SAS R IML (Introduction at the Master s Level)

Transcription

1 SAS R IML (Introduction at the Master s Level) Anton Bekkerman, Ph.D., Montana State University, Bozeman, MT ABSTRACT Most graduate-level statistics and econometrics programs require a more advanced knowledge of analytical and programming skills than the skills taught in undergraduate courses. However, many students enter graduate programs without these skills. This creates challenges for both students and instructors, as each seeks to balance teaching (learning) both theoretical concepts and the skills to apply those concepts empirically. One approach to improve the development of those skills in incoming graduate students is by holding a rigorous, targeted SAS mini-course prior to the beginning of a teaching semester. The mini-course enables instructors to focus only on helping students develop SAS skills, thus improving the efficiency and effectiveness of the learning process. Moreover, the course provides an opportunity to teach more advanced concepts, including the use of the interactive matrix language (IML) and the macro language. These advanced skills can aid in students abilities to grasp a more detailed understanding of complex statistical and econometric topics. This paper provides an overview of a SAS mini-course offered to students entering the Master s of Applied Economics program at Montana State University. INTRODUCTION Most economics and statistics master s degree programs are expected to be completed by students within months. In programs that require a master s thesis, students must have a set of empirical analysis skills that are necessary to efficiently and effectively conduct research. An example of such skills is the ability to manage data and develop code for statistical analyses. However, the required skill level for graduate students is often different from that expected by undergraduates. For example, in undergraduate econometrics courses, linear regression models are frequently introduced using summation notation and students are taught to estimate these models using statistical analysis packages (e.g., the REG procedure). Graduate level courses, however, typically require that students develop a deeper understanding of regression models, often within a matrix algebra context. Many students begin their graduate programs without these skills, resulting in two common outcomes. One outcome is that students must independently learn the analytical tools to complete assignments. A second outcome is that teachers provide some coding instruction, but it may be significantly limited and unstructured because there is a limited amount of time allocated to discussion theoretical topics and applied techniques. In both cases, the knowledge of necessary empirical skills may be reduced, students may obtain an incomplete understanding of when and how the skills should be applied, and there may be a general reduction in the quality of instruction. Consequently, an alternative approach may be necessary to introduce students to the use of statistical analysis in order to minimize the challenges faced by both students and instructors. One such approach is to develop a rigorous, focused mini-course that would introduce, train, and provide practice in statistical analysis software prior to the beginning of a semester-long statistics or econometrics class. At Montana State University (MSU), this concept was implemented to create a SAS boot camp for incoming students in the Master s of Applied Economics program. The boot camp introduces students to the basics of SAS software as well as provides instruction for more advanced topics, including the interactive matrix language (IML) and the macro language. The focused mini-course offers several important benefits. First, students are more comfortable and less time-constrained in completing empirically-based assignments during the semester. Because students are less consumed in grasping coding concepts while completing these assignments, they are more able to understand the underlying statistical and econometric concepts, improving their overall knowledge, the quality of their work, and allowing for more rigorous inclass discussions. Second, instructors are better able to structure lectures and the associated content. For example, lectures could be effectively enhanced by showcasing SAS examples during class time without the need to explain the underlying code. This paper provides an example of a SAS boot camp developed specifically for graduate students. The primary intent is to introduce the concept and structure of an advanced mini-course and motivate a constructive discussion for improving its effectiveness and making the course structure generalizable for other institutions. Additionally, because graduates of many statistics and economics master s programs immediately enter the labor force, input from representatives of industries that hire these graduates can offer further insight into ways to improve SAS instruction at the graduate level. 1

2 AUDIENCE AND OBJECTIVES The participants are students entering a graduate level statistics or economics program. The level of programming expertise and knowledge of SAS are assumed to be minimal or non-existent for most students. Some students, however, may have experience with other statistical computing software such as the R language or STATA R, knowledge of which is commonly acquired in undergraduate statistics and/or econometrics courses. All mini-course participants are expected to have successfully completed at least one course or have strong familiarity with linear algebra. At the conclusion of a mini-course, there are three major objectives. First, students are expected to have familiarity with SAS and a number of basic data management and statistical analysis techniques. Second, students should be comfortable using the IML procedure for manipulating matrices, using loops and conditional statements, and transferring data sets to and from IML. Lastly, students should become familiar with locating and interpreting SAS documentation. The three objectives are intended to allow all participating students to attain a similar foundation of SAS knowledge and programming skills, which will enable them to successfully complete empirical assignments, follow class lectures that rely on SAS-based demonstrations, and locate and implement additional information that will assist in completing more advanced tasks. LECTURE ENVIRONMENT The SAS boot camp is held prior to the start of a semester or term, because the goal of mini-course is to be preparatory rather than an accompaniment to a course throughout the semester. This format helps students focus on learning and understanding SAS and programming fundamentals. The mini-course consists of 2-3 sessions, with each session lasting 1-2 hours. Students meet in a computer lab and have access to SAS. The instructor s computer screen is displayed to the students. All students are provided with a resource packet containing information and code presented throughout the minicourse. For example, a resource packet used at Montana State University can be accessed at the following URL: basics.pdf. The packet is intended to be both a guide used throughout the boot camp as well as a resource for students during and after the semester. That is, the provided information not only offers students an opportunity to more easily follow the presentation of materials during the minicourse, but it also enables each student to reference standardized notes after the conclusion of the boot camp. Feedback from students who have completed the course provides evidence that a customized set of notes increases students abilities to efficiently and effectively recall programming techniques. That is, because the mini-course follows a customized guide, students are better able to locate information after the completion of the boot camp than if they were required to search other resources. CONTENT The content of a graduate level introductory SAS mini-course should contain and be structured in a manner that will maximize students abilities to succeed in an intended statistics or econometrics course. For the first econometrics course in the Master s in Applied Economics program at Montana State University, the mini-course seeks to provide strong foundations in three areas: data management, visual representation of data, and the empirical application of linear algebra. An overview of the econometrics course and lecture notes can be accessed at the following URL: notes.pdf. Figure 1 provides an overview of the mini-course structure and associated topics. As with most introductory SAS courses, the boot camp first provides an overview of the SAS system, discusses basic techniques for writing code using the enhanced editor, and offers tips for basic troubleshooting. This provides an important foundation for understanding the manner in which the SAS system reads and processes commands critical knowledge that improves the efficacy of teaching advanced topics. Furthermore, a substantial amount of time during the first mini-course session is dedicated to teaching data management skills, including importing, creating and storing data sets, manipulating columns and rows, merging and appending data sets, and exporting data. In addition to fundamental data management skills, the mini-course introduces students to techniques for visualizing basic data information. These techniques are both analytical and graphical data summarization. For example, the MEANS, UNIVARIATE, and FREQ are presented and interpretation of output is discussed. Furthermore, the students are introduced to the SGPLOT and SGPANEL procedures for conducting visual data analysis. The graphical procedures 2

3 Figure 1: Structure of a SAS Boot Camp at Montana State University are intended to parallel and complement results of the analytical data summarization. For example, the graphical procedures are used to produce scatter, series, and bar charts as well as histograms and fitted densities. A significant departure from basic SAS techniques is the instruction of advanced topics, including the use of the IML procedure and the macro language. Unlike most undergraduate econometrics courses, many graduate-level classes use matrix algebra to teach underlying topics and interpretations. Consequently, many assignments ask students to use matrix algebra to solve problems and prove concepts. In many cases, it is useful (if not necessary) to assign problems that cannot be completed by hand (i.e., inverting matrices with dimensions greater than 3 3) or to ask students to explicitly illustrate a particular concept. For example, students who have successfully completed an undergraduate econometrics course (which uses SAS) would estimate a linear regression model Y = Xβ +ε using the REG procedure. The procedure s output conveniently displays parameter estimates, associated t statistics, p-values, and other useful inferences. At the graduate-level, students are required to understand the underlying concepts of the REG procedure that is, solving the classic equation β = (X X) 1 X Y and determining the associated inference statistics. That is, during the course, students would be assigned tasks that would require them to construct code resembling the following. b = inv(x *x)*x *y; *Beta_hat; e = y - x*b; *Regression residuals; y_hat = x*b; *Predicted values; var = ((e *e)/(nrow(y)-ncol(x)))*inv(x *x); *Covariance matrix ; /* Inferences */ se = sqrt(vecdiag(var)); *Standard errors; t = b/se; *t-statistics; p = 2*(1 - cdf("t",abs(t),nrow(y)-ncol(x))); *p-values; /* R-squared, AIC, and BIC measures */ R_sq = 1 - ((e *e)/(nrow(y)-ncol(x)))/(((y - y[:,]) *(y - y[:,]))/(nrow(y)-1)); AIC = log((e *e)/nrow(y)) + (2*ncol(x)/nrow(y)); BIC = log((e *e)/nrow(y)) + (ncol(x)/nrow(y))*log(nrow(y)); /*Confidence intervals: ci = [LB,UB] */ ci = (b - tinv(0.995,nrow(y)-ncol(x))#se) (b + tinv(0.995,nrow(y)-ncol(x))#se); 3

4 The boot camp is intended to provide the technical foundation for students to be able to develop the above code. At Montana State University, the following concepts are reviewed: Constructing vectors and matrices. Manipulating vectors and matrices. Appending and sub-setting vectors and matrices. Constructing special vectors and matrices, such as an identity matrix or a vector of ones. Understanding matrix operations, including the difference between matrix and elementwise operations. Importing and exporting SAS datasets into and from the IML procedure. Generating simple summary statistics. Using loops and conditional statements. Although working with a matrix language is a new experience for many students, most grasp matrix operations concepts relatively well, especially if they are proficient with matrix algebra. For many, however, the use of loops and conditional statements is novel, often resulting in the need for extra time to be appropriated to teaching the concept. There are at least two important benefits of ensuring that students have a relatively strong understanding of these concepts. First, the programming logic necessary to conceptualize and construct an efficient loop and/or conditional statement will help students improve their abilities to develop original and effective empirical analyses. Second, this logic can be easily applied to other SAS methods that implement loops and conditional statements. One example of this application is the SAS macro language. Typically, an overview of the macro language is introduced last during the mini-course, because the concepts underlying the macro language encompass many of those introduced in the topics discussed above. Although the macro language can be a powerful tool for completing many objectives, the primary use of the macro language in the first semester econometrics course at MSU is for constructing simulations. Simulations provide an intuitive, hands-on tool for empirically investigating and proving many theoretical concepts, especially those that can be difficult for students to grasp (e.g., p-values; the law of large numbers; normality of an OLS estimator). Even if students are not required to complete assignments using the SAS macro language, a fundamental knowledge of the concepts and programming details will allow instructors to use macro-based simulations during lectures, substantially improving the efficacy of teaching particularly complex topics in statistics and econometrics. The following macro language concepts are reviewed: Overview of creating a macro code block. Defining and using macro variables. Differentiating local macro variables from global variables. Loops and conditional statements in a macro code block. The use of macro variables outside of a macro code block. CONCLUSION Many graduate students enter statistics and economics programs without a strong (and often without any) foundation in empirical analysis. This can create challenges for both students and instructors, who must balance the instruction of fundamental concepts and the analytical skills necessary to apply those concepts. Furthermore, the analytical skills necessary to teach graduate students can be more advanced than those taught in many undergraduate programs. Developing a focused mini-course for teaching SAS programming skills and conducting the mini-course prior to the start of a semester can provide graduate students and their instructors with an opportunity to build the necessary analytical 4

5 foundation. The primary benefits include a student body that can is better able to complete analytical assignments, instructors that can use SAS more effectively in the classroom, and a lower amount of time appropriated to teaching SAS during lectures. One drawback is that instructors would need to allocate time prior to the beginning of the semester to organize and instruct the mini-course. However, experience in conducting a SAS boot camp at Montana State University indicates that the benefits have largely outweighed the drawbacks. CONTACT INFORMATION Please address comments and questions to: Anton Bekkerman, Ph.D. 205 Linfield Hall Montana State University P.O. Box Bozeman, MT Phone: (406) anton.bekkerman@montana.edu SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. R indicates USA registration. Other brand and product names are trademarksof their respective companies. 5