An estimate of departmental cost functions

This study presents an estimate of departmental cost functions at selected private liberal arts colleges. Longitudinal data for seven academic departments at 31 institutions were analyzed separately by a multiple regression data analytic procedure. The general least squares estimates are then used to calculate average and marginal costs at the average value for each department. These latter estimates indicate that departmental costs are relatively inelastic, a finding that indicates that the financial problems will be compounded by increases in average departmental costs in an era of enrollment decline.     

Informal faculty-student contact and commuter college freshmen

Based on prior research conducted at residential colleges and universities, nonclassroom informal faculty-student contact appears to be an element of student socialization. This study extends this line of research to a commuter student population. The extent to which informal contact socializes students by influencing their educational aspiration level in a commuter setting is investigated using a longitudinal data collection with the student as unit of analysis. Ordinary least squares and two-stage least squares techniques are used to analyze the data. Significant interactions between informal faculty-student contact and race were found. White and nonwhite students were sbusequently analyzed separately. The ordinary least squares (OLS) multiple regression results suggest that informal contact makes a slight but significant contribution to the explanation of freshmen aspirations for whites, but not for nonwhites. The two-stage least squares (2SLS) analysis suggests that the assumption that contact influences aspiration may not be valid and, indeed, that aspiration level may cause students to seek to initiate informal contact with faculty.     

How Exactly Does Place Matter in Crime Analysis? Place,Space, and Spatial Heterogeneity

This article has four aims. First is to clarify the origins and different meanings of place, space, and other basic concepts in spatial analysis. The second aim is to reiterate the illogicality of the spatial homogeneity assumption in ordinary least squares (OLS) regression. An illustration of the comparison between traditional OLS and geographically weighted regression modeling is included for this purpose. The third aim is to explain that place matters in crime analysis not only when crime data are spatially clustered, but when relationships between correlates are found to be conditional upon place. The final aim is to convince criminology and criminal justice faculty to begin discussing the inclusion of spatial modeling as a compulsory topic in the curriculum.     

Enrollment demand with constrained supply in a higher education institution

Studies of enrollment demand typically assume that public institutions accept all eligible applicants. In that case the coefficients of a regression equation that explains enrollment as a function of variables that affect student demand are properly interpreted as unknown demand function parameters. However, if enrollments are limited by institutional constraints on the supply of places, another approach to estimating student demand behavior is needed. In this paper we develop a model that explains the determination of enrollments in these cases and a way to estimate the coefficients of a student demand equation that is part of the model. The results are much better than those obtained from a conventional model of enrollment demand estimated using ordinary least squares.     

Detecting selection bias,using propensity score matching,and estimating treatment effects: an application to the private returns to a master’s degree

Most research in the area of higher education is plagued by the problem of endogeneity or self-selection bias. Unlike ordinary least squares (OLS) regression, propensity score matching addresses the issue of self-selection bias and allows for a decomposition of treatment effects on outcomes. Using panel data from a national survey of bachelor’s degree recipients, this approach is illustrated via an analysis of the effect of receiving a master’s degree, in various program areas, on wage earning outcomes. The results of this study reveal that substantial self-selection bias is undetected when using OLS regression techniques. This article also shows that, unlike OLS regression, propensity score matching allows for estimates of the average treatment effect, average treatment on the treated effect, and the average treatment on the untreated effect on student outcomes such as wage earnings.     

Analyzing multilevel data: comparing findings from hierarchical linear modeling and ordinary least squares regression

This study examined the differing conclusions one may come to depending upon the type of analysis chosen, hierarchical linear modeling or ordinary least squares (OLS) regression. To illustrate this point, this study examined the influences of seniors’ self-reported critical thinking abilities three ways: (1) an OLS regression with the student as the unit of analysis, (2) an OLS regression with the institution as the unit of analysis, and (3) a three-level hierarchical linear model. Overall, results demonstrate that one would come to substantively different conclusions regarding the influences on students’ perceived critical thinking ability depending upon the type of analysis chosen, especially in regards to the effects of the institutional characteristics.     

Work in college and subsequent wage rates

This is an empirical study of early postenrollment wage determinants of white young men in the 1966 to 1971 period. Data are from the National Longitudinal Survey for young men. The focus is on student labor force status as a determinant of postenrollment wage rates. As such, the results are related to the combined employment and college enrollment goal expressed repeatedly in federal work-study programs from the 1930s to date. Results suggest that work while enrolled may not only support the student, but mitigate transition problems to full-time work after enrollment. The major result, found with OLS multiple regression techniques, is that student job holding significantly and positively increased postenrollment wage rates relative to youth who neither worked nor looked for work as students. This indirect effect implies that the social cost of the college work-study program may be less than the federal outlays if the extra work experience enables a youth to obtain a more productive and higher paying job after enrollment.     

Multilevel Modeling and Ordinary Least Squares Regression: How Comparable Are They?

Studies analyzing clustered data sets using both multilevel models (MLMs) and ordinary least squares (OLS) regression have generally concluded that resulting point estimates, but not the standard errors, are comparable with each other. However, the accuracy of the estimates of OLS models is important to consider, as several alternative techniques (e.g., bootstrapping) used when analyzing clustered data sets only make adjustments to standard errors but not to the regression coefficients. Using a Monte Carlo simulation, we analyzed 54,000 data sets using both MLM and OLS under varying conditions and we show that coefficients of not just OLS models, but MLMs as well, may be biased when relevant higher-level variables are omitted from a model, a situation that is likely to occur when using large-scale, secondary data sets. However, we demonstrate that by including aggregated level-one variables at the higher level, the resulting bias can be effectively removed.     

Modeling Group Differences in OLS and Orthogonal Regression: Implications for Differential Validity Studies

In evaluating the relationship between two measures across different groups (i.e., in evaluating “differential validity”) it is necessary to examine differences in correlation coefficients and in regression lines. Ordinary least squares (OLS) regression is the standard method for fitting lines to data, but its criterion for optimal fit (minimizing the squared vertical distances between the points and the line) is less natural in many contexts than the criterion used in orthogonal regression (minimizing the squared Euclidean distances of points from the line). OLS regression is appropriate if the goal is to predict some unknown dependent variable from a known independent variable, but in examining the relationship between two variables, which both contain error, OLS regression introduces bias. This bias, associated with regression toward the mean, can suggest that the test scores have different relationships, and therefore different meanings, in two groups, when the two sets of test scores have the same relationship and the same meanings in the two groups. The impact of regression toward the mean in differential validity studies is illustrated with two synthetic and two real data sets. Each of the two real data sets include two measures of competence in applying legal principles to fact situations (an essay test and a multiple-choice test) for candidates in two groups (Black/White in the first example and women/men in the second example).     

Ordinary Least Squares and Quantile Regression: An Inquiry-Based Learning Approach to a Comparison of Regression Methods

We present a short, inquiry-based learning course on concepts and methods underlying ordinary least squares (OLS), least absolute deviation (LAD), and quantile regression (QR). Students investigate squared, absolute, and weighted absolute distance functions (metrics) as location measures. Using differential calculus and properties of convex functions, students discover the sample mean, median, and pth quantile by minimizing sums of distances. Students use these metrics to define loss functions for OLS, LAD, and QR, and explore methods to minimize them. We discuss classroom experiences over two semesters. Classroom activities, Maple worksheets, and R demonstration code are available at a companion website.     

Least Squares Models to Correct for Rater Effects in Performance Assessment

This study describes three least squares models to control for rater effects in performance evaluation: ordinary least squares (OLS); weighted least squares (WLS); and ordinary least squares, subsequent to applying a logistic transformation to observed ratings (LOG-OLS). The models were applied to ratings obtained from four administrations of an oral examination required for certification in a medical specialty. For any single administration, there were 40 raters and approximately 115 candidates, and each candidate was rated by four raters. The results indicated that raters exhibited significant amounts of leniency error and that application of the least squares models would change the pass-fail status of approximately 7% to 9% of the candidates. Ratings adjusted by the models demonstrated higher reliability and correlated slightly higher than observed ratings with the scores on a written examination.     

Tests of alignment among assessment,standards, and instruction using generalized linear model regression

An essential component in school accountability efforts is for assessments to be well-aligned with the standards or curriculum they are intended to measure. However, relatively little prior research has explored methods to determine statistical significance of alignment or misalignment. This study explores analyses of alignment as a special case of the generalized linear model (GLM). A general approach for such analyses is suggested, and examples are given for analyses with traditional alignment and GLM regression using data from two previously published studies. Results from the GLM are compared with ordinary least squares (OLS) regression. Findings show that the GLM method allows more informative analysis of differences between source documents than alignment indices alone, including determination of whether marginal discrepancies are statistically significant or not.     

Why might relative fit indices differ between estimators?

Previous research indicates that relative fit indices in structural equation modeling may vary across estimation methods. Sugawara and MacCallum (1993) explained that the discrepancy arises from difference in the function values for the null model with no further derivation given. In this study, we derive explicit solutions for parameters of the null model. The null model specifies the variances of the observed variables as model parameters and fixes all the covariances to be zero. Three methods of estimation are considered: the maximum likelihood (ML) method, the ordinary least squares (OLS) method, and the generalized least squares (GLS) method. Results indicate that ML and LS yield an identical estimator, which is different from GLS. Function values and associated chi‐square statistics of the null model vary across estimation methods. Consequently, relative fit indices using the null model as the reference point in computation may yield different results depending on the estimation method chosen. An illustration example is given and implications of this study are discussed.     

Quasi-experimental estimates of class size effect in primary schools in Poland

In this paper we analyze class size effects in the case of primary schools in Poland. We use two empirical strategies to avoid endogeneity bias. First, we use average class size in a grade as an instrumental variable for actual class size. This allows us to control for within school selection of pupils with different abilities to classes of different sizes. Additionally, we estimate fixed effects for schools to control for differences between them. Second, we exploit the fact that there is an informal maximum class size rule. We estimate class size effect only for those enrollment levels where some schools decide to add a new class and thus dramatically lower class sizes. For such enrollment levels variance of class size is mainly exogenous and we argue that this allows estimation of quasi-experimental class size effects. In this case we again use average class size as an instrument with enrollment as a key control variable. Using both strategies we obtain similar findings. We found that the positive effects observed with OLS regression disappear when we use instrumental variables. If we avoid endogeneity bias, then class size negatively affects student achievement. However, this effect is rather small. We discuss methodology, possible bias of results and the importance of our findings to current policy issues in Poland.     

What Is the Long‐Run Impact of Learning Mathematics During Preschool?

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention‐produced change at age 4 is associated with a 0.24‐SD gain in achievement in late elementary school. This impact is approximately half the size of the association produced by correlational models relating later achievement to preschool math change, and is approximately 35% smaller than the effect reported by highly controlled ordinary least squares (OLS) regression models (Claessens et al., 2009; Watts et al., 2014 ) using national data sets. Implications for developmental theory and practice are discussed.     

Does greater community involvement mean more parent-teacher interaction? Evidence from seven developing countries

Advocates for school autonomy and decentralisation argue that community involvement in school decisions would bring positive educational outcomes by increasing parent-teacher interaction. In this study, I investigate to what extent community involvement associates with parents-teacher personalised meetings in seven developing countries using Programme for International Student Assessment for Development (PISA-D) 2015 data. Employing ordinary least squares (OLS) regression models, I find that the correlation between community engagement in various school activities and parent-teacher interaction is largely insignificant. Findings rather suggest that private ownership and, in some cases, higher instructional resources of schools are associated with increasing parent-teacher communication. These findings remain similar in several specifications suggesting that community involvement as part of decentralising the education sector should not be seen as a panacea for overcoming challenges in schools in developing countries.     

Gender gap in returns to schooling in Palestine

This study provides estimates of the private returns to schooling in Palestine utilizing eight quarterly labor force surveys for 1999 and 2001. This period was chosen to investigate the differential impact of the Israeli closure policy on Palestinian male and female workers. Although gross enrollment ratios for males and females reveal little to no difference in the primary, middle and tertiary levels of schooling, returns to schooling are significantly different. On average, females earned 14–15% less than males in 1999. The gender gap is narrowed during 2001 due to rising male unemployment in the Palestinian areas. Performing the regression for males and females separately, it is found that returns to schooling are larger for women (at least at the margin). The gap in returns to schooling was reduced in 2001; however, female returns to schooling as estimated by OLS suffer from selectivity bias which worsened during 2001. The work in Israel premium increased for women and decreased for men. Finally, Palestinian public sector employment parallels periods of restricted access to Israeli labor markets; its average wages are lower and years of schooling are higher relative to private sector employment.     

自相关问题检验和参数估计方法研究

随机误差项的自相关是计量经济学模型中普遍存在的问题，本文首先分析了自相关的影响和产生原因；其次介绍了虚假自相关和真实自相关的检验方法，分析了各种方法的应用条件、注意事项和优、缺点；然后介绍了存在自相关时，应采用的模型参数估计方法-广义最小二乘法；最后，对自相关问题的检验方法进行总结，指出了它的发展方向。     

经济理论中最小二乘法线性拟合参数估计的等价性问题

在当今西方经济学至少是所谓的"高级"西方经济理论中,数学已经成为阐述理论内容的基本要素或者说是通用语言.线性回归模型是最常用的经济计量模型,用于研究风险、保险、资产组合等经济问题,也可以用作经济预测.本文研究了线性回归模型中的参数估计问题,运用最小二乘法进行参数估计的数学分析基础.最小二乘法只是使用了函数的稳定点而没有运用数学分析的极值理论里的第一充分条件和第二充分条件,本文讨论最小二乘法的估计参数方法和数学分析的极值理论的方法是等价的.     

变系数回归模型的参数估计

讨论了变系数回归模型中变系数的加权最小二乘估计和变系数的加权可估函数的线性估计的最优性;推广了Gauss-Markov定理;并且构造出参数σ2的估计量.