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.

Delays in childhood immunization in a conflict area: a study from Sierra Leone during civil war

ABSTRACT: BACKGROUND: Sierra Leone has undergone a decade of civil war from 1991 to 2001. From this period few data on immunization coverage are available, and conflict-related delays in immunization according to the Expanded Programme on Immunization (EPI) schedule have not been investigated. We aimed to study delays in childhood immunization in the context of civil war in a Sierra Leonean community. METHODS: We conducted an immunization survey in Kissy Mess-Mess in the Greater Freetown area in 1998/99 using a two-stage sampling method. Based on immunization cards and verbal history we collected data on immunization for tuberculosis, diphtheria, tetanus, pertussis, polio, and measles by age group (0-8/9-11/12-23/24-35 months). We studied differences between age groups and explored temporal associations with war-related hostilities taking place in the community. RESULTS: We included 286 children who received 1690 vaccine doses; card retention was 87%. In 243 children (85%, 95% confidence interval (CI): 80-89%) immunization was up-to-date. In 161 of these children (56%, 95%CI: 50-62%) full age-appropriate immunization was achieved; in 82 (29%, 95%CI: 24-34%) immunization was not appropriate for age. In the remaining 43 children immunization was partial in 37 (13%, 95%CI: 9-17) and absent in 6 (2%, 95%CI: 1-5). Immunization status varied across age groups. In children aged 9-11 months the proportion with age-inappropriate (delayed) immunization was higher than in other age groups suggesting an association with war-related hostilities in the community. CONCLUSION: Only about half of children under three years received full age-appropriate immunization. In children born during a period of increased hostilities, immunization was mostly inappropriate for age, but recommended immunizations were not completely abandoned. Missing or delayed immunization represents an additional threat to the health of children living in conflict areas.

Comparison of magnetic properties and petrography between dykes and lava flows from La Cienega, New Mexico and Thunder Bay area, Canada

Data on the evolution of geomagnetic paleointensity are crucial for understanding the geodynamo and Earth’s thermal history. Although basaltic flows are preferred for paleointensity experiments, quickly cooled mafic dykes have also been used. However, the paleointensity values obtained from the dykes are systematically lower than those from lava flows. This bias may originate from the difference in cooling histories and resultant magnetic mineralogies of extrusive and intrusive rocks. To explore this hypothesis, the magnetic mineralogy of two feeder dyke-lave flow systems, from Thunder Bay (Canada) and La Cienega (New-Mexico), has been studied using magnetic and microscopy methods. Within each system, the flow and dyke show different stages of deuteric oxidation of titanomagnetite, but the oxidation stages also differ between the two systems. It is concluded that the tested hypothesis is viable, but the relationships between the magnetic and mineralogical properties of flows and dykes are complex and need a further investigation.

Evolution of the Southern Kenya Rift from Miocene to present with a focus on the Magadi area

The Kenya (a.k.a., Gregory) Rift is a geologically active area located within the eastern branch of the larger East African Rift System (EARS). The study area is located in the southern Kenya Rift between 1° South and the Kenya-Tanzania border (covering approximately 1.5 square degrees, semi-centered on Lake Magadi) and is predominantly filled with extrusive igneous rocks (mostly basalts, phonolites and trachytes) of Miocene age or younger. Sediments are thin, less than 1.5Ma, and are confined to small grabens. The EARS can serve both as an analogue for ancient continental rifting and as a modern laboratory to observe the geologic processes responsible for rifting. This study demonstrates that vintage (as in older, quality maps published by the Kenya Geological Survey, that may be outdated based on newer findings) quarter-degree maps can be successfully combined with recently published data, and used to interpret satellite (mainly Landsat 7) images to produce versatile, updated digital maps. The study area has been remapped using this procedure and although it covers a large area, the mapping retains a quadrangle level of detail. Additionally, all geologic mapping elements (formations, faults, etc.) have been correlated across older map boundaries so that geologic units don't end artificially at degree boundaries within the study area. These elements have also been saved as individual digital files to facilitate future analysis. A series of maps showing the evolution of the southern Kenya rift from the Miocene to the present was created by combining the updated geologic map with age dates for geologic formations and fault displacements. Over 200 age dates covering the entire length of the Kenya Rift have been compiled for this study, and 6 paleo-maps were constructed to demonstrate the evolution of the area, starting with the eruption of the Kishalduga and Lisudwa melanephelinites onto the metamorphic basement around 15Ma. These eruptions occurred before the initial rift faulting and were followed by a massive eruption of phonolites between 13-10 Ma that covered most of the Kenya dome. This was followed by a period of relative quiescence, until the initial faulting defined the western boundary of the rift around 7Ma. The resulting graben was asymmetrical until corresponding faults to the east developed around 3Ma. The rift valley was flooded by basalts and trachytes between 3Ma and 700ka, after which the volcanic activity slowed to a near halt. Since 700ka most of the deposition has been comprised of sediments, mainly from lakes occupying the various basins in the area. The main results of this study are, in addition to a detailed interpretation of the rift development, a new geologic map that correlates dozens of formations across old map boundaries and a compilation of over 300 age dates. Specific products include paleomaps, tables of fault timing and displacement, and volume estimates of volcanic formations. The study concludes with a generalization of the present environment at Magadi including discussions of lagoon chemistry, mantle gases in relation to the trona deposit, and biology of the hot springs. Several biologic samples were collected during the 2006 field season in an attempt to characterize the organisms that are commonly seen in the present Lake Magadi environment. Samples were selected to represent the different, distinctive forms that are found in the hotsprings. Each sample had it own distinctive growth habit, and analysis showed that each was formed by a different cyanobacterial. Actual algae was rare in the collected samples, and represented by a few scattered diatoms.

Amphibian Biodiversity Survey - Wetland Area Southwest of Montana Tech

The primary goal of this project was to launch a pilot population study in the spring-fed wetland area southwest of Montana Tech to establish baseline data on density, distribution, abundance, and diversity of amphibians in the area. The current confirmed species at the select site is the Columbia spotted frog (Rana luteiventris). Based on preliminary habitat assessment and existing literature, other species possibilities included the long-toed salamander (Ambrystoma macrodactylum) boreal chorus frog (Pseudacris maculata), the Rocky Mountain tailed frog (Ascaphus montanus), and the leopard frog (Rana pipiens), (Werner et al. 2004) though the latter species is considered unlikely based on the specie’s declining status (Werner 2003; Werner et al. 2004). The project’s secondary goal was to collect basic habitat and environmental data: vegetation, precipitation, temperature. The third goal was to explore correlations between species prevalence and environmental data to expand the scientific understanding of population dynamics in the field of amphibian studies (see: Ferner, 2007; Dodd, 2010).

The Geology of the Southern Central Portion of the Morrison Cave Area.

Morrison Cave is located about 50 miles southeast of Butte, Montana. It was named after the man who discovered it. Later it was taken over by the State and renamed Morrison Cave State Park. Recently the government with the aid of the Civilian Conservation Corps has built a new road to the cave and has made the interior more accessible. The name of the cave is now Lewis and Clark Cavern National Monument.

Ground Water in the Lake Basin Field and Adjacent Area

This thesis consists of studying the stratigraphic and structural features of the Lake Basin Field and an adjacent area with special emphasis upon the ground water conditions present.

A Geological Report on an Area Five Miles Southeast of Renova, Montana, and on an Area Seven Miles South of Jefferson Island, Montana

This trip was conducted to give those students working for their respective degrees an excellent opportunity to work under actual field conditions. A total of three weeks was taken to complete the required work. Two weeks were spent in the field gathering data, and making maps, and the last week was spent in the drawing room at the college preparing the final map.

Report on Pole Canyon Area and Area Three Miles Southeast of Jefferson Island

The primary purpose of the trip was to acquaint the students with some of the problems that occur in the field, and also how to make geologic maps of sections, outcrops, faults, and other geologic features of the earths surface.

Stratigraphic Studies of the Ordovician and Devonian Formations Throughout the Northwest Plains Area

As yet the knowledge of Ordovician and Devonian physiography in this vast northwest region remains almost a complete secret. Very little, in any, work has been done along this line with the exception of those areas where the various formations outcrop.

Geologic Field Mapping in an Area Eight Miles North of Three Forks, Montana

The Three Forks are includes parts of Jefferson, Madison, Broadwater Pond Gallatin counties, Montana. Sedimentary formations lie at the surface nearly everywhere in the area, and the rugged surface topography has been developed through the folding and tilting of these formations and their dif­ferential erosion.

The Geology of the Limespur-Sappington Area

The area to be surveyed was divided up into sections add each crew of three or four members was assigned one of these sections. The first two days were spent in studying and mapping the geologic section in the South Boulder Canyon where we obtained practice in alidade surveying, brunton, pacing, and auto traverse.

Geology of Upper Bear Gulch and Dry Boulder Creek Area Madison County, Montana

Potential gold mines lie high among the rugged peaks of the Tobacco Root Mountains of southwestern Montana. This is a region where little geologic work has been done, though extensive mine operations have been carried on, and valuable ore has been shipped.

Geology of the Lost Creek-Modesty Creek Area Deerlodge County, Montana

In 1915 the United States Geological Survey published a folio by Calkins and Emmons on the geology of the Philipsburg Quadrangle, which ad­joins the area now under study to the west. Geology of this portion of Montana had not been mapped previously; consequently the purpose of this thesis is to make a geological reconnais­sance of the stratigraphy and structure of the area.

Geology and Ore Deposits of the Salt Chuck-Rush and Brown Mine Area Prince of Wales Island, Alaska

The Salt Chuck, Rush and Brown, and adjacent mines and claims form an area of approximately 15 square miles near the head of Kasaan Bay about 10 miles northwest of the village of Kasaan on Prince of Wales Island in southeastern Alaska. It is an area of moderate relief in which the hills rise from the water’s edge to heights of some 500 feet. Most of the area is covered with dense vegetation and muskeg.