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Novel regression models for discrete responsePeluso, Alina January 2017 (has links)
In a regression context, the aim is to analyse a response variable of interest conditional to a set of covariates. In many applications the response variable is discrete. Examples include the event of surviving a heart attack, the number of hospitalisation days, the number of times that individuals benefit of a health service, and so on. This thesis advances the methodology and the application of regression models with discrete response. First, we present a difference-in-differences approach to model a binary response in a health policy evaluation framework. In particular, generalized linear mixed methods are employed to model multiple dependent outcomes in order to quantify the effect of an adopted pay-for-performance program while accounting for the heterogeneity of the data at the multiple nested levels. The results show how the policy had a positive effect on the hospitals' quality in terms of those outcomes that can be more influenced by a managerial activity. Next, we focus on regression models for count response variables. In a parametric framework, Poisson regression is the simplest model for count data though it is often found not adequate in real applications, particularly in the presence of excessive zeros and in the case of dispersion, i.e. when the conditional mean is different to the conditional variance. Negative Binomial regression is the standard model for over-dispersed data, but it fails in the presence of under-dispersion. Poisson-Inverse Gaussian regression can be used in the case of over-dispersed data, Generalised-Poisson regression can be employed in the case of under-dispersed data, and Conway-Maxwell Poisson regression can be employed in both cases of over- or under-dispersed data, though the interpretability of these models is ot straightforward and they are often found computationally demanding. While Jittering is the default non-parametric approach for count data, inference has to be made for each individual quantile, separate quantiles may cross and the underlying uniform random sampling can generate instability in the estimation. These features motivate the development of a novel parametric regression model for counts via a Discrete Weibull distribution. This distribution is able to adapt to different types of dispersion relative to Poisson, and it also has the advantage of having a closed form expression for the quantiles. As well as the standard regression model, generalized linear mixed models and generalized additive models are presented via this distribution. Simulated and real data applications with different type of dispersion show a good performance of Discrete Weibull-based regression models compared with existing regression approaches for count data.
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Forecasting Foreign Direct Investment in South Africa using Non-Parametric Quantile Regression ModelsNetshivhazwaulu, Nyawedzeni 16 May 2019 (has links)
MSc (Statistics) / Department of Statistics / Foreign direct investment plays an important role in the economic growth
process in the host country, since foreign direct investment is considered as
a vehicle transferring new ideas, capital, superior technology and skills from
developed country to developing country. Non-parametric quantile regression
is used in this study to estimate the relationship between foreign direct
investment and the factors in
uencing it in South Africa, using the data for
the period 1996 to 2015. The variables are selected using the least absolute
shrinkage and selection operator technique, and all the variables were selected
to be in the models. The developed non-parametric quantile regression models
were used for forecasting the future in
ow of foreign direct investment
in South Africa. The forecast evaluation was done for all models and the
laplace radial basis kernel, ANOVA radial basis kernel and linear quantile
regression averaging were selected as the three best models based on the accuracy
measures (mean absolute percentage error, root mean square error
and mean absolute error). The best set of forecast was selected based on the
prediction interval coverage probability, Prediction interval normalized average
deviation and prediction interval normalized average width. The results
showed that linear quantile regression averaging is the best model to predict
foreign direct investment since it had 100% coverage of the predictions. Linear
quantile regression averaging was also con rmed to be the best model
under the forecast error distribution. One of the contributions of this study
was to bring the accurate foreign direct investment forecast results that can
help policy makers to come up with good policies and suitable strategic plans
to promote foreign direct investment in
ows into South Africa. / NRF
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