How to Estimate a GLM in EViews

To estimate a GLM model in EViews you must first create an equation object. You may select Object/New Object.../Equation or Quick/Estimate Equation… from the main menu, or enter the keyword equation in the command window. Next select GLM - Generalized Linear Model in the Method dropdown menu. Alternately, entering the keyword glm in the command window will both create the object and automatically set the estimation method. The dialog will change to show settings appropriate for specifying a GLM.

Specification

The main page of the dialog is used to describe the basic GLM specification.

We will focus attention on the GLM Equation specification section since the Estimation settings section in the bottom of the dialog is should be self-explanatory.

Dependent Variable and Linear Predictor

In the main edit field you should specify your dependent variable and the linear predictor.

There are two ways in which you may enter this information. The easiest method is to list the dependent response variable followed by all of the regressors that enter into the predictor. PDL specifications are permitted in this list, but ARMA terms are not. If you wish to include an offset in your predictor, it should be entered on the Options page (see “Specification Options”).

Alternately, you may enter an explicit linear specification like “Y=C(1)+C(2)*X”. The response variable will be taken to be the variable on the left-hand side of the equality (“Y”) and the linear predictor will be taken from the right-hand side of the expression (“C(1)+C(2)*X”). Offsets may be entered directly in the expression or they may be entered on the Options page. Note that this specification should not be taken as a literal description of the mean equation; it is merely a convenient syntax for specifying both the response and the linear predictor.

Family

Next, you should use the Family dropdown to specify your distribution. The default family is the Normal distribution, but you are free to choose from the list of linear exponential family and quasi-likelihood distributions. Note that the last three entries (Exponential Mean, Power Mean (p), Binomial Squared) are for quasi-likelihood specifications not associated with exponential families.

If the selected distribution requires specification of an ancillary parameter, you will be prompted to provide the values. For example, the Binomial Count and Binomial Proportion distributions both require specification of the number of trials , while the Negative Binomial requires specification of the excess-variance parameter .

For descriptions of the various exponential and quasi-likelihood families, see “Distribution”.

Link

Lastly, you should use the Link dropdown to specify a link function.

EViews will initialize the Link setting to the default for to the selected family. In general, the canonical link is used as the default link, however, the Log link is used as the default for the Negative Binomial family. The Exponential Mean, Power Mean (p), and Binomial Squared quasi-likelihood families will default to use the Identity, Log, and Logit links, respectively.

If the link that you select requires specification of parameter values, you will be prompted to enter the values.

For detailed descriptions of the link functions, see “Link”.

Options

Click on the Options tab to display additional settings for the GLM specification. You may use this page to augment the equation specification, to choose a dispersion estimator, to specify the estimation algorithm and associated settings, or to define a coefficient covariance estimator.

Specification Options

The Specification Options section of the Options tab allows you to augment the GLM specification.

To include an offset in your linear predictor, simply enter a series name or expression in the Offset edit field.

The Frequency weights edit field should be used to specify replicates for each observation in the workfile. In practical terms, the frequency weights act as a form of variance weighting and inflate the number of “observations” associated with the data records.

You may also specify prior variance weights in the using the Weights dropdown and associated edit fields. To specify your weights, simply select a description for the form of the weighting series (Inverse std. dev., Inverse variance, Std. deviation, Variance), then enter the corresponding weight series name or expression. EViews will translate the values in the weighting series into the appropriate values for . For example, to specify directly, you should select Inverse variance then enter the series or expression containing the values. If you instead choose Variance, EViews will set to the inverse of the values in the weight series. “Weighted Least Squares” for additional discussion.

Dispersion Options

The Method dropdown may be used to select the dispersion computation method. You will always be given the opportunity to choose between the Default setting or Pearson Chi-Sq., Fixed at 1, and User-Specified. Additionally, if the specified distribution is in the linear exponential family, you may choose to use the Deviance statistic.

The Default entry instructs EViews to use the default method for computing the dispersion, which will depend on the specified family. For families with a free dispersion parameter, the default is to use the Pearson Chi-Sq. statistic, otherwise the default is Fixed at 1. The current default setting will be displayed directly below the dropdown.

Coefficient Covariance Options

The Covariance method dropdown specifies the estimator for the coefficient covariance matrix. You may choose between the Ordinary method, which uses the inverse of the estimated information matrix, or you may elect to use Huber/White sandwich estimator, or the heteroskedasticity and auto-correlation consistent HAC (Newey-West) approach.

If you select the HAC covariance method, a HAC options button will appear prompting so that you may customize the whitening and kernel settings. By default, EViews HAC estimation will employ a Bartlett kernel with fixed Newey-West sample-size based bandwidth and no pre-whitening (see “HAC Consistent Covariances (Newey-West)” for additional discussion).

The Information matrix dropdown allows you to specify the method for estimating the information matrix. For covariances computed in the standard fashion, you may choose between the default Hessian - observed, Hessian - expected, and OPG - BHHH. If you are computing Huber/White covariances, only the two Hessian based selections will be displayed.

(Note that in some earlier versions of EViews, the information matrix default method was tied in with the optimization method. This default dependence has been eliminated.)

Lastly you may use the d.f. Adjustment checkbox choose whether to apply a degree-of-freedom correction to the coefficient covariance. By default, EViews will perform this adjustment.

Estimation Options

The Estimation section of the page lets you specify the optimization algorithm, starting values, and other estimation settings.

The Optimization Algorithm and Step method dropdown menus control your estimation method.

• The default Optimization Algorithm is Newton-Raphson, but you may instead select BFGS, OPG - BHHH, Fisher Scoring (IRLS), or EViews legacy.

• The default Step method is Marquardt, but you may use the menu to select Dogleg or Line search.

If you select optimization using EViews legacy, you will be prompted to select a legacy method in place of a step method. The Legacy method dropdown offers the choice of the default Quadratic Hill Climbing (Newton-Raphson with Marquardt steps), Newton-Raphson with line search, IRLS - Fisher Scoring, and BHHH (OPG with line search).

By default, the Starting Values dropdown is set to EViews Supplied. The EViews default starting values for are obtained using the suggestion of McCullagh and Nelder to initialize the IRLS algorithm at for the binomial proportion family, and otherwise, then running a single IRLS coefficient update to obtain the initial . Alternately, you may specify starting values that are a fraction of the default values, or you may instruct EViews to use your own values.

You may use the IRLS iterations edit field to instruct EViews to perform a fixed number of additional IRLS updates to refine coefficient values prior to starting the specified estimation algorithm.

The Max Iterations and Convergence edit fields are self-explanatory. Selecting the Display settings checkbox instructs EViews to show detailed information on tolerances and initial values in the equation output.

Coefficient Name

You may use the Coefficient name section of the dialog to change the coefficient vector from the default C. EViews will create and resize the vector if necessary.