Gauss Primer - Department of Economics
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1. a column vector y 1 0 5 c MAXC x returns a column vector containing the largest element in each column of a matrix Example x 125 206 347 y maxc x will return a column vector y 3 4 7 d STDC x returns a column vector containing the standard deviation of each column of a matrix Example x 125 206 347 y stdc x will return a column vector y 1 2 1 4 Plotting or graphing variables There are a wide variety of graphing capabilities in GAUSS The following sequence of commands illustrates the steps required to generate a simple XY plot of the variables y1 y2 and y3 against x a Step 1 Activate the graphics library library pgraph Step 2 Reset global graphics variables graphset Step 3 Combine the series of y variables into a matrix y yl y2 y3 Step 4 Provide graphics title title Plot of y1 y2 and y3 against x Step 5 Set legend on _plegctl 1 Step 6 Call the main plotting routine Xy X Y 5 More complex graphing capabilities and controls are detailed in Volume I Chapter 13 of the GAUSS manuals 5 Running a linear regression Ordinary Least squares can be computed in a variety of fashions Suppose we have an nx1 vector y containing the dependent variables and an nxk matrix x containing the independent variables Then the ordinary least squares estimates of the parameter vector b can be computed using a Direct calculation b2. data you can load this matrix into GAUSS using the command LOAD x n m mydata b GAUSS data sets It is often convenient if you will be referring often to a data set to create a GAUSS data set Creating such a data set requires a series of steps outlined below in the annotated example in which we are trying to save the n x 3 matrix as three variables in a GAUSS data set with names var1 var2 and var3 e Step 1 Define the name of the data set outfilel gdata e Step 2 Assign names to each column of the data matrix to be saved vnames varl var2 var3 e Step 3 Write data to GAUSS data set call saved x outfile1 vnames c GAUSS data can be retrieved by e Step 1 Defining the name of the GAUSS data file infilel gdata e Step 2 Opening the GAUSS data file open file1 infile1 e Step 3 Reading in the data using the READR command z readr file1 r where r denotes the number of rows to be read e Step 4 Retrieve the names of the variables read in vnames getname infile1 3 Obtaining basic statistics on variables Basic statistics can be obtained using the following commands a MEANC x returns the mean of every column of a matrix Example x 125 206 347 y meanc x will return a column vector y 2 2 6 b MINC x returns a column vector containing the smallest element in each column of a matrix Example x 125 206 347 y minc x will return
3. A SIMPLE INTRODUCTION TO GAUSS GAUSS is an econometrics statistical package available in the Department of Economics in the 68 Heady Hall lab The purpose of this document is to provide a brief introduction on how one can access GAUSS and the basic GAUSS commands Additional information can be found in the GAUSS manuals available in the PC lab It is especially helpful to work through the tutorial in Chapter 3 of Volume I ACCESSING AND RUNNING GAUSS There are a variety of ways in which GAUSS commands can be entered and executed 1 Interactive mode GAUSS commands can be entered and executed line by line using GAUSS s interactive mode referred to as COMMAND mode in the user s manual Either of the following approaches will place you in COMMAND mode a C If you have a version of GAUSS on your computer GAUSS can be started from the DOS prompt by typing gaussi GAUSS can be started from the 68 Heady Hall lab menu by first entering the Statistical Programs sub menu and then choosing the Gauss option Interactive mode is exited by hitting the escape key Batch Mode A previously written GAUSS program can be run in batch mode as follows Note This option is readily available only for those who have GAUSS installed on their own PC However see alternative 3 below a Create a file containing your commands Save it with a meaningful name such as myfile b Now type gauss r myfile The r option resets the file GAU
4. SS LOG which stores any error messages generated during the running of the program In order to direct the output to a file rather than the screen the batch program should contain a statement of the form output file myfile out reset 3 Executing a previously prepared GAUSS program in COMMAND mode Create a file containing your commands Save it with a meaningful name such as myfile Enter GAUSS s COMMAND mode See above At the gauss prompt type run filename In order to direct the output to a file rather than the screen the your program should contain a statement of the form output file myfile out reset d If you wish to edit or even create the program prior to running it e type edit filename This will put you into EDIT mode in GAUSS You can then make any changes to the program that you wish to make e To exit EDIT mode enter ALT X GAUSS will then give you several options including WRITE This updates your program without executing it and returns you to COMMAND mode QUIT This returns you to COMMAND mode without updating your program EXECUTE This updates your program and returns you to COMMAND mode Alternatively if you just want to execute the program press F2 This will save the changes you have made to your program and execute it e Upon executing the program you will be placed in COMMAND mode To return to editing your program you can either type edit fil
5. ename or SHIFT F1 GAUSS COMMAND LANGUAGE BASICS All GAUSS commands end with a semicolon You can have more than one command on a given line as long as semicolons separate them In COMMAND mode a carriage return is the same as a semicolon Single line comments are nested between two signs as in here is a single comment Multiple line comments are bracketed by at the beginning and at the end written in the form here is a multiple line comment GAUSS is a very different from the statistical packages such as TSP and SHAZAM GAUSS has fewer canned routines requiring more programming on the part of the user but is significantly stronger in terms of its matrix and data manipulation capabilities allowing one to develop efficient routines for procedures not covered by TSP and SHAZAM Furthermore GAUSS is significantly faster an important feature when the procedure of interest involves a lot of matrix manipulations and or do loops Here are some commonly required steps in a GAUSS program and the corresponding commands 1 Specifying and manipulating a matrix a A simple matrix can be generated using the let command let x 123 45 6 7 8 9 or simply x 123 456 789 Either of these will create the 3 x 3 matrix 1 2 3 4 5 6 7 8 9 b Notice that spaces are used to separate elements of a row and commas are used to separate rows c A matrix can also be formed by concatenating other matrices or
6. vectors For example if you enter a 1 1 3 2 b 2 3 4 5 h a b k alb Then h is a 1x4 row vector equal to 1 1 3 2 2 3 4 5 and k is a 2X2 matrix equal to 1 1 3 2 2 3 4 5 d Portions of a matrix can be referred to as follows e The i j th element of the matrix x is referred to as x i j e The ith row of the matrix x is referred to as x i e The jth column of the matrix x is referred to as x j e Rows i through k of matrix x are referred to as x i k e Matrix versus element by element operators GAUSS distinguishes matrix multiplication and division from element by element operations on matrices Thus X y Z yields the inner product of the matrices y and z where y has the same number of columns as z has rows In contrast x y Z yields the element by element multiplication of y and z where typically y and z will either have the same number of rows and columns or one will be a scalar Similarly x b A yields x A b whereas x b A does element by element division Similar distinctions exist for the logical operators lt gt gt and lt A dot prior to each operator indicates that element by element comparisons are to be made whereas without this dot entire matrices are compared 2 Creating and retrieving a data set a Data can be read into a matrix from a file using the LOAD command In particular if you have a file mydata containing an n X m matrix of
7. x y x x The OLS command output file ols out reset call ols 0 y x The 0 in the first argument indicates that the data are provided directly in the program as opposed to being read from a GAUSS file The command OLS will by default include a constant This can be altered by setting the global variable __con 0 One can also retrieve results from the OLS regression using the format vnam m b stb vc stddev sigma cx rsq resid dwstat ols 0 y x instead of call ols 0 y x The returned variables are vnam k 2 x1 vector of variable names m k 2 x k 2 moment matrix b k 1 x1 least squares parameter estimates stb k 1 x1 vector of t statistics ve k 1 x k 1 variance covariance matrix estimates stddev k 1 x1 vector of estimated parameter standard errors sigma Standard deviation of residual cx kxk correlation matrix of y x rsq R resid nx1 residual vector dwstat Durbin Watson statistic See Volume II of the GAUSS manual for details regarding the format of these variables returned by the OLS command c OLSQR and OLSQR2 provide alternatives to OLS that are slower but can better handle situations of near singularity
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