Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

Improved Regression Estimation of a Multivariate Relationship with Population Data on the Bivariate Relationship

Regression coefficients specify the partial effect of a regressor on the dependent variable. Sometimes the bivariate or limited multivariate relationship of that regressor variable with the dependent variable is known from population-level data. We show here that such population- level data can be used to reduce variance and bias about estimates of those regression coefficients from sample survey data. The method of constrained MLE is used to achieve these improvements. Its statistical properties are first described. The method constrains the weighted sum of all the covariate-specific associations (partial effects) of the regressors on the dependent variable to equal the overall association of one or more regressors, where the latter is known exactly from the population data. We refer to those regressors whose bivariate or limited multivariate relationships with the dependent variable are constrained by population data as being ‘‘directly constrained.’’ Our study investigates the improvements in the estimation of directly constrained variables as well as the improvements in the estimation of other regressor variables that may be correlated with the directly constrained variables, and thus ‘‘indirectly constrained’’ by the population data. The example application is to the marital fertility of black versus white women. The difference between white and black women’s rates of marital fertility, available from population-level data, gives the overall association of race with fertility. We show that the constrained MLE technique both provides a far more powerful statistical test of the partial effect of being black and purges the test of a bias that would otherwise distort the estimated magnitude of this effect. We find only trivial reductions, however, in the standard errors of the parameters for indirectly constrained regressors.

Factors Associated With The Age Of The Onset Of Diabetes In Women Aged 50 years Or More: A Population-based Study.

Investigate factors associated with the onset of diabetes in women aged more than 49 years. Cross-sectional, population-based study using self-reports with 622 women. The dependent variable was the age of occurrence of diabetes using the life table method. Cox multiple regression models were adjusted to analyse the onset of diabetes according to predictor variables. Sociodemographic, clinical and behavioural factors were evaluated. Of the 622 women interviewed, 22.7% had diabetes. The mean age at onset was 56 years. The factors associated with the age of occurrence of diabetes were self-rated health (very good, good) (coefficient=-0.792; SE of the coefficient=0.215; p=0.0001), more than two individuals living in the household (coefficient=0.656, SE of the coefficient=0.223; p=0.003), and body mass index (BMI) (kg/m(2)) at 20-30 years of age (coefficient= 0.056, SE of the coefficient=0.023; p=0.014). Self-rated health considered good or very good was associated with a higher rate of survival without diabetes. Sharing a home with two or more other people and a weight increase at 20-30 years of age was associated with the onset of type 2 diabetes.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

Multicollinearity and financial constraint in investment decisions: a Bayesian generalized ridge regression

This paper addresses the investment decisions considering the presence of financial constraints of 373 large Brazilian firms from 1997 to 2004, using panel data. A Bayesian econometric model was used considering ridge regression for multicollinearity problems among the variables in the model. Prior distributions are assumed for the parameters, classifying the model into random or fixed effects. We used a Bayesian approach to estimate the parameters, considering normal and Student t distributions for the error and assumed that the initial values for the lagged dependent variable are not fixed, but generated by a random process. The recursive predictive density criterion was used for model comparisons. Twenty models were tested and the results indicated that multicollinearity does influence the value of the estimated parameters. Controlling for capital intensity, financial constraints are found to be more important for capital-intensive firms, probably due to their lower profitability indexes, higher fixed costs and higher degree of property diversification.

How adult specialists deal with the principles of a successful transition.

OBJECTIVES: To evaluate whether adult specialists comply with the basic principles for a successful transition of adolescents with chronic disorders, and to determine whether the characteristics of the adult specialists have an influence on applying these principles. METHODS: Out of 299 adult specialists in four French-speaking Swiss cantons, 209 (70%) answered a paper-and-pencil mailed questionnaire between May and July 2007. Only those having received the transfer of at least one adolescent in the previous 2 years (N=102) were included in the analysis. We analyzed four dependent variables: discussing common concerns of adolescent patients, seeing the patient alone, having a transition protocol, and having a previous contact with the pediatric specialist. A logistic regression was performed for each dependent variable controlling for the physicians' characteristics (number of transfers, age, gender, workplace, and perceived experience). RESULTS: Fifty-four percent of the physicians did not spend time alone with their patients, and sensitive issues such as sexuality or substance use were not widely discussed with their young patients. Most respondents (59%) did not have an established protocol, and 54% did not have any contact with the pediatric specialist. In the multivariate analyses, the adult specialists' characteristics had little impact. CONCLUSIONS: For many adolescents with chronic disorders the transition from pediatric to adult healthcare seems to be limited to a simple transfer, often lacking adequate communication between physicians. Applying simple but basic principles such as a good coordination between providers would probably improve the quality of healthcare of adolescents with chronic illness.

Blood pressure modifies the association between serum adiponectin and uric acid, in a sex-dependent manner

Purpose: Plasma adiponectin and serum uric acid (SUA) levels are negatively correlated. To better understand the possible mechanisms linking adiponectin and uric acid, we analyzed whether the association between adiponectin and SUA differed by hypertension status (or blood pressure level) and by sex. Methods and materials: We analyzed data from the populationbased CoLaus study (Switzerland). Fasting plasma adiponectin levels were assessed by ELISA and SUA by uricase-PAP. Blood pressure (BP) was measured using a validated automated device and hypertension was defined as having office BP 140/90 mm Hg or being on current antihypertensive treatment. Results: In the 2897 men and 3181 women, aged 35-74, BMI (mean ± SD) was 26.6 ± 4.0 and 25.1 ± 4.8 Kg/m2, systolic blood pressure (SBP) was 132.2 ± 16.6 and 124.8 ± 18.3 mm Hg, median (interquartile range) plasma adiponectin was 6.2 (4.1-9.2) and 10.6 (6.9-15.4) mg/dL, and hypertension prevalence was 42.0% and 30.2%, respectively. The age- and BMI- adjusted partial correlation coefficients between log-adiponectin and SUA were 0.09 and 0.06 in normotensive men and women (P <0.01), and 0.004 (P = 0.88) and 0.15 (P <0.001) in hypertensive men and women, respectively. In median regression adjusted for BMI, insulin, smoking, alcohol consumption, menopausal status and HDL-cholesterol, there was a significant three-way interaction between SUA, SBP and sex for their effect on adiponectin (dependent variable, P = 0.005), as well as interactions between SBP and sex (P = 0.014) and between SUA and sex (P = 0.033). Conclusion: Plasma adiponectin and SUA are negatively associated, independently of BMI and insulin, in a population-based study in Caucasians. However, BP modifies this inverse relationship, as it was significant mainly in women with elevated BP. This observation suggests that the link between adiponectin and SUA may be mediated by sex hormones and the hypertension status.

Tests of Joint Hypotheses for Time Series Regression with a Unit Root

This Paper Studies Tests of Joint Hypotheses in Time Series Regression with a Unit Root in Which Weakly Dependent and Heterogeneously Distributed Innovations Are Allowed. We Consider Two Types of Regression: One with a Constant and Lagged Dependent Variable, and the Other with a Trend Added. the Statistics Studied Are the Regression \"F-Test\" Originally Analysed by Dickey and Fuller (1981) in a Less General Framework. the Limiting Distributions Are Found Using Functinal Central Limit Theory. New Test Statistics Are Proposed Which Require Only Already Tabulated Critical Values But Which Are Valid in a Quite General Framework (Including Finite Order Arma Models Generated by Gaussian Errors). This Study Extends the Results on Single Coefficients Derived in Phillips (1986A) and Phillips and Perron (1986).

Cleanliness versus cow comfort – an insolvable problem?

Cubicle should provide good resting comfort as well as clean udders. Dairy cows in cubicle houses often face a restrictive environment with regard to resting behaviour, whereas cleanliness may still be impaired. This study aimed to determine reliable behavioural measures regarding resting comfort applicable in on-farm welfare assessments. Furthermore, relationships between cubicle design, cow sizes, management factors and udder cleanliness (namely teats and teat tips) were investigated. Altogether 15 resting measures were examined in terms of feasibility, inter-observer reliability (IOR) and consistency of results per farm over time. They were recorded during three farm visits on farms in Germany and Austria with cubicle, deep litter and tie stall systems. Seven measures occurred to infrequently to allow reliable recording within a limited observation time. IOR was generally acceptable to excellent except for 'collisions during lying down', which only showed good IOR after improvement of the definition. Only three measures were acceptably repeatable over time: 'duration of lying down', 'percentage of collisions during lying down' and 'percentage of cows lying partly or completely outside lying area'. These measures were evaluated as suitable animal based welfare measures regarding resting behaviour in the framework of an on-farm welfare assessment protocol. The second part of the thesis comprises a cross-sectional study on resting comfort and cow cleanliness including 23 Holstein Friesian dairy herds with very low within-farm variation in cubicle measures. Height at withers, shoulder width and diagonal body length were measured in 79-100 % of the cows (herd size 30 to115 cows). Based on the 25 % largest animals, compliance with recommendations for cubicle measures was calculated. Cleanliness of different body parts, the udder, teats and teat tips was assessed for each cow in the herd prior to morning milking. No significant correlation was found between udder soiling and teat or teat tip soiling on herd level. The final model of a stepwise regression regarding the percentage of dirty teats per farm explained 58.5 % the variance and contained four factors. Teat dipping after milking which might be associated with an overall clean and accurate management style, deep bedded cubicles, increasing cubicle maintenance times and decreasing compliance concerning total cubicle length predicted lower teat soiling. The final model concerning teat tip soiling explained 46.0 % of the variance and contained three factors. Increasing litter height in the rear part of the cubicle and increased alley soiling which is difficult to explain, predicted for less soiled teat tips, whereas increasing compliance concerning resting length was associated with higher percentages of dirty teat tips. The dependent variable ‘duration of lying down’ was analysed using again stepwise regression. The final model explained 54.8 % of the total variance. Lying down duration was significantly shorter in deep bedded cubicles. Further explanatory though not significant factors in the model were neck-rail height, deep bedding or comfort mattresses versus concrete floor or rubber mats and clearance height of side partitions. In the attempt to create a more comprehensive lying down measure, another analysis was carried out with percentage of ‘impaired lying down’ (i.e. events exceeding 6.3 seconds, with collisions or being interrupted) as dependent variable. The explanatory value of this final model was 41.3 %. An increase in partition length, in compliance concerning cubicle width and the presence of straw within bedding predicted a lower proportion of impaired lying down. The effect of partition length is difficult to interpret, but partition length and height were positively correlated on the study farms, possibly leading to a bigger zone of clear space for pelvis freedom. No associations could be found between impaired lying down and teat or teat tip soiling. Altogether, in agreement with earlier studies it was found that cubicle dimensions in practice are often inadequate with regard to the body dimensions of the cows, leading to high proportions of impaired lying down behaviour, whereas teat cleanliness is still unsatisfactory. Connections between cleanliness and cow comfort are far from simplistic. Especially the relationship between cubicle characteristics and lying down behaviour apparently is very complex, so that it is difficult to identify single influential factors that are valid for all farm situations. However, based on the results of the present study the use of deep bedded cubicles can be recommended as well as improved management with special regard to cubicle and litter maintenance in order to achieve both better resting comfort and teat cleanliness.

A study of the effect of heat source location in a ventilated room using multiple regression analysis

Multiple regression analysis is a statistical technique which allows to predict a dependent variable from m ore than one independent variable and also to determine influential independent variables. Using experimental data, in this study the multiple regression analysis is applied to predict the room mean velocity and determine the most influencing parameters on the velocity. More than 120 experiments for four different heat source locations were carried out in a test chamber with a high level wall mounted air supply terminal at air change rates 3-6 ach. The influence of the environmental parameters such as supply air momentum, room heat load, Archimedes number and local temperature ratio, were examined by two methods: a simple regression analysis incorporated into scatter matrix plots and multiple stepwise regression analysis. It is concluded that, when a heat source is located along the jet centre line, the supply momentum mainly influences the room mean velocity regardless of the plume strength. However, when the heat source is located outside the jet region, the local temperature ratio (the inverse of the local heat removal effectiveness) is a major influencing parameter.

Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included

An Analysis of the Telecommunications Business in China by Linear Regression

In this paper, we study the influence of the National Telecom Business Volume by the data in 2008 that have been published in China Statistical Yearbook of Statistics. We illustrate the procedure of modeling “National Telecom Business Volume” on the following eight variables, GDP, Consumption Levels, Retail Sales of Social Consumer Goods Total Renovation Investment, the Local Telephone Exchange Capacity, Mobile Telephone Exchange Capacity, Mobile Phone End Users, and the Local Telephone End Users. The testing of heteroscedasticity and multicollinearity for model evaluation is included. We also consider AIC and BIC criterion to select independent variables, and conclude the result of the factors which are the optimal regression model for the amount of telecommunications business and the relation between independent variables and dependent variable. Based on the final results, we propose several recommendations about how to improve telecommunication services and promote the economic development.

Multicollinearity and financial constraint in investment decisions: a bayesian generalized ridge regression

This paper addresses the investment decisions considering the presence of financial constraints of 373 large Brazilian firms from 1997 to 2004, using panel data. A Bayesian econometric model was used considering ridge regression for multicollinearity problems among the variables in the model. Prior distributions are assumed for the parameters, classifying the model into random or fixed effects. We used a Bayesian approach to estimate the parameters, considering normal and Student t distributions for the error and assumed that the initial values for the lagged dependent variable are not fixed, but generated by a random process. The recursive predictive density criterion was used for model comparisons. Twenty models were tested and the results indicated that multicollinearity does influence the value of the estimated parameters. Controlling for capital intensity, financial constraints are found to be more important for capital-intensive firms, probably due to their lower profitability indexes, higher fixed costs and higher degree of property diversification.

Shifting the focus: Addressing breast cancer disparities at the health care organization level

The purpose of this study was to understand the scope of breast cancer disparities within the Texas Medical Center. The goal was to increase the awareness of breast cancer disparities at the health care organization level, and to foster the development of organizational interventions to reduce breast cancer disparities. The study seeks to answer the following questions: 1. Are hospitals in the Texas Medical Center implementing interventions to reduce breast cancer disparities? 2. What are their interventions for reducing the effects of non clinical factors on breast cancer treatment disparities? 3. What are their measures for monitoring, continuously improving, and evaluating the success of their interventions? ^ This research project was designed as a mixed methods case study. Quantitative breast cancer data for the years 2000-2009 was obtained from the Texas Cancer Registry (TCR). Qualitative data collection and analysis was done by conducting a total of 20 semi-structured interviews of administrators, physicians and nurses at five hospitals (A, B, C, D and E) in the Texas Medical Center (TMC). For quantitative analysis, the study was limited to early stage breast cancer patients: local and regional. The dependent variable was receipt of standard treatment: Surgery (Yes/No), BCS vs Mastectomy, Chemotherapy (Yes/No) and Radiation after BCS (Yes/No). The main independent variable was race: non-Hispanic White (NHW) , non-Hispanic Black (NHB), and Hispanic. Other covariates included age at diagnosis, diagnosis date, percent poverty, grade, stage, and regional nodes. Multivariate logistic regression was used to test the adjusted association between receipt of standard care and race. Qualitative data was analyzed with the Atlas.ti7 software (ATLAS.ti GmbH, Berlin). ^ Though there were significant differences by race for all dependent variables when the data was analyzed as a single group of all hospitals; at the level of the individual hospitals the results were not consistent by race/ethnicity across all dependent variables for hospitals A, B, and E. There were no racial differences in adjusted analysis for receipt of chemotherapy for the individual hospitals of interest in this study. For hospitals C and D, no racial disparities in treatment was observed in adjusted multivariable analysis. All organizations in this study were aware of the body of research which shows that there are disparities in breast cancer outcomes for patient population groups. However, qualitative data analysis found that there were differences in interest among hospitals in addressing breast cancer disparities in their patient population groups. Some organizations were actively implementing directed measures to reduce the breast cancer disparity gap in outcomes for patients, and others were not. Despite the differences in levels of interest, quantitative data analysis showed that organizations in the Texas Medical Center were making progress in reducing the burden of breast cancer disparities in the patient populations being served.^

Probing three-way interactions in moderated multiple regression:Development and application of a slope difference test

Researchers often use 3-way interactions in moderated multiple regression analysis to test the joint effect of 3 independent variables on a dependent variable. However, further probing of significant interaction terms varies considerably and is sometimes error prone. The authors developed a significance test for slope differences in 3-way interactions and illustrate its importance for testing psychological hypotheses. Monte Carlo simulations revealed that sample size, magnitude of the slope difference, and data reliability affected test power. Application of the test to published data yielded detection of some slope differences that were undetected by alternative probing techniques and led to changes of results and conclusions. The authors conclude by discussing the test's applicability for psychological research. Copyright 2006 by the American Psychological Association.