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An Introduction to LIMDEP By Robert A. Yaffee Statistics, Social Science, and Mapping Group Academic Computing Services Information Technology Services New York University January 2002 LIMDEP is a versatile and powerful specialized program for econometric analysis, written by Professor William H. Greene. Version 7 of LIMDEP for Windows contains extensive families of regression, panel data, and duration models. The family of regression analysis includes classical linear, heteroskedastically consistent, serially correlated, and 3SLS models. A distinguishing feature of this package is a wide variety of limited dependent variable regression models. Among these regression models were poisson (regular and zero inflated) and negative binomial models, probit, logit models, ordered probability models, multinomial logit, nested logit, and discrete choice models. Other limited dependent variable models were tobit, censored, truncated, switching, and sample selection, and stochastic frontier regression models. The duration family includes nonparametric life tables, semi-parametric proportional hazards, and parametric models that include ordered logit and loglinear models. These models can accommodate time-varying covariates and unexplained heterogeneity. LIMDEP includes extensive documentation available with the package as well as on the World Wide Web. Invocation of LIMDEP We begin the procedure by invoking the LIMDEP program. To invoke LIMDEP, double

click on the LIMDEP icon . The opening dialog box, seen in Figure 1, appears on the screen.

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Figure 1 Project dialog box

When the user clicks on File and New, the Text/Command document dialog box

seen in Figure 2, opens.

Figure 2 Text Command Window dialog box

The user at this point will see that the Text/Command Document option is

selected. He can click on OK to open a command window, shown in Figure 3, appears.

Figure 3 Command Syntax Window

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The Basic Command Syntax

The user can write his program syntax in this window. A basic program is entered into this window to illustrate our exposition of the fundamental program command syntax in Figure 4 on the next page. Annotation of the commands follows.

Command Termination

In LIMDEP, the commands are entered and terminated with a $. The

subcommands are separated by semi-colons. Title Statement First, we insert a title statement in our program to notify us of the purpose of the

program. Titles may be stacked, one atop of the other, just before the statistical procedure, in order to properly describe it.

Title; First LIMDEP example program $ Title; Subtitle $ Title; Third title $

The Output Viewing File Second, we define the output file in which our output will be place for viewing

and analysis. Open; output=output1 $

Data Definition Next we have to define the in- line data and variable names. Reading Data files is

done with the READ command. The READ command contains subcommands that define the number of observations (nobs), the number of variables (nvar), and the variable names (names).

Read; nobs = 30; nvar = 8;

names = id, age, sex, gpa, ses, income, marital, religion $

Input data formats are not needed if the data in the variables in the data file are separated by one blank space. If the variables in the data file are not separated by blank spaces, LIMDEP requires a format specification to be entered. FORTRAN floating point or exponential formats are employed. LIMDEP does not handle string or integer formats. If formats were used for this data set, the input format for this data set could be included as follows:

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Read; nobs = 30; nvar = 8; names = id, age, sex, gpa, ses, income, marital, religion; (F2.0,1X,F2.0,1X,F1.0,1X,F3.1,1X,F2.0,1X,F6.0,2(1X,F1.0)) $

The formulation for the numeric formats is Fw.d, where F=numeric floating point format, w=column space width of variable, and d = number of decimals to the right of the decimal point. 1X = 1 blank space between other variables. If there were two spaces between the variables, then 2X would be used.

Variable definition is complete for continuous variables. However, discrete

variables in this version of LIMDEP do not possess value labels or formats for answer categories.

Reading External Data Files

If one wishes to read these data from an external file rather than from in line data,

then one needs to merely add a file= filename option to the Read command.

Read; nobs = 30; nvar = 8; Names = id, age, sex, gpa, ses, income, marital, religion; (F2.0,1X,F2.0,1X,F1.0,1X,F3.1,1X,F2.0,1X,F6.0,2(1X,F1.0)); File = Mydata.dat $ Importing Spreadsheet or Data Base Files In the event that the researcher wishes to read an external spreadsheet file, from Excel or Lotus, he would use the following Read command. Read; nobs = 30; nvar = 8; Names = id, age, sex, gpa, ses, income, marital, religion; (F2.0,1X,F2.0,1X,F1.0,1X,F3.1,1X,F2.0,1X,F6.0,2(1X,F1.0)); File = Mydata.wks; format = WKS $ In the event that the researcher wishes to read in an external database file, he would use the following read command. Such a database file could be a DB IV format or an Access format. Read; nobs = 30; nvar = 8; Names = id, age, sex, gpa, ses, income, marital, religion; (F2.0,1X,F2.0,1X,F1.0,1X,F3.1,1X,F2.0,1X,F6.0,2(1X,F1.0)); File = Mydata.dbf; format =DIF $

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Figure 4: Basic LIMDEP command syntax

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Data The data follow the file and data definition statements in the Read command.

Data Review

The analyst gives a set of variables (in this example, the complete set) a nickname or namelist. The nickname or namelist in this case is called xlist.

Namelist; xlist = age,sex,gpa,ses,income,marital,religion $

The listing of the data for the variables is accomplished with the LIST command.

The List command specifies that all of the variables in the namelist called Xlist should be listed. By reviewing this printout, the user check to be sure whether LIMDEP is reading the data correctly. The listing of the data includes line numbers and observation numbers to help check to be sure all data requested are read. List; xlist $

Range checks of the discrete and continuous distributions are facilitated with

frequency tables and graphical representation of variables with the Histogram commands. Part of the histogram command in the program syntax, shown between Figure 5

and 6, contains an Rhs designation. This refers to variables on the right hand side of the equation list.

Figure 5 shows two panels. The upper panel is called the Trace Windows. In it is

a complete list of commands as entered by the programmer and any and all warnings or error diagnostics pertaining to them? The lower panel is called the Output Window. In it the reviewer finds the output from the commands after they have been executed.

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Figure 5 Listing of data

Histogram; rhs = sex, adult, religion, age $

Figure 6 Frequency Distribution Tables

The first part of the histogram output consists of the Frequency and percentage tables in Figure 6. The range check using these categories can help the analyst spot miscodes or typographical errors. The second part of the histogram output contains the histogram shown in Figure 7 below. This graphical depiction facilitates the detection of typographical errors as well.

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SEX

Histogram for Variable SEXFr

eque

ncy

0

5

10

15

20

0 1

Figure 7 Histogram of Gender

AGE

Histogram for Variable AGE

Freq

uenc

y

0

2

4

6

8

18192021222324252627282930313233343536373839

Figure 8 Histogram of Age

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To evaluate the distributional characteristics of continuous distributions, summary statistics may be computed. The DSTATS command provides the mean as well as measures of dispersion of the variable, found in Figure 8. If one invokes the output = 3 option, covariance and correlation matrices of the variable list are also included in the output. Their icons are shown in the lower left of Figure 8. Dstats; rhs = age,ses,gpa,income; output=3 $

Figure 8 Dstats Summary Statistics, Covariance, and Correlation Matrix Output

Consistency Check: One can review the relationships between continuous variables by double checking on the correlation matrix output in the lower left of the preceding figure. The correlation matrix that appears in the box shown in Figure 9 permits the analyst to review the expected consistency between similar or related variables. In this way, he can check further to be sure that the variables are properly coded or recoded. Matrix COV.MAT. has 4 rows and 4 columns. AGE SES GPA INCOME +-------------------------------------------------------- AGE | 34.7402 -55.1471 -.6057 -.4415085D+05 SES | -55.1471 384.1333 4.9644 .5745933D+06 GPA | -.6057 4.9644 .2139 .2635391D+05 INCOME | -.4415085D+05 .5745933D+06 .2635391D+05 .6745324D+10 Correlation Matrix for Listed Variables AGE SES GPA INCOME AGE 1.00000 -.47738 -.22224 -.09121 SES -.47738 1.00000 .54773 .35696 GPA -.22224 .54773 1.00000 .69389 INCOME -.09121 .35696 .69389 1.00000

Figure 9 Covariance and Correlation Matrix Output

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Another form of consistency check may be performed between nominal variables. It is helpful for the analyst to check to see whether the relationships between discrete variables are as expected. To do so, he can perform a crosstabulation analysis between categorical variables by using the Crosstabs command. This Crosstabs command, unlike most in LIMDEP, permits the inclusion of value labels. Crosstabs; LHS = sex; RHS=Adult; Labels = male, female/ child, adult; output = P,R,C,T $ The Crosstabs command betweens with the designation of the procedure. The LHS, the left hand side of the equation, is associated with the gender variable, sex. The values of sex are male (coded as 0) and female( coded as 1 ). The RHS is associated with the Adult variable, the values of which are 0 for child and 1 for adult. The labels for these variables are inserted in the Labels subcommand. The crosstabulations requested in the output subcommand are those of the count, the expected, the row percentages, the column percentages and the total percentages. The count output is default. The other outputs are specifically requested in the output subcommand. In that command, shown above, the P requests the predicted or expected crosstabulations, the R requests the row percentages, the C refers to the column percentages, and the T invokes the total percentages. The output from the above command appears in Figure 10 below.

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Figure 10 Crosstabs Count, Expected, and Row Percents

Further down, he gets the crosstabulation of column percents, and total percents as well, shown in Figure 11.

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Figure 11 Expected Values

Two test of significance of the relationship are given in the form of the Pearson and Likelihood Ratio Chi-square tests shown above in Figure 10. In these ways, the analyst can perform the consistency checks with the crosstabulation of discrete data. The output does not contain the nonparametric correlations sometimes associated with crosstabulations. Scatterplots Exploratory data analysis is facilitated by scatter plotting bivariate relationships. These plots clearly show whether the relationship is nonexistent or real. They permit the analyst to discover the positive or negative nature of the relationship. They permit him to see whether the relationships highly or loosely related and whether they are linear and or curvilinear. He can examine the dispersion of the bivariate relationship and identify the existences of possible outliers from the expected relationship. The researcher might examine the relationship between the dependent variable and the candidate predictor variables in a hypothesized model. To do so, he could employ a series of Plot commands: Plot; LHS = income; RHS = GPA; title=GPA against Income $ In the Plot command, the rhs variable is the dependent variable. In this case, a school administrator is trying to ascertain what variables help explain grade point average (gpa) on the part of students. GPA is therefore the dependent variable in the study. The candidate predictor variables are assigned the LHS position. The title for each graph is included in a title subcommand. In the title, blank spaces are indicated by underscores. A typical scatterplot output appears as follows.

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GPA against Income

INCOME (x10^05)

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

2.00.924 1.542 2.160 2.778 3.396.306

GP

A

Figure 13 Scatterplot of GPA by Income

This relationship is clearly somewhat nonlinear and possibly amenable to a natural log transformation. Data Management: Sampling, Selection, Sorting, and Appending Files After the data cleaning and exploratory data analysis has been performed, one may choose to sample, sort, or subset portions of the data for further analysis. Also, LIMDEP version 7 permits the writing out of data sets. LIMDEP version 7 does all of this with ease. One can sample all of the data set, if one does not have a very large data set. Sampling: The researcher may sample all of the observations in the data set. He merely has to issue the command: Sample; all $ Alternatively, he can include a portion of the data set—for example, the first 100 observations with the following command: Sample; 1-100 $

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He may prefer to sample only particular segments of the data set. For example, he can select the first 100 observations and observations 300 through 400 with the following command: Sample; 1-100,300-400 $ If the researcher wishes to perform random sampling without replacement, he can do so with the DRAW command. Suppose he wishes to sample without replacement 486 observations. He can issue the command: Draw; N = 486 $ If the researcher wishes to randomly sample with replacement, he can use the DRAW command with the Rep option. Suppose he wishes to randomly sample with replacement 1998 cases, he merely enters Draw; N = 1998; rep $ In sum, LIMDEP allows the analyst to sample with or without replacement as well as to select segments of his data. Analyzing a Subset of the data It is commonplace for the analyst to wish to investigate a subset of the data. He can do so by including a subset or rejecting a subset. If the researcher wished to analyze only persons over 21 years of age to avoid peculiar influences of laws regulating minors, he might wish to reject all cases where respondent is less than 21 years of age. Assuming that the adult variable is coded as 0 for minors and 1 for adults, the researcher could issue either of the following commands: Reject; adult = 0 $ Reject; age > 20 $ Or he might either of the commands: Include; adult = 1 $ Include; age > 20 $ By doing so, he would subset out of the whole sample, only those adults for analysis. The command must be issued before the any of the statistical procedure commands for which it is to hold. Sorting the Data Whenever the researcher might need to sort the data by a variable, say date, he can employ the SORT command. The variable by which the data are to be sorted in

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ascending order is the variable associated with the left hand side, the LHS. The variables that are to be sorted accordingly are associated with the right hand side, the RHS subcommand. Sort; LHS = date; RHS = list of variables to be sorted, each of which is separated by a comma. The command is terminated by a $. Appending Data Observations can be appended to the data set with the append command. Suppose that the data to be appended is saved in an ASCII data file, called ADD.DAT. The general command syntax is Append; File=filename ; Nvar = number of variables ; Nobs = number of observations [ ; format = Fortran format, WKS, or binary] [; Names = names or list of names] [; by variables ] $ Suppose we have only two variables, the ID variable and the AGE variable. If we have only three observations but wish to add four more from ADD.DAT, then our Command syntax would be title; Testing the Appending of Data $ open; output=out2 $ read; nvar = 2; nobs = 3; names = id,age $ 01 30 02 40 03 50 list; id, age $ append; file=add.dat; nvar = 2; nobs =4; names = id, age ; by id$ sample; all $ list; id, age $ The output from this program to append data appears as

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Figure 13 Appending Observations to a Data Set Merging the Data Two data sets can be merged by a unique identifying variable. Although not displayed in the program, both data sets must be presorted by that unique identifying variable so that their case sequences are identical. The Read command is used to add variables (columns) from an external data set to your current data set. Let the identifier be the id variable. After both data sets have been sorted so that they have the same case sequence, they can be merged with the addition of a second Read command which reads the variables to be matched with the current sample. An example of such a program reads two variables from the addvar.dat data set to the current one. title; Match-Merging Two data Sets $ open; output=out2 $ read; nvar = 2; nobs = 3; names = id, age $ 01 30 02 40 03 50 sort; Lhs = id; rhs = age $ list; id, age $ read; file = addvar.dat; nvar = 2; nobs =3; names = sex, wt; by id$ sample; all $ list; id, age, sex, wt $

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The output from this merge is displayed.

Figure 14 Match-Merge Outputs

Writing Data Files LIMDEP can also write ASCII or Excel files to a disk. The Write command is very similar to the Read command. You merely have to give it the Write command, list the variables you want written to the ASCII file, and provide a file name. For example, Write; id, age, sex, wt ; file=new.dat $ produces the output on the next page. In this case, the data are written to an external ASCII file, called new.dat. When New.Dat is opened up in the lower panel of Figure 15, the analyst can see what was produced. These data can then be used by other programs or other procedures within LIMDEP.

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Figure 15 Writing Data to an ASCII output file

To write an Excel file, the user would merely use a format = xls option along with the write command. Nomenclature and Reserved Names LIMDEP is not case sensitive. However, names in LIMDEP must begin with a letter. The names should be 8 characters or less in length. To construct the names, the ASCII character set can be used with the Windows version of LIMDEP. The names should be constructed from the underscore ‘_’, the 26 letters and 10 digits. The use of other punctuation can cause unexpected consequences. Reserved names include: ONE, B, VARB, N, PI, S, SY, YBAR, DEGFRDM, KREG, LAG, LEAD, LMDA, LOGL, NREG, RHO, RSQRD, SSQRD, SUMSQDEV, and EXITCODE. Transformations With rules of nomenclature in mind, the programmer can construct new variables and transform other variables with the CREATE command. LIMDEP has a wide variety of functions that can be used to create the new variables. A list of variables can be constructed with one create command.

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Examples of the Create command are: Create; XSQ = X^2 $ Create; LY = log(Y); X12 = X1 + X2; TREND = (a + b*x) $ The Create command can also be used to as a conditional if construction. The syntax of this form of the Create command is: Create; if (logical expression) name = expression $ For example, to construct a minor-adult variable from age, the following Create command can be employed, if there are no missing values: Create; if (age > 21) adult = 1; (Else) adult = 0 $ In this way, variables may be recoded into different variables. Another RECODE transformation command recodes existing variables. Instead of recoding the variables into different variables, this recode command can collapse or reverse the coding of an existing variable. For example, a user may wish to collapse a variable from a Likert- type scale into a trichotomy. If his Likert-type answer categories are coded as (5) agree strongly, (4) agree, (3) uncertain, (2) disagree, and (1) disagree strongly, he may collapse this variable into an (1) agree, (0) unsure, (-1) disagree. To do so, he would use the recode: Recode; Oldvar; 1,2 = -1; 3 = 0; 4,5 = 1 $ The output is produced: Variable transformations include the deletion of variables that are no longer used with the DELETE command. Delete; oldvar1 oldvar2 $ Variables may also be transformed with the RENAME command. The syntax format for this command is Rename; oldname = newname $

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By creating, recoding, deleting, renaming, and sorting, existing variables may be transformed for further analysis. Missing Values Missing values must be recoded to -999, which is the LIMDEP internal missing value code. If other variables have other missing values, they can be recoded to – 999, and thereby treated as missing. When a value in a particular variable has been coded as -999 that value will be treated as missing. If a variable embedded in a transformation command has a missing value code, then the transformation involving that missing value will also be missing. This situation could engender a pairwise missing condition unless steps are taken to skip cases which have missing values. To program LIMDEP to cause cases values coded as -999 to be dropped, LIMDEP offers the SKIP command. Listwise deletion of cases is invoked by using a Reject and a Skip command in sequence. Suppose one of the cases had a -999 code in the income variable. To drop that case for statistical analysis, the analyst enters the sequence of commands before the statistical procedure: Reject; income = - 999 $ SKIP In this way, that case would be deleted from the statistical analysis. Calculators

LIMDEP contains Calculators to facilitate computation and matrix processing.

To find the calculators, the programmer can click on the Tools option in the header bar. A pop down window will appear showing the options for the scalar calculator and the matrix calculator.

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Figure 15 Finding the Calculators

The scalar calculator can perform arithmetic calculations. By clicking on the scalar calculator, a pop down window appears:

Figure 16 Multiplying 433 by 34

To multiply 433 by 34, the user enters the multiplication in the expression box

and hits the enter key. The result appears in the output window below the expression box.

LIMDEP has its own matrix language and calculation. To define a matrix, the

user selects from Figure 15, the matrix calculator. Once the matrix calculator windows pops down, the analyst first defines matrix a as a = [1, 2/4, 9], then he defines matrix z as the inverse of matrix a with the command, z = Ginv(a). Matrix a then is squared, and finally, the Moore-Penrose generalized inverse of a is computed with the MPINV = G2nv(a), command. The analyst wishes to compute C = a’a. He enters the commands in the Expression window of the matrix calculator.

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Figure 17 Entering a Matrix Computation

After hitting the enter key, a matrix is created and kept for further computation. In the lower panel are the lists of matrices created with the commands in Figure 17.

The extensive matrix language makes a powerful LIMDEP device for custom-

building one’s own statistical processes.

A Classical and A Robust Regression Model A simple example is given of how to run a very basic regression model. First, a classical ordinary least squares model is run. Second, a robust regression model with a White’s heteroskedastically consistent variance estimator is run. The dependent variable is a continuous variable of Grade Point Average (GPA). The independent variables include socioeconomic status (SES), income, sex, and age. The program syntax and output for the ordinary least squares regression procedure is given in Figure 20.

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Figure 20 Classical Regression Program Syntax

The program syntax involves a number of scatterplots of the dependent variable against each independent variable designed to display the linearity of the models. As part of the first regression model, the classical ordinary least squares (OLS) model, the standardized residuals and predicted variables are generated. Next the standardized residuals are plotted against the standardized predicted values as a homogeneity of residual variance test. The standardized residuals are also plotted with their values so the analyst can check for outliers that might bias the findings. The summary mean and dispersion statistics are tested with the Dstats command to see whether the residuals were normally distributed. The scatterplots revealed a possible nonlinearity in the income variable (Fig. 13). Such nonlinearity often reveals itself in the residuals. Therefore, the model is rerun with with robust regression analysis. In this model, the mere addition of the hetero option in the regression command generates a heteroskedastically corrected model. The output of that model can be found in Figure 21 below.

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Figure 21 Robust Regression Output

The robust regression model adjusted for degrees of freedom explains 53.4 percent of the variance, corrected for the number of variables in the model. This model is corrected for heteroskedasticity, so it should not be a problem. Nonetheless, there are three outliers in a sample of 30. Depending on their influence, these outliers could distort the mean. The small sample size could contribute to making those outliers influential enough to be problematic. The researcher would be well advised to obtain a larger sample size for his analysis. Limitations LIMDEP is a specialized econometrics statistical package and not a general purpose statistical package. Researchers using this package are interested in models of limited dependent variables and panel data analysis. The data management features are somewhat limited. More specifically, the management of titles, value labels, data types, missing value codes, graphs, and general purpose or overall nonparametric statistical techniques happens to be less than complete. LIMDEP has limited labeling capability. Value labels are also not widely or easily applicable to discrete variables. This might seem unusual in a package designed to permit the analysis of limited or discrete variables. Indeed, there are no provisions for general value labels or formats for discrete variables.

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To be sure, some data types are not accommodated. LIMDEP does not handle string or integer variables. It does not manipulate text or labeled data. String or integer level variables must be converted to numeric or exponent ial data types for LIMDEP to process them properly. The user can import ASCII, formatted ASCII, DIF, WKS, Binary, and Excel (XLS) files (the latter can be copied and pasted) into LIMDEP. Alternatively, one can use DBMSCOPY or Stat/Transfer to convert files into LIMDEP. Missing value processing are uniform. There is just one basic missing value code. That is -999 and other codes need to be recoded to that value in order to avoid errors. LIMDEP handles basic graphing. It can produce histograms, scatterplots, multiple and matrix scatterplots. Nonetheless, there could be a wider variety of graphs available and the entitling or labeling of graphs could be improved. The lhs and rhs positions are counterintuitive on the scatterplots. LIMDEP is a powerful but specialized econometrics package that handles a vast array of limited dependent variable and panel data models. It leaves those who are interested in doing basic statistics—such as, t-tests, correlations, experimental design, reliability testing, general purpose nonparametric statistics, power and sample size analysis, or exact tests—to general purpose packages. Researchers would need to employ those techniques might wish to use SAS, STATA, S-PLUS, SYSTAT, or SPSS. For what it seeks to do, LIMDEP deserves serious consideration. Principal Advantages

For what LIMDEP attempts to do, the econometrics package is comparatively powerful and versatile. It provides a wide variety of limited and discrete dependent variable models with cross-sectiona l or panel data. For binary models, LIMDEP could handle fixed and random effects. LIMDEP can also handle ordered probability models for panel data.

LIMDEP programs count data models that include a family of poisson regression models with normal heterogeneity, with underreporting, with excess zeroes, with group effects and sample selection FIML estimation. The negative binomial models can accommodate random effects with normal group effects.

For the discrete dependent variables, LIMDEP allows the user to run tobit, logit, and probit models. These models could handle random effects and heteroskedasticity. LIMDEP also handles extreme value and multinomial probit models.

Not only does it handle linear regression models, LIMDEP handles nonlinear regression models as well. It also runs nonparametric, semi-parametric, and parametric survival models. The latter family of models could handle gamma heterogeneity.

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The matrix language provides the advanced user with considerable capability to custom build his analysis. Job Submission and Retrieval Once the LIMDEP program has been written to the Command window, the programmer can select it and run it. To select the commands to be run, the analyst can click edit in the header bar. A drop down menu will appear.

Figure 22 Click on edit in header bar

When the user clicks on Select All, the whole program becomes selected and appears to be highlighted or blackened, as shown in Figure 23 below.

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Figure 23 Selecting All of the Program

Once the program has been selected, the user can click on the green Go icon in the header bar of Figure 23 to submit the program. The program listing, warning, and error diagnostics will appear in the Trace Window. Once the errors have been correct, the output will appear in the Output Window, as shown in Figure 5 or Figure 21. Exiting LIMDEP The user should save his files, go to the File option in the header bar. Click on that and then click on exit. Queries or comments about this article can be addressed to robert.yaffee@nyu.edu