Tak K. Mak

Knowledge Management Systems Development: Theory and Practice

The intricate crafting of online educational systems lie within three principal activities: Design of the system, implementation, and proper post-implementation assessment. There is not enough knowledge or experience in all regards. Efficient execution of these three major activities necessitates the use of design and pedagogical models to achieve cost and time efficiency, as well as high pedagogical quality. Models represent a structured approach to analysis and promote quantifiable feedback that can be monitored. Components of an online educational system would benefit from a design process. Similarly, utilization of the online educational system would benefit from a structured approach to design, implementation, and student’s assessment. Following the technology adoption theory, understanding individual’s behavior towards technology usage would focus on instrumental beliefs driving intentions. However, this may not be the case with online educational systems because the context and setup is significantly different from previous technology adoption studies. Therefore, the implementation of an online educational system should be designed based on established pedagogical principles, and once developed the assessment of students’ behavior should be monitored using management information systems methodology. In this paper, we present the design of an online education system, and the experience of the students using the system. A survey methodology approach is followed and assessment results are discussed. The technology acceptance model and the theory of planned behavior were used to identify significant constructs as antecedents to intentions. Scale validation for both models indicates that the operational measures have acceptable psychometric properties. Confirmatory factor analysis supports both models. Structural equation analysis provides evidence for the superiority of the theory of planned behavior in explaining students’ behavior towards educational online systems. Limitation, implications, design recommendations, and suggestions for future research are then discussed.

A functional approach to estimating finite population distribution functions

Existing estimators of a finite population distribution function that utilize auxiliary information are often constructed by a point wise argument. As a result, these estimators are not always monotone. We adopt a functional approach to the problem and propose two estimators based on compositions of functions. Asymptotic variance formulae are derived for the proposed es-timators. Comparisons are made with existing estimators in a simulation study using three natural populations.

Modeling and estimating variances in regression

ABSTRACT It is well known that ignoring heteroscedasticity in regression analysis adversely affects the efficiency of estimation and renders the usual procedure for constructing prediction intervals inappropriate. In some applications, such as off-line quality control, knowledge of the variance function is also of considerable interest in its own right. Thus the modeling of variance constitutes an important part of regression analysis. A common practice in modeling variance is to assume that a certain function of the variance can be closely approximated by a function of a known parametric form. The logarithm link function is often used even if it does not fit the observed variation satisfactorily, as other alternatives may yield negative estimated variances. In this paper we propose a rich class of link functions for more flexible variance modeling which alleviates the major difficulty of negative variances. We suggest also an alternative analysis for heteroscedastic regression models that exploits the principle of “separation” discussed in Box (Signal-to-Noise Ratios, Performance Criteria and Transformation. Technometrics 1988, 30, 1–31). The proposed method does not require any distributional assumptions once an appropriate link function for modeling variance has been chosen. Unlike the analysis in Box (Signal-to-Noise Ratios, Performance Criteria and Transformation. Technometrics 1988, 30, 1–31), the estimated variances and their associated asymptotic variances are found in the original metric (although a transformation has been applied to achieve separation in a different scale), making interpretation of results considerably easier.

Estimation procedures for categorical survey data with nonignorable nonresponse

We consider surveys with one or more callbacks and use a series of logistic regressions to model the probabilities of nonresponse at first contact and subsequent callbacks. These probabilities are allowed to depend on covariates as well as the categorical variable of interest and so the nonresponse mechanism is nonignorable. Explicit formulae for the score functions and information matrices are given for some important special cases to facilitate implementation of the method of scoring for obtaining maximum likelihood estimates of the model parameters. For estimating finite population quantities, we suggest the imputation and prediction approaches as alternatives to weighting adjustment. Simulation results suggest that the proposed methods work well in reducing the bias due to nonresponse. In our study, the imputation and prediction approaches perform better than weighting adjustment and they continue to perform quite well in simulations involving misspecified response models.

Heteroscedastic regression models with non-normally distributed errors

Although regression estimates are quite robust to slight departure from normality, symmetric prediction intervals assuming normality can be highly unsatisfactory and problematic if the residuals have a skewed distribution. For data with distributions outside the class covered by the Generalized Linear Model, a common way to handle non-normality is to transform the response variable. Unfortunately, transforming the response variable often destroys the theoretical or empirical functional relationship connecting the mean of the response variable to the explanatory variables established on the original scale. Further complication arises if a single transformation cannot both stabilize variance and attain normality. Furthermore, practitioners also find the interpretation of highly transformed data not obvious and often prefer an analysis on the original scale. The present paper presents an alternative approach for handling simultaneously heteroscedasticity and non-normality without resorting to data transformation. Unlike classical approaches, the proposed modeling allows practitioners to formulate the mean and variance relationships directly on the original scale, making data interpretation considerably easier. The modeled variance relationship and form of non-normality in the proposed approach can be easily examined through a certain function of the standardized residuals. The proposed method is seen to remain consistent for estimating the regression parameters even if the variance function is misspecified. The method along with some model checking techniques is illustrated with a real example.

Maximum likelihood estimation of familial correlations

The “correlated random effects model” is discussed for analysing familial data with an arbitrary number of classes of possibly variable sizes. It is seen that the maximum likelihood estimates of the parameters can be numerically computed through the EM algorithm. Explicit expressions for the Hessian matrix and Fishers information matrix are obtained, so that both the Newton-Raphson and the scoring algorithms can be directly implemented. It is seen theoretically and numerically that the scoring algorithm takes very few iterations to converge, regardless of the choice of starting values. The EM algorithm, on the other hand, has the potential to handle very large problems. The connection of this model with the classical common correlation model is discussed. Through a mathematical equivalence between the two models, the maximum likelihood estimates of the common correlation model can be computed as simple functions ofthe estimates found in the correlated random effect model. This alternative approach of com...

Assessment of an Online Education System – Comparing Two Theoretical Models

The intricate construction of online educational systems lies within three principal activities: Design, implementation and proper post-implementation assessment. There is not enough knowledge or experience in those regards. Efficient execution of these three major activities necessitates the use of design and pedagogical models to achieve cost and time efficiency, as well as high pedagogical quality. Utilization of online educational systems would benefit from a structured approach to design, implementation, and student’s assessment. In this paper, we present the design of an online education system and its implementation, and we analyze student’s behavior towards the system using the theory of planned behavior and the technology acceptance model. A survey methodology approach was followed. The partial least squares method was used for the assessment of the results discussed. Structural equation analysis provides evidence for the superiority of the theory of planned behavior in explaining student’s behavior towards online educational systems. Limitation, implications, design recommendations, and suggestions for future research are discussed.

Monte Carlo Approximations of the Quantiles of a Sample Statistic

We consider in this article the problem of numerically approximating the quantiles of a sample statistic for a given population, a problem of interest in many applications, such as bootstrap confidence intervals. The proposed Monte Carlo method can be routinely applied to handle complex problems that lack analytical results. Furthermore, the method yields estimates of the quantiles of a sample statistic of any sample size though Monte Carlo simulations for only two optimally selected sample sizes are needed. An analysis of the Monte Carlo design is performed to obtain the optimal choices of these two sample sizes and the number of simulated samples required for each sample size. Theoretical results are presented for the bias and variance of the numerical method proposed. The results developed are illustrated via simulation studies for the classical problem of estimating a bivariate linear structural relationship. It is seen that the size of the simulated samples used in the Monte Carlo method does not have to be very large and the method provides a better approximation to quantiles than those based on an asymptotic normal theory for skewed sampling distributions.