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abstract: The purpose of this study was to examine under which conditions "good" data characteristics can compensate for "poor" characteristics in Latent Class Analysis (LCA), as well as to set forth guidelines regarding the minimum sample size and ideal number and quality of indicators. In particular, we studied to which extent including a larger number of high quality indicators can compensate for a small sample size in LCA. The results suggest that in general, larger sample size, more indicators, higher quality of indicators, and a larger covariate effect correspond to more converged and proper replications, as well as fewer boundary estimates and less parameter bias. Based on the results, it is not recommended to use LCA with sample sizes lower than N = 100, and to use many high quality indicators and at least one strong covariate when using sample sizes less than N = 500. / Dissertation/Thesis / M.A. Psychology 2012

abstract: A simulation study was conducted to explore the influence of partial loading invariance and partial intercept invariance on the latent mean comparison of the second-order factor within a higher-order confirmatory factor analysis (CFA) model. Noninvariant loadings or intercepts were generated to be at one of the two levels or both levels for a second-order CFA model. The numbers and directions of differences in noninvariant loadings or intercepts were also manipulated, along with total sample size and effect size of the second-order factor mean difference. Data were analyzed using correct and incorrect specifications of noninvariant loadings and intercepts. Results summarized across the 5,000 replications in each condition included Type I error rates and powers for the chi-square difference test and the Wald test of the second-order factor mean difference, estimation bias and efficiency for this latent mean difference, and means of the standardized root mean square residual (SRMR) and the root mean square error of approximation (RMSEA). When the model was correctly specified, no obvious estimation bias was observed; when the model was misspecified by constraining noninvariant loadings or intercepts to be equal, the latent mean difference was overestimated if the direction of the difference in loadings or intercepts of was consistent with the direction of the latent mean difference, and vice versa. Increasing the number of noninvariant loadings or intercepts resulted in larger estimation bias if these noninvariant loadings or intercepts were constrained to be equal. Power to detect the latent mean difference was influenced by estimation bias and the estimated variance of the difference in the second-order factor mean, in addition to sample size and effect size. Constraining more parameters to be equal between groups—even when unequal in the population—led to a decrease in the variance of the estimated latent mean difference, which increased power somewhat. Finally, RMSEA was very sensitive for detecting misspecification due to improper equality constraints in all conditions in the current scenario, including the nonzero latent mean difference, but SRMR did not increase as expected when noninvariant parameters were constrained. / Dissertation/Thesis / Masters Thesis Educational Psychology 2016

Diploma thesis abstract Thesis title: Statistical inference in multivariate distributions based on copula models Author: Vojtěch Kika This diploma thesis aims for statistical inference in copula based models. Ba- sics of copula theory are described, followed by methods for statistical inference. These are divided into three main groups. First of them are parametric methods for copula parameter estimation which assume fully parametric structure, thus for both joint and marginal distributions. The second group consists of semi- parametric methods for copula parameter estimation which, unlike parametric methods, do not require parametric structure for marginal distributions. The last group describes goodness-of-fit tests used for testing the hypothesis that consi- dered copula belongs to some specific copula family. The thesis is accompanied by a simulation study that investigates the dependence of the observed coverage of the asymptotic confidence intervals for copula parameter on the sample size. Pseudolikelihood method was chosen for the simulation study since it is one of the most popular semiparametric methods. It is shown that sample size of 50 seems to be sufficient for the observed coverage to be close to the theoretical one. For Frank and Gumbel-Hougaard copula families even sample size of 30 gives us...

In this thesis, the theory and application of black-box optimization methods are explored. More specifically, we looked at two families of algorithms, descent methods andresponse surface methods (closely related to trust region methods). We also looked at possibilities in using a dimension reduction technique called active subspace which utilizes sampled gradients. This dimension reduction technique can make the descent methods more suitable to high-dimensional problems, which turned out to be most effective when the data have a ridge-like structure. Finally, the optimization methods were used on a real-world problem in the context of pre-hospital care where the objective is to minimize the ambulance response times in the municipality of Umea by changing the positions of the ambulances. Before applying the methods on the real-world ambulance problem, a simulation study was performed on synthetic data, aiming at finding the strengths and weaknesses of the different models when applied to different test functions, at different levels of noise. The results showed that we could improve the ambulance response times across several different performance metrics compared to the response times of the current ambulancepositions. This indicates that there exist adjustments that can benefit the pre-hospitalcare in the municipality of Umea. However, since the models in this thesis work find local and not global optimums, there might still exist even better ambulance positions that can improve the response time further. / I denna rapport undersöks teorin och tillämpningarna av diverse blackbox optimeringsmetoder. Mer specifikt så har vi tittat på två familjer av algoritmer, descentmetoder och responsytmetoder (nära besläktade med tillitsregionmetoder). Vi tittar också på möjligheterna att använda en dimensionreduktionsteknik som kallas active subspace som använder samplade gradienter för att göra descentmetoderna mer lämpade för högdimensionella problem, vilket visade sig vara mest effektivt när datat har en struktur där ändringar i endast en riktning har effekt på responsvärdet. Slutligen användes optimeringsmetoderna på ett verkligt problem från sjukhusvården, där målet var att minimera svarstiderna för ambulansutryckningar i Umeå kommun genom att ändra ambulanspositionerna. Innan metoderna tillämpades på det verkliga ambulansproblemet genomfördes också en simuleringsstudie på syntetiskt data. Detta för att hitta styrkorna och svagheterna hos de olika modellerna genom att undersöka hur dem hanterar ett flertal testfunktioner under olika nivåer av brus. Resultaten visade att vi kunde förbättra ambulansernas responstider över flera olika prestandamått jämfört med responstiderna för de nuvarande ambulanspositionerna. Detta indikerar att det finns förändringar av positioneringen av ambulanser som kan gynna den pre-hospitala vården inom Umeå kommun. Dock, eftersom modellerna i denna rapport hittar lokala och inte globala optimala punkter kan det fortfarande finnas ännu bättre ambulanspositioner som kan förbättra responstiden ytterligare.

The last decades have seen an increase in both the amount and complexity of the data used in modern industries in business and technology. A key element for managing these data sets is using machine learning algorithms to process structures and find patterns. Variable selection applies to facilitate and improve these processes by finding and removing redundant variables. One way to achieve this is by eliminating variables based on how much they correlate, a premise for this thesis. This study examines how a reduction of correlated variables affects the predictive accuracy of six different machine learning algorithms. Two demarcations are made. First, the correlation between the explanatory variables is set to a high level and secondly, each variable’s correlation with the dependent variable is set to a modest level. The hypothesis states that removing highly correlated explanatory variables should not negatively affect the accuracy. By conducting a Monte Carlo simulation with three models, each consisting of a different number of correlated variables, the change in accuracy could be compared and evaluated. The result suggests an adverse change in accuracy for all algorithms except one. The differences are relatively low, with the largest accuracy decrease being -5.49 percentage points. The conclusion is that the hypothesis does not hold when the explanatory variables are at a modest level of correlation with the dependent variable.

Driving is a high-risk adventure which many enjoy on a daily basis. The driving task is highly complex, ever-changing, and one which requires continuous attention and rapid decision making. It is a task that is not without risk, where the cost to reach the desired destination can be too great – your life could be at stake. Driving is not without incidents. Rear-end collision is a common problem in the Swedish traffic environment, with over 100 police-reported individual incidents per year. The amount of rear-end collisions can be hypothetically reduced by introducing new technology in the driver’s vehicle, technology which attempts to improve the driver’s safety driving. This technology is called Advanced Driver Assistance Systems – ADAS. In this study two ADAS were evaluated in a driving simulator study: An Adaptive Cruise Control (ACC) which operates on both hazardous and non-hazardous events, and a Collision Warning System (CWS) which operates solely on non-hazardous events. Both of these ADAS function to guard against risky driving and are based on the assumption that drivers will not act in such a manner that they would willingly reduce the effectiveness of the system. A within-subjects simulation study was conducted where participants drove under three conditions: 1) with an adaptive cruise controller, 2) a frontal rear-end collision warning system ADAS, and 3) unaided, in order to investigate differences between the three driving conditions. Particular focus was on whether the two ADAS improved driving safety. The study results indicate that driving enhanced by the two ADAS made the participating drivers drive less safely.

In traditional meta-analysis, a random-effects model is used to deal with heterogeneity and the random-effect is assumed to be normally distributed. However, this can be problematic in the presence of outliers. One solution involves using a heavy tailed distribution for the random-effect to more adequately model the excess variation due to the outliers. Failure to consider an alternative approach to the standard in the presence of unusual or outlying points can lead to inaccurate inference. A heavy tailed distribution is favoured because it has the ability to down-weight outlying studies appropriately, therefore the removal of a study does not need to be considered. In this thesis, the performance of the t-distribution and a finite mixture model are assessed as alternatives to the normal distribution through a comprehensive simulation study. The parameters varied are the average mean of the non-outlier studies, the number of studies, the proportion of outliers, the heterogeneity and the outlier shift distance from the average mean. The performance of the distributions is measured using bias, mean squared error, coverage probability, coverage width, Type I error and power. The methods are also compared through an empirical study of meta-analyses from The Cochrane Library (2008). The simulation showed that the performance of the alternative distributions is better than the normal distribution for a number of scenarios, particularly for extreme outliers and high heterogeneity. Generally, the mixture model performed quite well. The empirical study reveals that both alternative distributions are able to reduce the influence of the outlying studies on the overall mean estimate and thus produce more conservative p-values than the normal distribution. It is recommended that a practitioner consider the use of an alternative random-effects distribution in the presence of outliers because they are more likely to provide robust results. / Thesis / Master of Science (MSc)

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