Multivariate Multiple Regression Models Research Articles

Multivariate analysis of correlates of children nutritional status in Harar region, Ethiopia

<p class="abstract"><strong>Background:</strong> Malnutrition is defined as deficiencies, excesses or imbalances in a person’s intake of energy and/or nutrients. In Ethiopia malnutrition is one of the most serious health and welfare problems among infants and young children. Malnutrition among children under five years of age is a chronic problem in most regions of Ethiopia, including the Harari region. The main objective of this study was to assess risk factors attributed to nutritional status of children in Harari region.</p><p class="abstract"><strong>Methods:</strong> Data was obtained from Ethiopian Demographic Health Survey, 2016. Different factors were considered as determinants of nutritional status of a child. The study used Multivariate Multiple Linear Regression model to identify significant correlates of children nutritional status. </p><p class="abstract"><strong>Results:</strong> The descriptive statistics in the study revealed that out of a total of 233 children included in the study 21% are underweighted, 19.3% are stunted and 11.2% are wasted in the study area. From Multivariate multiple linear regression, breast feeding factors, health status of child and child vaccination status significantly affect nutritional status of the under five children.</p><p class="abstract"><strong>Conclusions:</strong> The factor analyses conducted in this study indicated that only two factors (instead of 5 original observed variables or items) were sufficient to explain 78.605% of the total variation in PCFA of observed items related to child nutritional status. Factors duration of breast feeding, birth order of a child, current age of child is statistically significant in affecting child malnutrition.</p>

43 State Mental Energy Influences Posture During Vision-Occluded States

Abstract Background Fatigue has been postulated to influence postural control, which may lead to an increased risk for falling among older adults.1 Mental and physical energy and fatigue have recently been reported to be four distinct mood states.2,3 Thus, to test Grobe’s1 theory of the influence of fatigue on postural control, we must examine all four mood states. Objective This study examined the influence of mental and physical energy and fatigue on postural control. Methods Adults (N=133, Males=50, Females=83, Age=25.8±7.96, BMI=24.8±3.8) aged 18-69 years were recruited from the community and asked to complete a series of surveys that measured their current mental and physical energy and fatigue states. After the completion of the surveys, subjects were instructed to complete the modified Clinical Test of Sensory Interaction in Balance (mCTSIB) using the APDM mobility monitors. Necessary assumptions were verified, and four multivariate multiple regression models were developed. Results Analyses yielded a significant association between posture and state mental energy (p=.048), but only when subjects were standing with their eyes closed while on a foam surface. Increased feelings of mental energy were associated with decreased total frequency dispersion (b=-358.62) and increased jerk in the coronal plane (b=11.78). No other associations were found. Discussion Results of our study suggest that as mental energy decreases there is a concomitant decrease in postural control when subjects are placed in conditions where they are unable to rely on visual feedback on unstable surfaces to maintain balance. Progressive increases in postural instability lead to increased risks of falls, most commonly in the elderly population. Falls are a significant risk factor for mortality. This study supports the clinical recommendation either to: (1) improve integration of vestibular and somatosensory input into postural control; or (2) train compensatory strategies for low lighting environments during episodes of decreased mental energy.

Regression Model to Evaluate the Impact of Basic Sanitation Services in Households and Schools on Child Mortality in the Municipalities of the State of Alagoas, Brazil

The aim of this article is to measure the impact of basic sanitation services on the mortality rate of children under five years of age (U5MR) in the municipalities of the State of Alagoas, Brazil. A multivariate multiple linear regression model was applied for all 102 cities of Alagoas for data years 1991, 2000 and 2010. The research findings are evidence that access to basic sanitation services in the municipalities of the State of Alagoas, especially household sanitary sewage, is associated with a statistically significant reduction of U5MR, p < 0.01 . The estimates show that the 10% increase in access to household sanitary sewage is associated to a reduction of 5.7 deaths per 1000 born alive (BA). Based on a simulation of universal basic access sanitation services in the municipalities of the State of Alagoas, it is observed that only this public policy would be able to reduce child mortality by more than 94%. The end results of this study are important subsidies to guide basic sanitation policies not only in the State of Alagoas, Brazil, but also in developing regions all over the world, considering the evidences of social and environmental impact.

Screening of heritage data for improving toughness of creep-resistant martensitic steels

Data science techniques were used to quantify the effect of alloying additions on the tensile behavior of martensitic steels. The effort was undertaken to exploit the heritage data to establish the next experimental design space for the class of 9–12 wt% Cr steels for the application of turbine rotors with an operating temperature of 650 ∘C and above. Linear, lasso, and multivariate multiple regression models were utilized to identify which alloying elements contribute towards strength and ductility. Visualization techniques such as t-distributed stochastic neighbor embedding and pair-wire element specific comparisons were utilized to explore information gaps that exist within the data. The study found that tantalum, recently added to improve the creep rupture lifetime, does not show any effect on tensile properties. All combined, the results suggest that the low tempering temperature has compensated for the low alloying additions in the past, therefore, new experiments are needed to isolate the effects of tempering temperature from those of individual elements.

A new Bayesian multivariate exponentially weighted moving average control chart for phase II monitoring of multivariate multiple linear profiles

AbstractRecently, statistical profile monitoring methods have become efficient tools for monitoring the quality of a product (or a production process) using control charts. The key idea is to describe the relationship between a response variable and a set of explanatory variables in the form of a statistical regression model, which called profile. Traditionally, those control charts are constructed with standard “frequentistic” regression models. Recently, it has been proposed to apply Bayesian regression models instead, and it has been empirically demonstrated that Bayesian regression models have the potential to perform significantly better. In this paper, we introduce a novel Bayesian multivariate exponentially weighted moving average control chart for monitoring multivariate multiple linear profiles in phase II. The key idea is to use the data from historical data sets to generate informative prior distributions for the regression models in phase II. The results of our empirical simulation studies show that the Bayesian multivariate multiple linear regression model is superior to its classical “frequentistic” counterpart in terms of the average run length. Our empirical findings are in agreement with findings reported in recently published articles. To shed more light onto the merit of the proposed Bayesian method, we carry out a sensitivity analysis, in which we investigate how the amount of phase I data influences the results. We also demonstrate the applicability and superiority of the proposed Bayesian method by a real‐world application.

Sex and puberty-related differences in metabolomic profiles associated with adiposity measures in youth with obesity.

Specific patterns of metabolomic profiles relating to cardiometabolic disease are associated with increased weight in adults. In youth with obesity, metabolomic data are sparse and associations with adiposity measures unknown. Primary, to determine associations between adiposity measures and metabolomic profiles with increased cardiometabolic risks in youth with obesity. Secondary, to stratify associations by sex and puberty. Participants were from COBRA (Childhood Overweight BioRepository of Australia; a paediatric cohort with obesity). Adiposity measures (BMI, BMI z-score, %truncal and %whole body fat, waist circumference and waist/height ratio), puberty staging and NMR metabolomic profiles from serum were assessed. Statistics included multivariate analysis (principal component analysis, PCA) and multiple linear regression models with false discovery rate adjustment. 214 participants had metabolomic profiles analyzed, mean age 11.9years (SD ± 3.1), mean BMI z-score 2.49 (SD ± 0.24), 53% females. Unsupervised PCA identified no separable clusters of individuals. Positive associations included BMI z-score and phenylalanine, total body fat % and lipids in medium HDL, and waist circumference and tyrosine; negative associations included total body fat % and the ratio of docosahexaenoic acid/total fatty acids and histidine. Stratifying by sex and puberty, patterns of associations with BMI z-score in post-pubertal males included positive associations with lipid-, cholesterol- and triglyceride-content in VLDL lipoproteins; total fatty acids; total triglycerides; isoleucine, leucine and glycoprotein acetyls. In a paediatric cohort with obesity, increased adiposity measures, especially in post-pubertal males, were associated with distinct patterns in metabolomic profiles.

Assessment on the awareness level about diarrhoea and its management among mothers attending outpatient department in a rural hospital of West Bengal, India

Background: Diarrhoea is one of the leading causes of under-five childhood morbidity and mortality in India, despite the availability of easy interventions through oral rehydration at the community level. The level of knowledge varies from country to country and within the country, further variations exist in state, district and sub district level based on difference in socio-demographic characteristics of the population. And based on these variations, different community needs different health education efforts in its extent and approaches. It was therefore relevant to explore the level of awareness about diarrhoea and its management among the mothers who were the first level of caregivers.
 Objective: To assess the level of knowledge about diarrhoea and oral rehydration therapy among the mothers having their children of 6 months to 5 yrs with diarrhea
 Materials and methods: It was a facility based cross-sectional descriptive epidemiological study conducted among 62 mothers having their children of 6 months to five years with diarrhoea. Mothers attended a rural hospital under the geographical area of Madhyamgram in North 24 Parganas district of West Bengal, India. Data was collected by face to face interview of the mothers in the outpatient department of the hospital using a pre-designed and pre-tested questionnaire. The analysis was done in Statistical Package for Social Sciences (SPSS), version 20.0 using bivariate and multivariate (multiple logistic regression model) to examine the statistical significance at 95% confidence interval.
 Results: Mean knowledge score was 7.8 (Range 0-17). Lower knowledge score group (0-8) accounted to 36 persons (37.1%) and higher knowledge group (9-19) accounted to 26 persons (62.9%). Knowledge about alarming symptoms of the dehydration was significantly poor. At the individual level, literacy of women and their caste were strongly associated with the knowledge about diarrhoea and its management. At the household level, the way of the disposal of household garbage was also strongly associated.
 Conclusion: Considering the poor knowledge of the mothers, the study recommends for extensive health education measures widely in the community with a special focus for the illiterate and socio-economically lower groups, and also for the families having the practice of open garbage disposal.
 Bangladesh Journal of Medical Science Vol.18(2) 2019 p.267-273

The association between problematic online gaming and perceived stress: The moderating effect of psychological resilience.

Background and aimsVulnerability to stress appears to be a potential predisposing factor for developing specific internet-use disorders, such as Internet Gaming Disorder (IGD). Studies investigating the protective effect of psychological resilience against the impact of perceived stress on IGD and weekly gameplay have yet to be reported in the existing literature. The aim of this study was to examine the potential moderating relationships between perceived stress and online gaming (more specifically operationalized as IGD and weekly gameplay) with psychological resilience.MethodsAn online survey was administered to 605 participants (males = 82%, Mage = 24.01 years, SDage = 6.11). A multivariate multiple regression model was applied to test for the possible contribution of perceived stress and psychological resilience to weekly gameplay and IGD.ResultsPerceived stress was associated with higher scores of IGD, whereas psychological resilience was related to lower scores of IGD. In addition, the combination of having higher perceived stress and lower level of psychological resilience was associated with a particularly high hours of gameplay per week.Discussion and conclusionsThese findings further support the importance of personal traits (perceived stress and psychological resilience) in online gaming (IGD severity and weekly gameplay), and also emphasize the unique moderating relationship between perceived stress and weekly gameplay with lack of resilience. Enhancing psychological resilience to decrease the likelihood of online gamers who experience higher level of stress from spending more hours per week gaming is recommended.

An exploratory multivariate study examining correlates of trait mental and physical fatigue and energy

ABSTRACT Background: Mental and physical energy and fatigue can be assessed as either stable long-term traits or as a temporary state. Although researchers recognize the need to separate the two, most research has focused on state, leaving trait understudied. Therefore, the objective of this study was to apply demographic, lifestyle and psychosocial variables known to be associated with state fatigue and energy to examine predictors of trait mental and physical energy and fatigue. Methods: A convenience sample (N = 671) completed an online survey measuring mood, physical activity, mental workload, polyphenol (plant-based healthy micronutrients) consumption in the diet, and sleep quality. A multivariate multiple regression model was fit to simultaneously test associations between covariates for each four trait fatigue indicators. Results: Poor sleep quality was the only consistent predictor of both energy and fatigue (mental and physical), with confusion correlating with all but physical energy. Age and depression were predictors of mental and physical fatigue, but caffeine consumption was predicted by higher physical fatigue only. Mental workload and physical activity on off-days predicted physical energy only, while polyphenol consumption and BMI predicted mental energy only. Conclusions: Findings suggest that mental/ physical energy and fatigue may be separate constructs that can be treated as empirically distinct. The distinctions between physical and mental fatigue are less pronounced, needing further exploration. Subsequent research should explore other potentially important biopsychosocial sources of variation in trait mental and physical energy and fatigue.

Multivariate Analysis of Correlates of Under Five Children Malnutrition in Tigray Region, Ethiopia

Malnutrition is defined as deficiencies, excesses or imbalances in a person’s intake of energy and/or nutrients. Malnutrition among children under five years of age is a chronic problem in most regions of Ethiopia, including the Tigray region. The main objective of this study is to assess the prevalence of under-five child malnutritions and the risk factors attributed to nutritional status of children in Tigray region based on Ethiopian Demographic Health Survey, 2016 datasets. The information collected from 370 children was considered in the study, and variables like maternal socio and demographic characteristics, child demographic characteristics, health and environmental factors were considered as determinants of nutritional status of a child. The study used descriptive statistics and Multivariate multiple linear regression models to identify significant correlates of perinatal mortality. Factor analysis based on principal component analysis was done to reduce the data and components with Eigen value of more than one were considered for further investigation. The descriptive statistics in the study reveals that out of a total of 370 children included in the study 25.4% are underweighted, 30.8% are stunted and 17.3% are wasted. Accordingly of total children malnourished 5.9% are severely underweighted while 19.5% are moderately underweighted, about 12.7% are severely stunted and 18.1% moderately stunted and 6.5% are severely wasted and 10.8% are moderate wasted respectively. From Multivariate multiple linear regressions, breast feeding factors, socioeconomic status of households, health status of child, having medical treatments during pregnancy and child vaccination status have significant impacts on nutritional status of the under five children. The factors duration of breast feeding, number of household members, living children, birth order of a child, current age of child, place of residence, sanitation services like drinking water and availability of toilet, mother educational level and father education level, age of mother, economic level of household, receiving measles, polio and vitamin A in the last six months, and child health status indicators like having diarrhea recently, having fever and cough in the last two months had statistically significant effect on child malnutrition.

Multivariate multiple regression models of poly(ethylene-terephthalate) film degradation under outdoor and multi-stressor accelerated weathering exposures.

Developing materials for use in photovoltaic (PV) systems requires knowledge of their performance over the warranted lifetime of the PV system. Poly(ethylene-terephthalate) (PET) is a critical component of PV module backsheets due to its dielectric properties and low cost. However, PET is susceptible to environmental stressors and degrades over time. Changes in the physical properties of nine PET grades were modeled after outdoor and accelerated weathering exposures to characterize the degradation process of PET and assess the influence of stabilizing additives and weathering factors. Multivariate multiple regression (MMR) models were developed to quantify changes in color, gloss, and haze of the materials. Natural splines were used to capture the non-linear relationship between predictors and responses. Model performance was evaluated via adjusted-R2 and root mean squared error values from leave-one-out cross validation analysis. All models described over 85% of the variation in the data with low relative error. Model coefficients were used to assess the influence of weathering stressors and material additives on the property changes of films. Photodose was found to be the primary degradation stressor and moisture was found to increase the degradation rate of PET. Direct moisture contact was found to impose more stress on the material than airbone moisture (humidity). Increasing the concentration of TiO2 was found to generally decrease the degradation rate of PET and mitigate hydrolytic degradation. MMR models were compared to physics-based models and agreement was found between the two modeling approaches. Cross-correlation of accelerated exposures to outdoor exposures was achieved via determination of cross-correlation scale factors. Cross-correlation revealed that direct moisture contact is a key factor for reliable accelerated weathering testing and provided a quantitative method to determine when accelerated exposure results can be made more aggressive to better approximate outdoor exposure conditions.

102. Address the dosimetry in radiometabolic therapy; relationship between dosimetric value and clinical parameters in differentiated thyroid cancer

Purpose Use rationally the Red Marrow (RM) and Whole Body (WB) dosimetry pre and during therapy in Differentiated Thyroid Cancer (DTC) focalinzing the relationship between clinical parameters. Methods We enrolled 120 patients (278 dosimetries-196 with complete clinical data) with DTC (March 2012–December 2017). We made double dosimetric study the week before the therapy (19 MBq 131I) and during therapy (range 1019–9342 MBq, mean 6253 MBq, median 6208 MBq), collecting serial blood samples and WB counts according to the AIFM Italian dosimetric protocol and EANM SOP. With a simple regression analysis, we studied the capability of residence times (tau) and mGy/MBq (RM and WB) to predict the respective post therapy values (Fig. 1). We moreover considered a multivariate multiple regression model to control for clinical values (sex, age, histology, variant, multifocality, bilaterality, Tsh Ipo, Tg Ipo, FT4, staging and another tumour). Results All the variables pre-treatment have a significant role in explaining the levels of the corresponding variables post-treatment (Fig. 1). For all the variables, a PRE unitary increase determines a much smaller increase in post values (from 0.3 to 0.5). When considering all the variables as possible predictors (Table 1), none of them seems to have an effect on WBposttau, apart from WBpretau. For RMposttau, instead, we found correlation with RMpretau, WBpretau, age and the presence of another tumour. Concerning WBpostmGyMBq and RMpostmGyMBq, both appear to be reduced for N1b staging; WBpostmGyMBq reduced for advanced tumours and increased for large values of WBpretau. RMpostmGyMBq increases with age and RMpretau. A large parte of the total variability of WBpostmGyMBq and RMpostmGyMBq remains unexplained. Conclusions Dosimetry connected with clinical values could be a useful tool to help in patient management to predict behaviour and efficacy. Mandatory next step is to study follow up. Download : Download high-res image (220KB) Download : Download full-size image

Sex and sexual orientation in relation to tobacco use among young adult college students in the US: a cross-sectional study

BackgroundSexual minority young adults represent a high-risk population for tobacco use. This study examined cigarette and alternative tobacco product (ATP) use prevalence across sexual orientation (heterosexual, gay/lesbian, and bisexual) among college-attending young adult men and women, respectively.MethodsBaseline data from a two-year longitudinal study of 3386 young adult college students aged 18–25 in Georgia were analyzed. Correlates examined included sociodemographics (age, sex, sexual orientation, race/ethnicity, college type, and parental education). Outcomes included past 30-day use of tobacco (cigarette, little cigars/cigarillos [LCCs], e-cigarettes, hookah, any tobacco product used, and number of tobacco products used, respectively). Two-group, multivariate multiple regression models were used to examine predictors of tobacco use among men and women, respectively.ResultsAmong men (N = 1207), 34.7% used any tobacco product; 18.6% cigarettes; 12.3% LCCs; 16.8% e-cigarettes; and 14.7% hookah. Controlling for sociodemographics, gay sexual orientation (OR = 1.62, p = 0.012) was associated with higher odds of cigarette use; no other significant associations were found between sexual orientation and tobacco use. Among women (N = 2179), 25.3% used any tobacco product; 10.4% cigarettes; 10.6% LCCs; 7.6% e-cigarettes; and 10.8% hookah. Being bisexual was associated with cigarette (p < 0.001), LCC (p < 0.001), and e-cigarette use (p = 0.006). Lesbian sexual orientation was associated with cigarette (p = 0.032) and LCC use (p < 0.001). Being bisexual predicted any tobacco product used (p = 0.002), as well as number of tobacco products used (p = 0.004). Group comparisons showed that the effect of sexual minority status on LCC use was significantly different for men versus women.ConclusionSexual minority women, especially bisexual women, are at higher risk for using specific tobacco products compared to heterosexual women; homosexual men are at increased risk of cigarette use compared to heterosexual men. These nuances in tobacco use should inform interventions targeting sexual minorities.

Smart Cities and Mobility: Does the Smartness of Australian Cities Lead to Sustainable Commuting Patterns?

ABSTRACTSmart cities have become a popular concept because they have the potential to create a sustainable and livable urban future. Smart mobility forms an integral part of the smart city agenda. This paper investigates “smart mobility” from the angle of sustainable commuting practices in the context of smart cities. This paper studies a multivariate multiple regression model within a panel data framework and examines whether increasing access to broadband Internet connections leads to the choice of a sustainable commuting mode in Australian local government areas. In this case, access to the Internet is used as a proxy for determining urban smartness, and the use of different modes of transport including working at home is used to investigate sustainability in commuting behavior. The findings show that an increasing access to broadband Internet reduces the level of working from home, public transport use, and active transport use, but increases the use of private vehicles, perhaps to overcome the fragmentation of work activities the Internet creates. How to overcome the need for car-based travel for fragmented work activities while increasing smartness through the provisioning of broadband access should be a key smart city agenda for Australia to make its cities more sustainable.

Peer pressure and home environment as predictors of disruptive and risky sexual behaviours of secondary school adolescents.

Not much is understood about the predictive power of home environment and peer pressure on disruptive behaviour and risky sexual behaviour of adolescents. The study investigated the predictive power of home environment and peer pressure on disruptive behaviour and risky sexual behaviour of adolescents in secondary school class two in Enugu State, Nigeria. Four research questions and four null hypotheses guided the study. The design was a cross sectional survey of correlational study. The study was carried out in the six Education zones in Enugu State, Nigeria. The population was all the 31,680 senior secondary class two (SS11) adolescents in 285 secondary schools in Enugu State, Nigeria in 2015/2016 academic session. The instruments for data collection were an observation schedule, an interview session and a structured questionnaire of four clusters. To determine the R-squares for each regression model, a multivariate multiple regression model was conducted using "MANOVA" and "MVREG". This study indicates adolescents who reported their home environments to be stimulated displayed compliant behavior and none or lowered risky sexual behaviour, whilst those with chaotic and unstimulated home environment displayed disruptive behaviours. It was found that adolescents who show a heightened sensitivity to positive peer pressure demonstrated compliant and no or lowered risky sexual behavior whilst, those that are engaged with negative peer pressure strongly exhibit disruptive and risky sexual behaviour. Unstimulated home environment and negative peer group could consequently interact to predispose these adolescents to disruptive behaviour and risky sexual behaviour.

Corrected score estimators in linear multivariate multiple regression models with heteroscedastic measurement errors

Corrected score estimators in linear multivariate multiple regression models with heteroscedastic measurement errors

Effect of smoking on the association of HHEX (rs5015480) with diabetes among Korean women and heavy smoking men

BackgroundSeveral genome-wide association studies (GWAS) for serum fasting glucose levels have reported HHEX as possibly causal. The objective of this study was to examine the joint effect of smoking on the association of diabetes with the HHEX rs5015480 polymorphism among Korean subjects.MethodsThis replication study included a total of 4240 individuals, and multivariate linear regression and multiple logistic regression models were used. We examined the combined effect of smoking on the relationship between HHEX rs5015480 and diabetes.ResultsThe rs5015480 SNP in the HHEX gene was related to the mean FBS level (effect per allele, 1.572 mg/dL, p = 0.0122). Females with the CC genotype had a 2.68 times higher (range, 1.05–6.82 times) risk of diabetes than those with the TT/TC genotype. Although the association was stronger in female subjects (OR, 4.46; 95% CI, 1.15–17.3, p = 0.0304) among healthy individuals (N = 2461), the association between HHEX and diabetes was much stronger in male heavy smokers (OR, 4.03; 95% CI, 1.19–13.6, p = 0.0247) than in nonsmokers (p = 0.9709) and ex-smokers (p = 0.2399). The interaction of smoking was also statistically significant (P for interaction =0.0182).ConclusionsThis study clearly demonstrates that a genetic variant in HHEX influences fasting glucose levels in Korean women and male heavy smokers.

Parameter estimation of multivariate multiple regression model using bayesian with non-informative Jeffreys’ prior distribution

Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys’ prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys’ prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys’ prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.

Evaluation of statistical downscaling models using pattern and dependence structure in the monsoon‐dominated region of Pakistan

AbstractThe uphill topography and sudden spatial variation in the climate of the monsoon‐dominated region of Pakistan render it difficult to make predictions with dynamical climate models. This study evaluates the use of two statistical models for the downscaling of climate variables: the Multivariate Multiple Linear Regression Model (MMLRM) and the Multisite Multivariate Statistical Downscaling Model (MMSDSM). A randomisation technique was implemented to establish the extreme values and spatial dependence structure for a number of variables by adding correlated noise to the predictand data for multiple sites, generated from a multivariate normal distribution. In the case of precipitation, probability mapping techniques were used to make adjustments based on a gamma distribution. To cope with the dimensionality and multicollinearity problems of the input data (predictors), empirical orthogonal functions were used. The models were calibrated using the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) predictors for the period 1960–1990 and validated for 1990–2000. To investigate the efficacy of the proposed models, different statistical measures – such as root mean square error, mean bias error and analysis of how closely the observed variability was reproduced – were used. The results show mixed support for both models: MMLRM underestimates the variability, and MMSDSM has the ability to predict the extreme values and spatial dependence structure. The results of logistic regression analysis show that the precipitation probability values generated by the logistic model closely reproduced the patterns of observed precipitation – there is an increase in the occurrence of precipitation events during the monsoon season over the target area.

Proposed Distance-Based Test for Testing Multivariate Multiple Regression Coefficients under Restricted Alternatives

In constructing estimation and hypothesis testing procedures, it is important that all available information such as sign of parameter is used in order to maximize power of the test. Often prior information are known about the sign of regression coefficients (parameter) under test, the best example being that variances cannot be negative. Ignoring information about the signs of regression parameters can lead to loss of power in small samples. With this problem in mind, this paper concerned with developing restricted estimation and hypothesis testing approach in the context of multivariate multiple regression model. Developing the technique of estimating constraint regression coefficients and testing restricted parameters with the aid of information theoretic distance are the main contribution of this paper. The distribution of the existing two-sided test follows central chi-square distribution whereas the test statistic of our proposed distance-based one-sided test follows weighted mixture of chi-square distribution. Monte Carlo simulation indicates that our newly proposed test performs better than existing tests.