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. ^

Regularized logistic regression and multi-objective variable selection for classifying MEG data

This paper addresses the question of maximizing classifier accuracy for classifying task-related mental activity from Magnetoencelophalography (MEG) data. We propose the use of different sources of information and introduce an automatic channel selection procedure. To determine an informative set of channels, our approach combines a variety of machine learning algorithms: feature subset selection methods, classifiers based on regularized logistic regression, information fusion, and multiobjective optimization based on probabilistic modeling of the search space. The experimental results show that our proposal is able to improve classification accuracy compared to approaches whose classifiers use only one type of MEG information or for which the set of channels is fixed a priori.

Petroleomics By Electrospray Ionization Ft-icr Mass Spectrometry Coupled To Partial Least Squares With Variable Selection Methods: Prediction Of The Total Acid Number Of Crude Oils.

Negative-ion mode electrospray ionization, ESI(-), with Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was coupled to a Partial Least Squares (PLS) regression and variable selection methods to estimate the total acid number (TAN) of Brazilian crude oil samples. Generally, ESI(-)-FT-ICR mass spectra present a power of resolution of ca. 500,000 and a mass accuracy less than 1 ppm, producing a data matrix containing over 5700 variables per sample. These variables correspond to heteroatom-containing species detected as deprotonated molecules, [M - H](-) ions, which are identified primarily as naphthenic acids, phenols and carbazole analog species. The TAN values for all samples ranged from 0.06 to 3.61 mg of KOH g(-1). To facilitate the spectral interpretation, three methods of variable selection were studied: variable importance in the projection (VIP), interval partial least squares (iPLS) and elimination of uninformative variables (UVE). The UVE method seems to be more appropriate for selecting important variables, reducing the dimension of the variables to 183 and producing a root mean square error of prediction of 0.32 mg of KOH g(-1). By reducing the size of the data, it was possible to relate the selected variables with their corresponding molecular formulas, thus identifying the main chemical species responsible for the TAN values.

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.

Autonomia funcional em idosos : caracterização multidimensional em idosos utentes de um centro de saúde urbano

RESUMO: Tivemos como objectivo do presente trabalho avaliar a capacidade funcional, e factores eventualmente a ela associados, numa amostra de 152 idosos ambulatórios, sem doenças agudas ou graves, utentes de um centro de saúde urbano. Cada avaliação consistiu numa entrevista, mediante um inquérito sobre capacidade funcional, morbilidade, estado mental e aspectos sociais, e no estudo da composição corporal. As perguntas referentes às variáveis estudadas foram por nós desenvolvidas e estruturadas com base em escalas internacionais validadas e de utilização comum na avaliação de idosos, excepto para as variáveis em que não encontrámos escalas com essas características. Os seus quesitos foram incluídos como perguntas e respostas estruturadas e pré-codificadas, permitindo a atribuição de uma pontuação a cada variável e a sua posterior divisão dicotómica. Aplicámos as escalas de Katz e de Lawton para a avaliação das actividades de autonomia física e instrumental da vida diária, a escala de Grimby para a avaliação da actividade física, a escala de Hamilton e o teste de Folstein para a avaliação do estado mental nas vertentes afectiva e cognitiva e a escala de Graffar para caracterizar a classe social, e perguntas sobre locomoção, autoavaliação da saúde, queixas de saúde presentes e rede social. Fizemos o registo da morbilidade segundo a International Classification of Primary Care - ICPC. A avaliação antropométrica constou da medição do peso, da altura, dos perímetros do braço, da cintura, da anca e proximal da coxa, e das pregas bicipital, tricipital, sub-escapular e supra-ilíaca. Foi também feita a estimativa da composição corporal por cálculos derivados de índices antropométricos e de bioimpedância eléctrica corporal total, o doseamento de algumas proteínas plasmáticas e a quantificação da força de preensão. Analisámos os resultados obtidos por grupos quanto ao sexo e à idade, dividida nos escalões etários 65 a 74 anos e mais do que 74 anos. Por regressão linear múltipla, foi testado o efeito do sexo e da idade sobre os valores medidos, para cada uma das variáveis e cada uma das suas pontuações parciais, sendo considerado como evidência de um efeito estaticamente significativo um valor “p” inferior a 0,05.Resumimos do seguinte modo os dados obtidos e a sua comparação com os dos estudos que seleccionámos como referência: A média de idades da amostra foi de 74 anos, sendo um terço destes do sexo masculino. Na sua maioria eram independentes em locomoção e funcionalidade, praticavam alguma actividade física, classificavam a sua saúde como razoável ou boa, apresentavam sintomatologia activa, não tinham depressão ou demência, tinham quem os acompanhasse embora cerca de metade apresentasse algum grau de isolamento, eram de baixa classe social, tinham excesso de peso, valores elevados de massa gorda, parâmetros plasmáticos proteicos compatíveis com ausência de doenças agudas ou graves e considerável força muscular de preensão. Na análise descritiva por grupos quanto ao sexo e/ou à idade, verificou-se que as mulheres e os mais idosos apresentavam maior isolamento social e os valores mais baixos de massa magra, hemoglobina e força de preensão. As mulheres tinham maior prevalência de dependência em autonomia física, depressão e valores mais baixos de transferrina. Os mais idosos apresentavam maior dependência em funcionalidade, menor actividade física, maior prevalência de demência, índice de massa corporal menos elevado, e valores mais baixos de albumina. Não se verificou prevalência de piores resultados dicotómicos nos homens nem no escalão etário menos idoso. Não teve relação com o sexo ou a idade o compromisso em autonomia instrumental, a presença de morbilidade ou a baixa classe social, assim como a não perturbação da locomoção e dos níveis de somatomedina-C. A análise comparativa com estudos multidimensionais em idosos portugueses e europeus ambulatórios revelou que a nossa amostra apresentava muitas características semelhantes às desses idosos. Assim, tinham elevada independência em locomoção, considerável independência em autonomia física e menor independência em autonomia instrumental; prática de actividade física ligeira, as mulheres dentro e os homens fora de casa; maior prevalência de morbilidade a nível dos aparelhos locomotor e cardiocirculatório, nos nossos idosos com pouca flutuação na autoavaliação de saúde; pequena prevalência de depressão e de demência; maior isolamento social nas mulheres e nas mais idosas; factores de classe social de baixo nível, diferindo apenas em relação aos idosos do norte da Europa que apresentavam elevada escolaridade e profissões mais diferenciadas; características biométricas sobreponíveis às dos idosos portugueses e às dos do sul da Europa, com tendência para o excesso de peso e proporção elevada de massa gorda; e doseamentos plasmáticos proteicos e força muscular de preensão compatíveis com ausência de doenças agudas ou crónicas graves. A comparação com os referidos estudos em relação ao risco de dependência, revelou semelhanças na associação entre dependência funcional e idade avançada, morbilidade, alteração do estado mental e isolamento social. Na amostra que estudámos não obtivemos associação entre dependência e o sexo feminino, facto que se verificou no estudo nacional de Almeida et al. e nos estudos multicêntricos europeus, ou o grau de escolaridade, como no estudo francês. Podemos concluir que, com o instrumento de avaliação que utilizámos, foi possível detectar e caracterizar perturbações numa amostra de idosos ambulatórios, a maioria funcionalmente independentes, sem alterações do estado mental, mas apresentando morbilidade activa, tendência para a obesidade, e actividade física ligeira. Nos que apresentaram alterações, estas foram mais frequentes no sexo feminino e nos indivíduos com mais de 74 anos. A escala de funcionalidade desenvolvida foi sensível aos efeitos da idade e permitiu o cálculo do risco de dependência em relação às outras variáveis estudadas, sendo mais marcante a associação com baixa actividade física, presença de queixas de saúde, demência e índice de massa corporal elevado. Consideramos que a metodologia que empregámos poderá contribuir para a avaliação de capacidades, cujo conhecimento sistemático nos idosos se impõe. ------------- ABSTRACT: The main objective of the present work was to evaluate functional capacity and related factors, in a sample of 152 ambulatory elderly, free from acute or serious disease, attending an urban health centre. Each evaluation included an interview, with a questionnaire about functional capacity, morbidity, mental health and social aspects, and the study of body composition. The questions were developed and structured in accordance with international validated scales usually applied in the evaluation of the elderly, whenever there were scales for that purpose. Their items were included as structured pre-coded questions and answers, so that each variable could have its own quotation and be dichotomised. We employed Katz and Lawton scales for basic and instrumental activities of daily living, Grimby scale for physical activity, Hamilton scale for depression, Folstein’s Mini Mental State Examination for cognitive ability and Graffar scale for social class, and questions about walking, health perception, active complaints and social network. The symptoms register was done according to the International Classification of Primary Care - ICPC. The anthropometric exam involved the determination of height and weight, arm, waist, hip and proximal thigh circumferences, and biceps, triceps, subscapular and suprailiac skinfolds. For the body composition calculation we employed equations derived from anthropometric indices, and from measurement of total body bioelectric impedance. We also measured some plasma proteins and handgrip strength. The analysis of results was done by sex and age groups, separating those with 65 to 74 years from those older than 74 years. The effects of sex and age were tested by linear multiple regression, for each variable and its components. Presented "p" values being considered statistically significative if less than 0,05. The results we obtained and their comparison with the studies we choose as reference can be summarised as follows: Mean age of the sample was 74 years and about one third were men. Most of them were independent in gait and functionality, practised some physical activity, rate their health as fair or good, had physical complaints, had not depression or dementia, had some companionship although almost half of them with stigmas of isolation, belonged to low social class, were in the range of overweight, had raised values of fat mass, plasma proteins in accordance with no acute or serious disease, and considerable handgrip strength. The analysis of groups by sex and age revealed that women and the eldest had the greater social isolation and the lowest values of free fat mass, haemoglobin and handgrip strength. Women had the higher dependence in basic activities of daily living, more depression and lower levels of transferrin. The eldest were more dependent in functionality, had greater prevalence of dementia, less physical activity, less raised body mass index and lower levels of albumin. Men alone and the age range of 65 to 74 did not show any prevalence of the worse dichotomised results. There was no relationship between sex or age and instrumental activities of daily living, morbidity or low social class, and unaffected gait or somatomedin-C levels. The comparison of results with multidimensional studies in portuguese and european ambulatory elderly showed that our sample had many similarities with theirs. They were independent in gait and activities of daily living; practiced light physical activity, women indoors and men outdoors; had greater morbidity at locomotor and cardiovascular systems, with small latitude in health evaluation; low prevalence of depression and dementia; social isolation predominantly in older women; and low social class factors, witch is only different from those of north Europe who had higher education levels and professional carriers; biometric characteristics similar to other portuguese and south Europe elders, with tendency for overweight and high proportion of fat mass; and plasma protein levels and handgrip strength in accordance with no acute or chronic serious disease. The comparison to the referred studies in relation to dependency risk, showed similarities in the association of dependency and age, morbidity,altered mental state and social isolation. We did not find association between dependency and sex, as it was found in the portuguese study of Almeida et al. and the european multicentric studies, or the education level, as in the french study. We conclude that, with the evaluation battery we employed, it was possible to detect and characterise alterations in a sample of ambulatory elderly, most of whom were functionally independent and had no alterations in mental state, but had active morbidity, tendency to obesity, and only light physical activity. Those that had some alteration, were more frequently women and the eldest. The functionality scale we developed showed to be sensitive to age effects and suitable for the calculation of risk of dependency, being more important the association with low physical activity, active complaints, dementia and high body mass index. We consider that the methodology we applied can contribute to the evaluation of capabilities that should be systematically sought for in the elderly.

Predicting SO2 pollution incidents by means of additive models with optimum variable selection

The aim of this paper is to predict time series of SO2 concentrations emitted by coal-fired power stations in order to estimate in advance emission episodes and analyze the influence of some meteorological variables in the prediction. An emission episode is said to occur when the series of bi-hourly means of SO2 is greater than a specific level. For coal-fired power stations it is essential to predict emission epi- sodes sufficiently in advance so appropriate preventive measures can be taken. We proposed a meth- odology to predict SO2 emission episodes based on using an additive model and an algorithm for variable selection. The methodology was applied to the estimation of SO2 emissions registered in sampling lo- cations near a coal-fired power station located in Northern Spain. The results obtained indicate a good performance of the model considering only two terms of the time series and that the inclusion of the meteorological variables in the model is not significant.

Stochastic Search Variable Selection in Vector Error Correction Models with an Application to a Model of the UK Macroeconomy

This paper develops methods for Stochastic Search Variable Selection (currently popular with regression and Vector Autoregressive models) for Vector Error Correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model.

Estimation of lean meat content in pig carcasses using X-ray Computed Tomography and PLS regression

Lean meat percentage (LMP) is an important carcass quality parameter. The aim of this work is to obtain a calibration equation for the Computed Tomography (CT) scans with the Partial Least Square Regression (PLS) technique in order to predict the LMP of the carcass and the different cuts and to study and compare two different methodologies of the selection of the variables (Variable Importance for Projection — VIP- and Stepwise) to be included in the prediction equation. The error of prediction with cross-validation (RMSEPCV) of the LMP obtained with PLS and selection based on VIP value was 0.82% and for stepwise selection it was 0.83%. The prediction of the LMP scanning only the ham had a RMSEPCV of 0.97% and if the ham and the loin were scanned the RMSEPCV was 0.90%. Results indicate that for CT data both VIP and stepwise selection are good methods. Moreover the scanning of only the ham allowed us to obtain a good prediction of the LMP of the whole carcass.

The use of classification and regression trees to predict the likelihood of seasonal influenza.

Background Individual signs and symptoms are of limited value for the diagnosis of influenza. Objective To develop a decision tree for the diagnosis of influenza based on a classification and regression tree (CART) analysis. Methods Data from two previous similar cohort studies were assembled into a single dataset. The data were randomly divided into a development set (70%) and a validation set (30%). We used CART analysis to develop three models that maximize the number of patients who do not require diagnostic testing prior to treatment decisions. The validation set was used to evaluate overfitting of the model to the training set. Results Model 1 has seven terminal nodes based on temperature, the onset of symptoms and the presence of chills, cough and myalgia. Model 2 was a simpler tree with only two splits based on temperature and the presence of chills. Model 3 was developed with temperature as a dichotomous variable (≥38°C) and had only two splits based on the presence of fever and myalgia. The area under the receiver operating characteristic curves (AUROCC) for the development and validation sets, respectively, were 0.82 and 0.80 for Model 1, 0.75 and 0.76 for Model 2 and 0.76 and 0.77 for Model 3. Model 2 classified 67% of patients in the validation group into a high- or low-risk group compared with only 38% for Model 1 and 54% for Model 3. Conclusions A simple decision tree (Model 2) classified two-thirds of patients as low or high risk and had an AUROCC of 0.76. After further validation in an independent population, this CART model could support clinical decision making regarding influenza, with low-risk patients requiring no further evaluation for influenza and high-risk patients being candidates for empiric symptomatic or drug therapy.

Assessing the Relationship between the Baseline Value of a Continuous Variable and Subsequent Change over Time

Analyzing the relationship between the baseline value and subsequent change of a continuous variable is a frequent matter of inquiry in cohort studies. These analyses are surprisingly complex, particularly if only two waves of data are available. It is unclear for non-biostatisticians where the complexity of this analysis lies and which statistical method is adequate.With the help of simulated longitudinal data of body mass index in children,we review statistical methods for the analysis of the association between the baseline value and subsequent change, assuming linear growth with time. Key issues in such analyses are mathematical coupling, measurement error, variability of change between individuals, and regression to the mean. Ideally, it is better to rely on multiple repeated measurements at different times and a linear random effects model is a standard approach if more than two waves of data are available. If only two waves of data are available, our simulations show that Blomqvist's method - which consists in adjusting for measurement error variance the estimated regression coefficient of observed change on baseline value - provides accurate estimates. The adequacy of the methods to assess the relationship between the baseline value and subsequent change depends on the number of data waves, the availability of information on measurement error, and the variability of change between individuals.

Instrumental leadership: Measurement and extension of transformational-transactional leadership theory.

Leaders must scan the internal and external environment, chart strategic and task objectives, and provide performance feedback. These instrumental leadership (IL) functions go beyond the motivational and quid-pro quo leader behaviors that comprise the full-range-transformational, transactional, and laissez faire-leadership model. In four studies we examined the construct validity of IL. We found evidence for a four-factor IL model that was highly prototypical of good leadership. IL predicted top-level leader emergence controlling for the full-range factors, initiating structure, and consideration. It also explained unique variance in outcomes beyond the full-range factors; the effects of transformational leadership were vastly overstated when IL was omitted from the model. We discuss the importance of a "fuller full-range" leadership theory for theory and practice. We also showcase our methodological contributions regarding corrections for common method variance (i.e., endogeneity) bias using two-stage least squares (2SLS) regression and Monte Carlo split-sample designs.

Characteristics of eyes with secondary loss of visual acuity receiving variable dosing ranibizumab for neovascular age-related macular degeneration.

PURPOSE: The aim of this work is to investigate the characteristics of eyes failing to maintain visual acuity (VA) receiving variable dosing ranibizumab for neovascular age-related macular degeneration (nAMD) after three initial loading doses. METHODS: A consecutive series of patients with nAMD, who, after three loading doses of intravitreal ranibizumab (0.5 mg each), were re-treated for fluid seen on optical coherence tomography. After exclusion of eyes with previous treatment, follow-up less than 12 months, or missed visits, 99 patients were included in the analysis. The influence of baseline characteristics, initial VA response, and central retinal thickness (CRT) fluctuations on the VA stability from month 3 to month 24 were analyzed using subgroups and multiple regression analyses. RESULTS: Mean follow-up duration was 21.3 months (range 12-40 months, 32 patients followed-up for ≥24 months). Secondary loss of VA (loss of five letters or more) after month 3 was seen in 30 patients (mean VA improvement from baseline +5.8 letters at month 3, mean loss from baseline -5.3 letters at month 12 and -9.7 at final visit up to month 24), while 69 patients maintained vision (mean gain +8.9 letters at month 3, +10.4 letters at month 12, and +12.8 letters at final visit up to month 24). Secondary loss of VA was associated with the presence of pigment epithelial detachment (PED) at baseline (p 0.01), but not with baseline fibrosis/atrophy/hemorrhage, CRT fluctuations, or initial VA response. Chart analysis revealed additional individual explanations for the secondary loss of VA, including retinal pigment epithelial tears, progressive fibrosis, and atrophy. CONCLUSIONS: Tissue damage due to degeneration of PED, retinal pigment epithelial tears, progressive fibrosis, progressive atrophy, or massive hemorrhage, appears to be relevant in causing secondary loss of VA despite vascular endothelial growth factor suppression. PED at baseline may represent a risk factor.

An alternative method for dating unknown tephras based on a segmented regression model

In CoDaWork’05, we presented an application of discriminant function analysis (DFA) to 4 differentcompositional datasets and modelled the first canonical variable using a segmented regression modelsolely based on an observation about the scatter plots. In this paper, multiple linear regressions areapplied to different datasets to confirm the validity of our proposed model. In addition to dating theunknown tephras by calibration as discussed previously, another method of mapping the unknown tephrasinto samples of the reference set or missing samples in between consecutive reference samples isproposed. The application of these methodologies is demonstrated with both simulated and real datasets.This new proposed methodology provides an alternative, more acceptable approach for geologists as theirfocus is on mapping the unknown tephra with relevant eruptive events rather than estimating the age ofunknown tephra.Kew words: Tephrochronology; Segmented regression

Life-Cycle Effects on Household Expenditures: A Latent-Variable Approach

Using data from the Spanish household budget survey, we investigate life- cycle effects on several product expenditures. A latent-variable model approach is adopted to evaluate the impact of income on expenditures, controlling for the number of members in the family. Two latent factors underlying repeated measures of monetary and non-monetary income are used as explanatory variables in the expenditure regression equations, thus avoiding possible bias associated to the measurement error in income. The proposed methodology also takes care of the case in which product expenditures exhibit a pattern of infrequent purchases. Multiple-group analysis is used to assess the variation of key parameters of the model across various household life-cycle typologies. The analysis discloses significant life-cycle effects on the mean levels of expenditures; it also detects significant life-cycle effects on the way expenditures are affected by income and family size. Asymptotic robust methods are used to account for possible non-normality of the data.