Using Wherry's Adjusted R 2 and Mallow's Cp for Model Selection From All Possible Regressions

Selecting a subset of predictors from a pool of potential predictors continues to be a common problem encountered by applied researchers in education. Because of several limitations associated with stepwise variable selection procedures, the examination of all possible regression solutions has been recommended. The authors evaluated the use of Mallow's C_p and Wherry's adjusted R ² statistics to select a final model from a pool of model solutions. Neither the C_p nor the adjusted R ² statistic correctly identified the underlying regression model any better and was generally worse than the stepwise selection method, which itself was poor. Using any of the model selection procedures studied here resulted in biased estimates of the authentic regression coefficients and underestimation of their standard errors. The use of theory and professional judgment is recommended for the selection of variables in a prediction equation.     

The Koppitz developmental scoring system for the Bender-Gestalt: Is it developmental?

The Bender-Gestalt was administered individually to 652 children, aged 5 to 11 years. The protocols were subsequently scored using the Koppitz Developmental System. A sample of scores were fitted to various developmental curves using a computer program called DATAFIT. The data approximated a curvilinear regression line more than a linear regression line. The R² for the total sample and for various combinations of age groups was relatively low. Implications regarding the limitations of various interpretive procedures were discussed.     

Putting ourselves on the line: the epistemology of the hyphen,intersubjectivity and social responsibility in qualitative research

As researchers, we are intertwined in our research relationships in two ways that put us on the line. First, our very beings are co-constituted and developed in an intersubjective exchange with the people we work with. Acknowledging our interdependence frees us to take an empathetic and hermeneutic stance that I have termed the epistemology of the hyphen, in our qualitative research relationships, and in the process, reject the objectivist, dissociative mode of procuring research. Instead, we produce knowledge that is socially responsible by virtue of its grounding in empathy and care. Second, I suggest that we are also on the line when it comes to the relationship between ourselves, and our audiences. The constraints and freedoms that contour our voices as qualitative researchers shape not only the stories we tell about our participants, but also ourselves as human beings. We must incorporate affect into our reports for them to do justice to ourselves, our readers and listeners, and our participants.     

Experiencing the outdoors: peak episodes are interesting but the memories are pleasant

Inspired by the distinction between hedonic and eudaimonic feeling states, we examined the distinction between feelings of pleasure and interest as well as subsequent motivation related to participation in outdoor events among students of physical education (n = 64) in a Norwegian university college. The students reported on their experiences during two three-day trips: one coastal trip and one ski trip. The participants also reported how they felt about the trips after one week and after one month. The feelings of pleasure and interest were contrasted by analysing mean scores, factor loadings and regression coefficients. Momentary experiences typically showed higher scores for feelings of interest than for feelings of pleasure, but there were some exceptions. The interest-higher-than-pleasure tendency tended to disappear for remembered experiences. The results support the notion that pleasure and interest are separable emotions with distinct functions, but our findings are far from conclusive. Implications for outdoor leadership and future research are discussed.     

混合流体完备方程组的局部解析解

With the straification theory we have proved the transversal layer s03,k(D) of complete equations for mixed fluid is not an empty set: s03,k(D)≠φfor all k(k≥1). Based on this conclusion and the "secondary equation" of s03,k(D), this paper fully presents the expressions of coefficients in all local analytic solutions of the equations. Therefore we provide the calculation formulas by which we can get the numerical solutions to any desired accuracy.     

On some projectively flat polynomial （α,β）-metrics

In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α a1β a2β2/α a4β4/α3 to be projectively flat, where ai (i=1,2,4) are constants with a1≠0, α is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.     

A blended model: simultaneously teaching a quantitative course traditionally,online, and remotely

As universities seek to bolster enrollment through distance education, faculty are tasked with maintaining comparable teaching/learning standards in traditional, blended, and online courses. Research has shown that there is an achievement gap between students taking courses exclusively offered online versus those enrolled in face-to-face classes. In an effort to mitigate these observed differences, the School of Business faculty at the research institution investigated various course models to meet the needs of a diverse, non-traditional, and multifaceted student population. Ultimately, a blended course model for statistics and quantitative method courses was developed that allowed students to choose between online, remote (via interactive television), and traditional course delivery modes each week. This model is more flexible and agile than existing blended courses that have more static components. Multiple regression analysis, χ², and t-tests are used to demonstrate the efficacy of our model in maintaining student performance standards.     

Application of land use regression for estimating concentrations of major outdoor air pollutants in Jinan, China

SO2, NO2, and PM10 are the major outdoor air pollutants in China, and most of the cities in China have regulatory monitoring sites for these three air pollutants. In this study, we developed a land use regression （LUR） model using regulatory monitoring data to predict the spatial distribution of air pollutant concentrations in Jinan, China. Traffic, land use and census data, and meteorological and physical conditions were included as candidate independent variables, and were tabulated for buffers of varying radii. SO2, NO2, and PM10 concentrations were most highly correlated with the area of industrial land within a buffer of 0.5 km （R2=0.34）, the distance from an expressway （R2=0.45）, and the area of residential land within a buffer of 1.5 km （R2=0.25）, respectively. Three multiple linear regression （MLR） equations were established based on the most significant variables （p〈0.05） for SO2, NO2, and PM10, and R2 values obtained were 0.617, 0.640, and 0.600, respectively. An LUR model can be applied to an area with complex terrain. The buffer radii of independent variables for SO2, NO2, and PM10 were chosen to be 0.5, 2, and 1.5 kin, respectively based on univariate models. Intercepts of MLR equations can reflect the background concentrations in a certain area, but in this study the intercept values seemed to be higher than background concentrations. Most of the cities in China have a network of regulatory monitoring sites. However, the number of sites has been limited by the level of financial support available. The results of this study could be helpful in promoting the application of LUR models for monitoring pollutants in Chinese cities.     

How a Dummy Replaces a Student's Test and Gets an F (Or,How Regression Substitutes for t tests and ANOVA)

Using dummy variables, this note offers a convenient illustration to demonstrate that regression can replace both the one‐factor analysis of variance and the two‐population t test with independent random samples. The exercise also helps to develop students’ intuition regarding regression coefficients.     

THE FORCED-FREE DISTINCTION IN Q TECHNIQUE1

Arguments favoring free- over forced-distribution Q sorts have assumed that forcing leads to loss of important statistical information and interferes with interval properties, rendering Pearson's r inappropriate for analysis. Q sorts with identical item orderings but with varied distributions are shown to provide essentially the same correlations and factor structures when coefficients are computed using Spearman's r^s, Kendall's τ, and Pearson's r, leading to the conclusion that the same results are obtained, despite distribution and whether interval or ordinal statistics are used.     

Estimating the Coefficient of Cross-Validity in Multiple Regression: A Comparison of Analytical and Empirical Methods

In predictive applications of multiple regression, interest centers on the estimation of the population coefficient of cross-validation rather than the population multiple correlation. The accuracy of 3 analytical formulas for shrinkage estimation (Ezekiel, Browne, & Darlington) and 4 empirical techniques (simple cross-validation, multicross-validation, jackknife, and bootstrap) were investigated in a Monte Carlo study. Random samples of size 20 to 200 were drawn from a pseudopopulation of actual field data. Regression models were investigated with population coefficients of determination ranging from .04 to .50 and with numbers of regressors ranging from 2 to 10. For all techniques except the Browne formula and multicross-validation, substantial statistical bias was evident when the shrunken R ² values were used to estimate the coefficient of cross-validation. In addition, none of the techniques examined provided unbiased estimates with sample sizes smaller than 100, regardless of the number of regressors.     

Estimation method for mixed-effect coefficient semiparametric regression model

Consider the mixed-effect coefficient semiparametric regression modelZ=X'α+Y'β+g(T)+e, whereX, Y andT are random vectors onR ^p×R ^q×[0, 1], α is a p-dimensional fixed-effect parameter, β is a q-dimensional random-effect parameter (Eβ=b, Cov(β)=Σ),g(.) is an unknown function on [0, 1], e is a random error with mean zero and variance σ², and (X, Y, T) and (β,e), β ande are mutually independent. We estimate α,b andg(.) by the nearest neighbor and the least square method. In this paper, we prove that estimations of α,b have asymptotic normality and obtain the best convergence raten ^−1/3 for the estimation ofg(.). Project supported by the NSFC and the Natural Science Foundation of Zhejiang Province.     

Monte Carlo Confidence Intervals for Complex Functions of Indirect Effects

One challenge in mediation analysis is to generate a confidence interval (CI) with high coverage and power that maintains a nominal significance level for any well-defined function of indirect and direct effects in the general context of structural equation modeling (SEM). This study discusses a proposed Monte Carlo extension that finds the CIs for any well-defined function of the coefficients of SEM such as the product of k coefficients and the ratio of the contrasts of indirect effects, using the Monte Carlo method. Finally, we conduct a small-scale simulation study to compare CIs produced by the Monte Carlo, nonparametric bootstrap, and asymptotic-delta methods. Based on our simulation study, we recommend researchers use the Monte Carlo method to test a complex function of indirect effects.     

Comparing Squared Multiple Correlation Coefficients Using Structural Equation Modeling

In social science research, a common topic in multiple regression analysis is to compare the squared multiple correlation coefficients in different populations. Existing methods based on asymptotic theories (Olkin & Finn, 1995) and bootstrapping (Chan, 2009) are available but these can only handle a 2-group comparison. Another method based on structural equation modeling (SEM) has been proposed recently. However, this method has three disadvantages. First, it requires the user to explicitly specify the sample R² as a function in terms of the basic SEM model parameters, which is sometimes troublesome and error prone. Second, it requires the specification of nonlinear constraints, which is not available in some popular SEM software programs. Third, it is for a 2-group comparison primarily. In this article, a 2-stage SEM method is proposed as an alternative. Unlike all other existing methods, the proposed method is simple to use, and it does not require any specific programming features such as the specification of nonlinear constraints. More important, the method allows a simultaneous comparison of 3 or more groups. A real example is given to illustrate the proposed method using EQS, a popular SEM software program.     

Decomposition in blocks at the level of wavelet coefficients andT(1) theorem on Hardy space

This paper deals with the establishment ofT(1) theorem on Hardy spaceH ¹ under condition of weak regularity. An operator or a function is identified on the basis of their wavelet coefficients which are regrouped on some blocks. The actions of each block operator (pseudo-annular operator) on each block function (atom) are exactly analyzed to establishT(1) theorem on Hardy space. Project supported by the National Natural Science Foundation of China (No. 1000102) and Education Ministry of China.     

Mini-research Experience in Simple Linear Regression

Within the undergraduate mathematics curriculum, the topic of simple least-squares linear regression is often first encountered in multi-variable calculus where the line of best fit is obtained by using partial derivatives to find the slope and y-intercept of the line that minimizes the residual sum of squares. A markedly different approach from linear algebra, which could also be introduced in multi-variable calculus, obtains the regression line by vector projection. The latter viewpoint offers elegant proof of the equation relating the total, explained and unexplained variations. Consideration of data with the same regression line and correlation opens the door for a “mini-research experience” (MRE). A sequel MRE gives rise to an open Research Experience for Undergraduates topic to analyze reflection sequences and a fundamental connection between complex analysis and regression analysis. A few general guidelines and basic goals for MREs are included for those whose main interest is in undergraduate research.     

Educational Forecasting at the University of Akron

The purpose of this study was to examine the power of quality of learning experience (QLE) indicators in predicting juniors’ and seniors’ persistence and attrition and to identify the relative salience of each of the QLE components in explaining persistence. Two different models were defined and assessed: the compensatory model and the multiple hurdles model. The models were tested using logistic regression and discriminant analysis. The major findings of the study were: (a) QLE indicators played a significant role in predicting juniors’ and seniors’ persistence. The R² coefficients for the compensatory and multiple hurdles models were 0.32 and 0.37, respectively, whereas the percentages of correct classifications were 85% and 88%. (b) The predictability and classification power were weaker for the compensatory model and stronger for the multiple hurdles framework. (c) The three dominant predictors of juniors’ and seniors’ persistence were student-faculty contact, students’ involvement in their academic program, and the content of that program. The implications of this study are explored.     

Benefits for coteachers of students with disabilities: Do contextual factors matter?

Drawing on Bandura’s social learning and social cognitive theory, we empirically investigate contextual factors that may influence perceived benefits of coteaching for teachers. Special and general education coteachers have reported that necessary contextual factors for them to be effective include: sufficient coplanning time, relationship quality, and parity. In this study, 147 special and general education coteachers from suburban and rural schools across the United States responded to the Co‐teacher Questionnaire to determine what contributes to their perceived benefits of coteaching students with disabilities. Hierarchical linear regression analyses indicated that coplanning ( β = 0.22; p ≤ 0.01) and relationship quality ( β = 0.30; p ≤ 0.01) positively influenced the coteachers’ perceived benefits of coteaching (Cohen’s f ² = 0.47), whereas parity was not corroborated to have a significant impact. These not previously empirically studied relationships inform the field by clarifying the importance of the contextual factors for coteachers. Implications for the practitioners and researchers are offered.     

I feel,therefore I teach? Teachers’ conceptions of the relationships between emotions and teaching/learning processes / ¿Siento,luego enseño? Concepciones docentes sobre las relaciones entre las emociones y los procesos de enseñanza/aprendizaje

During recent decades a shift in focus has been occurring that questions the historical cognitive-emotional dualism present in our culture and revalues the role of emotions in education. With this situation in mind, we wanted to discover what conceptions teachers have of the relationships existing between those emotions and the teaching-learning process. Given our cultural tradition, we depart from the assumption that it may be possible to differentiate the conceptions according to more or less integrated perspectives regarding the affective and cognitive functions in educational context. With the aim of identifying conception profiles and describing their specific characteristics, we interviewed 32 teachers whose discourses were categorized and statistically analysed using clustering and X². The results are interpreted to account for a progression shaped by four types of conceptions ranging from perspectives that are not concerned with emotions, to others believing inseparability exists between affective and cognitive functions. Implications for future studies are then analysed from the obtained results.