• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.1-11
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• 2012

We present methods to study the log-density ratio of the conditional densities of the predictors given the response variable in the logistic regression model. This allows us to select which predictors are needed and how they should be included in the model. If the conditional distributions are skewed, the distributions can be considered as gamma distributions. A simulation study shows that the linear and log terms are required in general. If the conditional distributions of xjy for the two groups overlap significantly, we need both the linear and log terms; however, only the linear or log term is needed in the model if they are well separated.

• Journal of the Korean Data and Information Science Society
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• v.23 no.1
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• pp.99-111
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• 2012

The log-density ratio of the conditional densities of the predictors given the response variable provides useful information for variable selection in the logistic regression model. In this paper, we consider the predictors that are needed and how they should be included in the model. If the conditional distributions are skewed, the distributions can be considered as gamma distributions. Under this assumption, linear and log terms are generally included in the model. The log-odds graph is a very useful graphical tool in this study. A graphical study is presented which shows that if the conditional distributions of x|y for the two groups overlap significantly, we need both the linear and quadratic terms. On the contrary, if they are well separated, only the linear or log term is needed in the model.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.107-113
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• 2011

We present methods for studying the log-density ratio, which allow us to select which predictors are needed, and how they should be included in the logistic regression model. Under multivariate normal distributional assumptions, we investigate the form of the log-density ratio as a function of many predictors. The linear, quadratic and crossproduct terms are required in general. If two covariance matrices are equal, then the crossproduct and quadratic terms are not needed. If the variables are uncorrelated, we do not need the crossproduct terms, but we still need the linear and quadratic terms.

• Educational Technology International
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• v.15 no.2
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• pp.71-88
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• 2014

A variety of studies to predict students' performance have been conducted since educational data such as web-log files traced from Learning Management System (LMS) are increasingly used to analyze students' learning behaviors. However, it is still challenging to predict students' learning achievement in blended learning environment where online and offline learning are combined. In higher education, diverse cases of blended learning can be formed from simple use of LMS for administrative purposes to full usages of functions in LMS for online distance learning class. As a result, a generalized model to predict students' academic success does not fulfill diverse cases of blended learning. This study compares two blended learning classes with each prediction model. The first blended class which involves online discussion-based learning revealed a linear regression model, which explained 70% of the variance in total score through six variables including total log-in time, log-in frequencies, log-in regularities, visits on boards, visits on repositories, and the number of postings. However, the second case, a lecture-based class providing regular basis online lecture notes in Moodle show weaker results from the same linear regression model mainly due to non-linearity of variables. To investigate the non-linear relations between online activities and total score, RF (Random Forest) was utilized. The results indicate that there are different set of important variables for the two distinctive types of blended learning cases. Results suggest that the prediction models and data-mining technique should be based on the considerations of diverse pedagogical characteristics of blended learning classes.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.401-411
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• 2007

In this paper we propose an influence measure for detecting potentially influential observations using the infinitesimal perturbation and the local influence in the log-linear regression model. Also, we propose a goodness-of-fit measure for variable selection. A real data set are used for illustration.

• Preventive Nutrition and Food Science
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• v.13 no.2
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• pp.104-111
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• 2008

As a way to account for the variability of the primary model parameters in the secondary modeling of microbial growth, three different regression approaches were compared in determining the confidence interval of the temperature-dependent primary model parameters and the estimated microbial growth during storage: bootstrapped regression with all the individual primary model parameter values; bootstrapped regression with average values at each temperature; and simple regression with regression lines of 2.5% and 97.5% percentile values. Temperature dependences of converted parameters (log $q_o$, ${\mu}_{max}^{1/2}$, log $N_{max}$) of hypothetical initial physiological state, maximum specific growth rate, and maximum cell density in Baranyi's model were subjected to the regression by quadratic, linear, and linear function, respectively. With an advantage of extracting the primary model parameters instantaneously at any temperature by using mathematical functions, regression lines of 2.5% and 97.5% percentile values were capable of accounting for variation in experimental data of microbial growth under constant and fluctuating temperature conditions.

• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.141-149
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• 2013

We present methods for studying the log-density ratio that enables the selection of the predictors and the form to be included in the logistic regression model. Under bivariate normal distributional assumptions, we investigate the form of the log-density ratio as a function of two predictors. If two covariance matrices are equal, then the crossproduct and quadratic terms are not needed. If the variables are uncorrelated, we do not need the crossproduct terms, but we still need the linear and quadratic terms. We also explore other conditions in which the crossproduct and quadratic terms are not needed in the logistic regression model.

• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.775-791
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• 2017

We frequently encounter binary data in real life. Logistic, Probit, Cauchit, Complementary log-log models are often used for binary data analysis. In order to analyze binary data, Liu (2004) proposed a Robit model, in which the inverse of cdf of the Student's t distribution is used as a link function. Kim et al. (2008) also proposed a generalized t-link model to make the binary regression model more flexible. The more flexible skewed distributions allow more flexible link functions in generalized linear models. In the sense, we propose a binary data regression model using skewed generalized t distributions introduced in Theodossiou (1998). We implement R code of the proposed models using the glm function included in R base and R sgt package. We also analyze Pima Indian data using the proposed model in R.

• Journal of Korea Water Resources Association
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• v.41 no.8
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• pp.807-823
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• 2008

This paper presents a technique for estimating discharge rating curve parameters. In typical practical applications, the original non-linear rating curve is transformed into a simple linear regression model by log-transforming the measurement without examining the effect of log transformation. The model of pseudo-likelihood estimation is developed in this study to deal with heteroscedasticity of residuals in the original non-linear model. The parameters of rating curves and variance functions of errors are simultaneously estimated by the pseudo-likelihood estimation(P-LE) method. Simulated annealing, a global optimization technique, is adapted to minimize the log likelihood of the weighted residuals. The P-LE model was then applied to a hypothetical site where stage-discharge data were generated by incorporating various errors. Results of the P-LE model show reduced error values and narrower confidence intervals than those of the common log-transform linear least squares(LT-LR) model. Also, the limit of water levels for segmentation of discharge rating curve is estimated in the process of P-LE using the Heaviside function. Finally, model performance of the conventional log-transformed linear regression and the developed model, P-LE are computed and compared. After statistical simulation, the developed method is then applied to the real data sets from 5 gauge stations in the Geum River basin. It can be suggested that this developed strategy is applied to real sites to successfully determine weights taking into account error distributions from the observed discharge data.

• Bulletin of the Korean Chemical Society
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• v.26 no.1
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• pp.139-145
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• 2005

Artificial neural networks (ANNs), for a first time, were successfully developed for the modeling and prediction of solvent effects on rate constant of [2+2] cycloaddition reaction of diethyl azodicarboxylate with ethyl vinyl ether in various solvents with diverse chemical structures using quantitative structure-activity relationship. The most positive charge of hydrogen atom (q$^+$), dipole moment ($\mu$), the Hildebrand solubility parameter (${\delta}_H^2$) and total charges in molecule (q$_t$) are inputs and output of ANN is log k$_2$ . For evaluation of the predictive power of the generated ANN, the optimized network with 68 various solvents as training set was used to predict log k$_2$ of the reaction in 16 solvents in the prediction set. The results obtained using ANN was compared with the experimental values as well as with those obtained using multi-parameter linear regression (MLR) model and showed superiority of the ANN model over the regression model. Mean square error (MSE) of 0.0806 for the prediction set by MLR model should be compared with the value of 0.0275 for ANN model. These improvements are due to the fact that the reaction rate constant shows non-linear correlations with the descriptors.