The purpose of this research is to investigate the performance of some ridge regression estimators for the logistic regression model in the presence of moderate to high correlation among the explanatory variables. As a performance criterion, we use the mean square error (MSE), the mean absolute percentage error (MAPE), the magnitude of bias, and the percentage of times the ridge regression estimator produces a higher MSE than the maximum likelihood estimator. A Monto Carlo simulation study has been executed to compare the performance of the ridge regression estimators under different experimental conditions. The degree of correlation, sample size, number of independent variables, and log odds ratio has been varied in the design of experiment. Simulation results show that under certain conditions, the ridge regression estimators outperform the maximum likelihood estimator. Moreover, an empirical data analysis supports the main findings of this study. This thesis proposed and recommended some good ridge regression estimators of the logistic regression model for the practitioners in the field of health, physical and social sciences.

When the delicate hormonal balance in early pregnancy is disrupted, the consequences can be significant. We have a poor understanding of the "cross-talk" in the fetal/placental/ovarian axis that occurs throughout pregnancy and is essential for normal fetal development. This lack of knowledge challenges our ability to recognize disruptions in this axis that may be a signal for future disease. As a result, our ability to apply preventive measures against adverse obstetric outcomes, such as preterm birth (PTB), are quite limited. Attempts to predict PTB using biomarkers of feto-placental health have been largely unsuccessful, but no one has considered the inclusion of ovarian biomarkers in these models. Anti-Mullerian hormone (AMH) is a biomarker of ovarian activity that has recently been found to decline in early pregnancy at a time that corresponds to the involution of the corpus luteum (CL). The signal for CL involution is believed to originate from the placenta; therefore, the AMH levels in pregnancy may reflect the degree of ovarian up or down-regulation based on feto-placental needs. As the major function of the CL in pregnancy is the production of progesterone, which acts as an anti-inflammatory agent in the placental bed, changes in CL-derived progesterone could result in higher or lower degrees of placental inflammation. Therefore, monitoring the changes in AMH levels may provide insight into the inflammatory state of the placenta which could then be used as a signal for possible adverse obstetric outcomes resulting from a pro-inflammatory state, such as PTB. The first aim of this project was to test the hypothesis of an association between AMH levels in early pregnancy and PTB risk. When the differences in AMH levels between the 1st and 2nd trimesters of pregnancy were stratified by the level of maternal serum alpha-fetoprotein (MSAFP) and controlled for maternal weight gain between trimesters, small or absent decreases in AMH levels were associated with a higher probability of preterm birth. However, when AMH was modeled alone, no significant associations were found. The need for changes in multiple biomarkers in the fetal/placental/ovarian axis suggests that a change is only significant if it can impact multiple axis points. Therefore, models that included two biomarkers from different part of the axis would find stronger associations than two biomarkers from a single point (e.g. two feto-placental biomarkers), and monitoring these changes may help identify women at risk for PTB. The strategy of the second aim was to determine if the changes in AMH levels in early pregnancy could be used to predict time to delivery. Again, only when the risks of AMH and MSAFP were combined was a significant, dose-dependent relationship found with time to delivery. In women with an MSAFP of >1 multiple of the median (MoM), smaller declines and/or elevations in AMH levels were significantly associated with shorter times to delivery. In fact, 19% of women in the highest risk group delivered prior to 32 weeks gestation compared to 7% in the lowest risk group, and all infants who delivered prior to 24 weeks gestation were in the highest risk category. Thus, the amount of change in the AMH level when MSAFP is elevated may reflect the level of disruption in the fetal/placental/ovarian axis, which can then be used to predict time to delivery. Finally, the third aim of this study was to determine if AMH levels were associated with a pro-inflammatory placental state other than PTB. The degree of placental inflammation is known to vary by fetal gender, with male placentas having higher levels of inflammation compared to female placentas. When AMH levels were compared between women with male vs. female fetuses in early pregnancy, 1st trimester AMH levels were found to be lower when carrying a male fetus. Further, sexually-dimorphic patterns in AMH levels were seen between genders when stratified by birth outcome (term vs. preterm delivery). The stronger ovarian response seen in women with female fetuses suggests a better survival function and may account for the discrepancies between PTB rates in males and females. This also strengthens our hypothesis that the dynamic changes in AMH levels reflect the degree of placental inflammation and the need for CL-derived progesterone. This project demonstrates that the changes in AMH levels may be representative of the cross-talk occurring in the fetal/placental/ovarian axis in early pregnancy. Further, changes in AMH levels may be an indication of the amount of inflammation in the placenta and the physiologic need for higher levels of progesterone to control this inflammatory state when considered along with MSAFP. Therefore, the consideration of AMH levels as a biomarker of ovarian activity along with biomarkers of feto-placental health may provide clinically useful information about the development of future diseases such as preterm birth.

Local thermodynamic models are practical alternatives to computationally expensive rigorous models that involve implicit computational procedures and often complement them to accelerate computation for real-time optimization and control. Human-centered strategies for development of these models are based on approximation of theoretical models. Genetic Programming (GP) system can extract knowledge from the given data in the form of symbolic expressions. This research describes a fully data driven automatic self-evolving algorithm that builds appropriate approximating formulae for local models using genetic programming. No a-priori information on the type of mixture (ideal/non ideal etc.) or assumptions are necessary. The approach involves synthesis of models for a given set of variables and mathematical operators that may relate them. The selection of variables is automated through principal component analysis and heuristics. For each candidate model, the model parameters are optimized in the inner integrated nested loop. The trade-off between accuracy and model complexity is addressed through incorporation of the Minimum Description Length (MDL) into the fitness (objective) function. Statistical tools including residual analysis are used to evaluate performance of models. Adjusted R-square is used to test model's accuracy, and F-test is used to test if the terms in the model are necessary. The analysis of the performance of the models generated with the data driven approach depicts theoretically expected range of compositional dependence of partition coefficients and limits of ideal gas as well as ideal solution behavior. Finally, the model built by GP integrated into a steady state and dynamic flow sheet simulator to show the benefits of using such models in simulation. The test systems were propane-propylene for ideal solutions and acetone-water for non-ideal. The result shows that, the generated models are accurate for the whole range of data and the performance is tunable. The generated local models can indeed be used as empirical models go beyond elimination of the local model updating procedures to further enhance the utility of the approach for deployment of real-time applications.

<p>Kvicksilverutsläppen har på senare år minskat i omfattning men utsläpp sker fortfarande och det finns ett stort lager i naturen. Oorganiskt kvicksilver är relativt ofarligt för levande organismer, men i akvatiska miljöer kan sulfatreducerande bakterier under syrefria förhållanden omvandla oorganiskt kvicksilver till den betydligt mer skadliga formen metylkvicksilver, meHg, som även är mer biotillgängligt än oorganiskt kvicksilver. Kvicksilver biomagnifieras uppåt i trofinivåerna, från att vara lägst halter i plankton och bottenfauna till att vara högst halter i rovfiskar. Kvicksilver ackumuleras även i fiskars muskelvävnad vilket innebär att yngre fiskar har lägre Hg-halter än gamla och stora individer. På grund av detta finns kostråd framtagna av Livsmedelsverket. Saluförd abborre, liksom ett flertal andra fiskarter, får inneha maximalt 0,5 mg Hg/kg fiskmuskel (färskvikt) och för gädda är gränsen satt till 1 mg Hg/kg fiskmuskel (färskvikt). Organiskt kvicksilver kan påverka foster negativt, och därför bör kvinnor i fertil ålder i största möjliga mån undvika kvicksilverrik fisk.</p><p> </p><p>Examensarbetet syftar till att belysa kvicksilversituationen i Stockholms skärgård för stationär kustfisk. Information har samlats in dels genom en litteraturstudie och dels genom fältundersökningar utförda av IVL Svenska Miljöinstitutet. Genom statistisk analys och stegvis multipel regression visades att kvicksilverhalten i sediment, vattnets klorofyllhalt och områdets vattenvolym bidrog med förklaringsgrad till halten Hg i fisk. Utifrån de mest signifikanta förklarande variablerna togs en statistisk modell fram i syfte att kunna prediktera teoretiska kvicksilverhalter i fisk. Olika modellkombinationer testades och utgående från en modellvalidering valdes den bästa modellen ut. Dess förklaringsgrad är 81 % där kvicksilverhalten i sediment är modellens enda variabel.</p><p> </p><p>Kvicksilversituationen i Stockholms skärgårds kustområden visades grafiskt med hjälp av interpolerade GIS-kartor. Samma områdesavgränsningar användes som i SMHI:s havsområderegister. Det visades att situationen över lag är relativt god, med undantag för de centrala delarna av Stockholm och på så vis kan Stockholm ses som en förorenande punktkälla.</p> / <p>Mercury emissions have been reduced in recent years but the discharges still exist and there exist a great mercury stock out in the nature. Inorganic mercury is relatively harmless for living organisms but during shortage of oxygen, sulphur reducing bacteria can transform inorganic mercury into the considerable more toxic substance methyl mercury, meHg, that are more bio available than inorganic mercury. Mercury biomagnify upwards the trophic levels, where the lowest content exists in algae and sediment living fauna and the highest content exist in predator fishes. Mercury also accumulates in fishes muscle tissue, meaning that young fishes have lower mercury content than old and big individuals. Food advices from the Swedish food agency exist because of this. Perch offered for sale are allowed to have a content of maximum 0.5 mg Hg/kg fish muscle (wet weight) and for pike the upper boundary content is 1 mg Hg/kg fish muscle (wet weight). Inorganic mercury can affect foetus negatively, and therefore women in fertile age should avoid fish with high mercury content for as long as possible.</p><p> </p><p>The aim of this exam work is to illustrate the mercury situation in the archipelago of Stockholm regarding stationary coast fish. Information was collected through a literature study and by field examines done by IVL Swedish Environmental Research Institute Ltd. Through statistical analyses and stepwise multiple regression it was shown that the mercury content in sediment, chlorophyll and the water volume of the area contributed by statistical explanation to the mercury concentration in fish. On the basis of the most significant variables a statistical model was created, with the purpose of predicting theoretical mercury contents in fish. Different model combinations were tested and by a model validation the best model were chosen. Its statistical explanation is 81 % were the mercury content in the sediment is the only input variable to the model.</p><p> </p><p>The mercury situation in the Stockholm archipelago was presented graphically by interpolated maps created with GIS. The same area boundary as SMHI’s maritime registry was used. It was shown that the situation in general is relatively good, with the exception of the central parts of Stockholm. Because of this Stockholm can be seen as a polluting point source.</p>

<p>I mars år 2000 blev det tillåtet för börsnoterade bolag att genomföra återköp av egna aktier i Sverige. En del kritiker hävdar att återköp kan användas till att påverka aktiekursen positivt, till förmån för bland annat optionsinnehavare. I denna uppsats har vi undersökt om antal utestående optioner till anställda ökar sannolikheten för genomförandet av aktieåterköp. För att ta reda på detta har vi undersökt data från samtliga bolag som var noterade på NASDAQ OMX Large Cap i Stockholm vid utgången av år 2007. Vi har analyserat datamaterialet med hjälp av enkel linjär regression samt logistisk regression. Vi finner en svag positiv korrelation i den enkla regressionsmodellen. Den logistiska regressionen påvisar dock ett starkare samband, vilket indikerar att återköp till viss del kan påverkas av bolagens optionsprogram.</p>

<p>Quantile regression have its advantage properties comparing to the OLS model regression which are full measurement of the effects of a covariate on response, robustness and Equivariance property. In this paper, I use a survey data in Belgium and apply a linear model to see the advantage properites of quantile regression. And I use a quantile regression model with the raw data to analyze the different cost of family on different numbers of children and apply a Wald test. The result shows that for most of the family types and living standard, from the lower quantile to the upper quantile the family cost on children increases along with the increasing number of children and the cost of each child is the same. And we found a common behavior that the cost of the second child is significantly more than the cost of the first child for a nonworking type of family and all living standard families, at the upper quantile (from 0.75 quantile to 0.9 quantile) of the conditional distribution.</p>

Graduation date: 2006 / Regression calibration inference seeks to estimate regression models with measurement error in explanatory variables by replacing the mismeasured variable by its conditional expectation, given a surrogate variable, in an estimation procedure that would have been used if the true variable were available. This study examines the effect of the uncertainty in the estimation of the required conditional expectation on inference about regression parameters, when the true explanatory variable and its surrogate are observed in a calibration dataset and related through a normal linear model. The exact sampling distribution of the regression calibration estimator is derived for normal linear regression when independent calibration data are available. The sampling distribution is skewed and its moments are not defined, but its median is the parameter of interest. It is shown that, when all random variables are normally distributed, the regression calibration estimator is equivalent to maximum likelihood provided a natural estimate of variance is non-negative. A check for this equivalence is useful in practice for judging the suitability of regression calibration. Results about relative efficiency are provided for both external and internal calibration data. In some cases maximum likelihood is substantially more efficient than regression calibration. In general, though, a more important concern when the necessary conditional expectation is uncertain, is that inferences based on approximate normality and estimated standard errors may be misleading. Bootstrap and likelihood-ratio inferences are preferable.

In diesem Beitrag wird eine Regressionsanalyse vorgestellt, die die Einflüsse auf die Entscheidung verheirateter deutscher Frauen untersucht, eine Erwerbstätigkeit aufzunehmen. Um Differenzen im Verhalten von ost- und westdeutschen Frauen zu ermitteln, erfolgte die Untersuchung getrennt in zwei Datensätzen. Zur Vermeidung von Annahmen über die Art des Zusammenhanges wurde das Generalisierte Additive Modell (GAM) gewählt, ein semiparametrisches Regressionsmodell. Diese Modellform, die nichtparametrische und parametrische Regressionsmethoden in sich vereint, hat bisher wenig Verbreitung in der Praxis gefunden. Dies lag vor allem am Schätz verfahren, dem Backfitting. Seit etwa einem Jahr gibt es neue Ansätze, in dieser Modellform zu schätzen. Die analytischen Eigenschaften des neuen Schätzers lassen sich leichter bestimmen. Mit dieser Schätzung konnten Unterschiede zwischen Ost und West genau herausgearbeitet werden und die funktionalen Zusammenhänge zwischen Einflußvariablen und Antwortvariable untersucht werden. Die Analyse brachte deutliche Unterschiede im Erwerbsverhalten zwischen der Frauen beider Landesteile zum Vorschein. / This paper will focus on the regression analysis of labor supply decisions of married German women. In order to determine differences East and West German women were compared seperately. To avoid assumptions about the functional type of correlation the Generalized Additive Model, a semiparametric regression model, was chosen. So far, this pattern consisting of nonparametric and parametric methods has not found acceptance in practical application. Reason for that is the backfitting-estimator. One year ago new ideas for the estimation by GAM were found. The analytical features of the new estimator are easier to determine. Using this method differences between East and West were discovered in detail and functional correlations between endogenous and exogenous variables were investigated. This analysis unveiled significant differences of labor supply behavior among East and West Germany.

Quantile regression have its advantage properties comparing to the OLS model regression which are full measurement of the effects of a covariate on response, robustness and Equivariance property. In this paper, I use a survey data in Belgium and apply a linear model to see the advantage properites of quantile regression. And I use a quantile regression model with the raw data to analyze the different cost of family on different numbers of children and apply a Wald test. The result shows that for most of the family types and living standard, from the lower quantile to the upper quantile the family cost on children increases along with the increasing number of children and the cost of each child is the same. And we found a common behavior that the cost of the second child is significantly more than the cost of the first child for a nonworking type of family and all living standard families, at the upper quantile (from 0.75 quantile to 0.9 quantile) of the conditional distribution.

I mars år 2000 blev det tillåtet för börsnoterade bolag att genomföra återköp av egna aktier i Sverige. En del kritiker hävdar att återköp kan användas till att påverka aktiekursen positivt, till förmån för bland annat optionsinnehavare. I denna uppsats har vi undersökt om antal utestående optioner till anställda ökar sannolikheten för genomförandet av aktieåterköp. För att ta reda på detta har vi undersökt data från samtliga bolag som var noterade på NASDAQ OMX Large Cap i Stockholm vid utgången av år 2007. Vi har analyserat datamaterialet med hjälp av enkel linjär regression samt logistisk regression. Vi finner en svag positiv korrelation i den enkla regressionsmodellen. Den logistiska regressionen påvisar dock ett starkare samband, vilket indikerar att återköp till viss del kan påverkas av bolagens optionsprogram.