paradigms (object- and pixel-based) for creating a land cover map of Asmara, the capital of Eritrea and its surrounding areas using a Landsat ETM+ imagery acquired in January 2000. The image classification methods used were maximum likelihood for the pixel-based approach and Bhattacharyya distance for the object-oriented approach available in, respectively, ArcGIS and SPRING software packages. Advantages and limitations of both approaches are presented and discussed. Classifications outputs were assessed using overall accuracy and Kappa indices. Pixel- and object-based classification methods result in an overall accuracy of 78% and 85%, respectively. The Kappa coefficient for pixel- and object-based approaches was 0.74 and 0.82, respectively. Although pixel-based approach is the most commonly used method, assessment and visual interpretation of the results clearly reveal that the object-oriented approach has advantages for this specific case-study.

Integration of Truncated Distributions in Exponential Family with Simulation Models of Logistics and Supply Chain Management

Truncated distributions of the exponential family have great influence in the simulation models. This paper discusses the truncated Weibull distribution specifically. The truncation of the distribution is achieved by the Maximum Likelihood Estimation method or combined with the expectation and variance expressions. After the fitting of distribution, the goodness-of-fit tests (the Chi-Square test and the Kolmogorov-Smirnov test) are executed to rule out the rejected hypotheses. Finally the distributions are integrated in various simulation models, e. g. shipment consolidation model, to compare the influence of truncated and original versions of Weibull distribution on the model.

Clustering of HCV coinfections on HIV phylogeny indicates domestic and sexual transmission of HCV

BACKGROUND: HCV coinfection remains a major cause of morbidity and mortality among HIV-infected individuals and its incidence has increased dramatically in HIV-infected men who have sex with men(MSM). METHODS: Hepatitis C virus (HCV) coinfection in the Swiss HIV Cohort Study(SHCS) was studied by combining clinical data with HIV-1 pol-sequences from the SHCS Drug Resistance Database(DRDB). We inferred maximum-likelihood phylogenetic trees, determined Swiss HIV-transmission pairs as monophyletic patient pairs, and then considered the distribution of HCV on those pairs. RESULTS: Among the 9748 patients in the SHCS-DRDB with known HCV status, 2768(28%) were HCV-positive. Focusing on subtype B(7644 patients), we identified 1555 potential HIV-1 transmission pairs. There, we found that, even after controlling for transmission group, calendar year, age and sex, the odds for an HCV coinfection were increased by an odds ratio (OR) of 3.2 [95% confidence interval (CI) 2.2, 4.7) if a patient clustered with another HCV-positive case. This strong association persisted if transmission groups of intravenous drug users (IDUs), MSMs and heterosexuals (HETs) were considered separately(in all cases OR >2). Finally we found that HCV incidence was increased by a hazard ratio of 2.1 (1.1, 3.8) for individuals paired with an HCV-positive partner. CONCLUSIONS: Patients whose HIV virus is closely related to the HIV virus of HIV/HCV-coinfected patients have a higher risk for carrying or acquiring HCV themselves. This indicates the occurrence of domestic and sexual HCV transmission and allows the identification of patients with a high HCV-infection risk.

Sex-specific clines support incipient speciation in a common European mammal

Hybrid zones provide excellent opportunities to study processes and mechanisms underlying reproductive isolation and speciation. Here we investigated sex-specific clines of molecular markers in hybrid zones of morphologically cryptic yet genetically highly-diverged evolutionary lineages of the European common vole (Microtus arvalis). We analyzed the position and width of four secondary contact zones along three independent transects in the region of the Alps using maternally (mitochondrial DNA) and paternally (Y-chromosome) inherited genetic markers. Given male-biased dispersal in the common vole, a selectively neutral secondary contact would show broader paternal marker clines than maternal ones. In a selective case, for example, involving a form of Haldane’s rule, Y-chromosomal clines would not be expected to be broader than maternal markers because they are transmitted by the heterogametic sex and thus gene flow would be restricted. Consistent with the selective case, paternal clines were significantly narrower or at most equal in width to maternal clines in all contact zones. In addition, analyses using maximum likelihood cline-fitting detected a shift of paternal relative to maternal clines in three of four contact zones. These patterns suggest that processes at the contact zones in the common vole are not selectively neutral, and that partial reproductive isolation is already established between these evolutionary lineages. We conclude that hybrid zone movement, sexual selection and/or genetic incompatibilities are likely associated with an unusual unidirectional manifestation of Haldane’s rule in this common European mammal.

Detection of nonrandom association of alleles from the distribution of the number of heterozygous loci in a sample.

The distribution of the number of heterozygous loci in two randomly chosen gametes or in a random diploid zygote provides information regarding the nonrandom association of alleles among different genetic loci. Two alternative statistics may be employed for detection of nonrandom association of genes of different loci when observations are made on these distributions: observed variance of the number of heterozygous loci (s2k) and a goodness-of-fit criterion (X2) to contrast the observed distribution with that expected under the hypothesis of random association of genes. It is shown, by simulation, that s2k is statistically more efficient than X2 to detect a given extent of nonrandom association. Asymptotic normality of s2k is justified, and X2 is shown to follow a chi-square (chi 2) distribution with partial loss of degrees of freedom arising because of estimation of parameters from the marginal gene frequency data. Whenever direct evaluations of linkage disequilibrium values are possible, tests based on maximum likelihood estimators of linkage disequilibria require a smaller sample size (number of zygotes or gametes) to detect a given level of nonrandom association in comparison with that required if such tests are conducted on the basis of s2k. Summarization of multilocus genotype (or haplotype) data, into the different number of heterozygous loci classes, thus, amounts to appreciable loss of information.

Crossing borders: Ethnic minorities matter? A meta analytic examionation of the alliance-outcome relationship

Objectives: The purpose of this meta analysis was to examine the moderating impact of substance use disorder as inclusion/exclusion criterion as well as the percentage of racial/ethnic minorities on the strength of the alliance-outcome relationship in psychotherapy. It was hypothesized that the presence of a dsm axis i substance use disorders as a criterion and the presence of racial/ethnic minority as a psychosocial indicator are confounded client factors reducing the relationship between alliance and outcome. Methods: A random effects restricted maximum-likelihood estimator was used for omnibus and moderator models (k = 94). results: the presence of (a) substance use disorder and, (b) racial/ethnic minorities (overall and specific to african americans) partially moderated the alliance-outcome correlation. The percentage of substance use disorders and racial/ethnic minority status was highly correlated. Conclusions: Socio-cultural contextual variables should be considered along with dsm axis i diagnosis of substance use disorders in analyzing and interpreting mechanisms of change.

Effect of nonnormal random components on level and power in group-randomized trials

The use of group-randomized trials is particularly widespread in the evaluation of health care, educational, and screening strategies. Group-randomized trials represent a subset of a larger class of designs often labeled nested, hierarchical, or multilevel and are characterized by the randomization of intact social units or groups, rather than individuals. The application of random effects models to group-randomized trials requires the specification of fixed and random components of the model. The underlying assumption is usually that these random components are normally distributed. This research is intended to determine if the Type I error rate and power are affected when the assumption of normality for the random component representing the group effect is violated. ^ In this study, simulated data are used to examine the Type I error rate, power, bias and mean squared error of the estimates of the fixed effect and the observed intraclass correlation coefficient (ICC) when the random component representing the group effect possess distributions with non-normal characteristics, such as heavy tails or severe skewness. The simulated data are generated with various characteristics (e.g. number of schools per condition, number of students per school, and several within school ICCs) observed in most small, school-based, group-randomized trials. The analysis is carried out using SAS PROC MIXED, Version 6.12, with random effects specified in a random statement and restricted maximum likelihood (REML) estimation specified. The results from the non-normally distributed data are compared to the results obtained from the analysis of data with similar design characteristics but normally distributed random effects. ^ The results suggest that the violation of the normality assumption for the group component by a skewed or heavy-tailed distribution does not appear to influence the estimation of the fixed effect, Type I error, and power. Negative biases were detected when estimating the sample ICC and dramatically increased in magnitude as the true ICC increased. These biases were not as pronounced when the true ICC was within the range observed in most group-randomized trials (i.e. 0.00 to 0.05). The normally distributed group effect also resulted in bias ICC estimates when the true ICC was greater than 0.05. However, this may be a result of higher correlation within the data. ^

THEORETICAL STUDIES ON THE METHODS OF RECONSTRUCTING PHYLOGENETIC TREES FROM DNA SEQUENCE DATA (MOLECULAR EVOLUTION, HOMINOID EVOLUTION, COMPUTER SIMULATION)

(1) A mathematical theory for computing the probabilities of various nucleotide configurations is developed, and the probability of obtaining the correct phylogenetic tree (model tree) from sequence data is evaluated for six phylogenetic tree-making methods (UPGMA, distance Wagner method, transformed distance method, Fitch-Margoliash's method, maximum parsimony method, and compatibility method). The number of nucleotides (m*) necessary to obtain the correct tree with a probability of 95% is estimated with special reference to the human, chimpanzee, and gorilla divergence. m* is at least 4,200, but the availability of outgroup species greatly reduces m* for all methods except UPGMA. m* increases if transitions occur more frequently than transversions as in the case of mitochondrial DNA. (2) A new tree-making method called the neighbor-joining method is proposed. This method is applicable either for distance data or character state data. Computer simulation has shown that the neighbor-joining method is generally better than UPGMA, Farris' method, Li's method, and modified Farris method on recovering the true topology when distance data are used. A related method, the simultaneous partitioning method, is also discussed. (3) The maximum likelihood (ML) method for phylogeny reconstruction under the assumption of both constant and varying evolutionary rates is studied, and a new algorithm for obtaining the ML tree is presented. This method gives a tree similar to that obtained by UPGMA when constant evolutionary rate is assumed, whereas it gives a tree similar to that obtained by the maximum parsimony tree and the neighbor-joining method when varying evolutionary rate is assumed. ^

Phylogenetic Relationships of Clawed Lobster Genera (Decapoda : Nephropidae) Based on Mitochondrial 16S rRNA Gene Sequences

Approximately 350 base pairs (bp) of the mitochondrial 16S rRNA gene were used to study the phylogenetic relationships among 5 genera of the clawed lobster family Nephropidae (infraorder Astacidea), including Homarus, Homarinus, Metanephrops, Nephrops, and Nephropsis. Maximum-parsimony analysis, using a hermit crab, Pagurus pollicaris (infraorder Anomura), as an outgroup. produced a tree topology in which Homarus and Nephrops formed a well-supported clade that excluded Homarinus. The same tree topology was obtained from both neighbor-joining and maximum-likelihood analyses, Some morphological characters that appear synapomorphic for Nephrops and Metanephrops may be due to convergence rather than symplesiomorphy. The current taxonomy, therefore, does not reflect the phylogeny of this group as suggested by the molecular data. More molecular data and studies using homologous morphological characters me needed to reach a better understanding of the phylogenetic history of clawed lobsters.