Search
   >> Home >> Products >> Features >> Panel data >> Generalized estimating equations

Generalized estimating equations: xtgee


The use of panel-data models has exploded in the past ten years as analysts more often need to analyze richer data structures. Some examples of panel data are nested datasets that contain observations of smaller units nested within larger units. An example might be counties (the replication) in various states (the panel identifier). Other examples of panel data are longitudinal, having multiple observations (the replication) on the same experimental unit (the panel identifier) over time. The xtgee command allows either type of panel data.

Stata estimates extensions to generalized linear models in which you can model the structure of the within-panel correlation. This extension allows users to fit GLM-type models to panel data.

The xtgee command offers a rich collection of models for analysts. These models correspond to population-averaged (or marginal) models in the panel-data literature.

What makes xtgee useful is the number of statistical models that it generalizes for use with panel data, the richer correlation structure with models available in other commands, and the availability of robust standard errors, which do not always exist in the equivalent command.

In this example, we consider a probit model in which we wish to model whether a worker belongs to the union based on the person's age and whether they are living outside of an SMSA. The people in the study appear multiple times in the dataset (this type of panel dataset is commonly referred to as a longitudinal dataset), and we assume that the observations on a given person are more correlated than those between different persons.

. webuse nlswork (National Longitudinal Survey. Young Women 14-26 years of age in 1968) . xtset idcode panel variable: idcode (unbalanced) . xtgee union age not_smsa, family(binomial) link(probit) corr(exchangeable) Iteration 1: tolerance = .05859927 Iteration 2: tolerance = .00346479 Iteration 3: tolerance = .0001277 Iteration 4: tolerance = 4.486e-06 Iteration 5: tolerance = 1.548e-07 GEE population-averaged model Number of obs = 19226 Group variable: idcode Number of groups = 4150 Link: probit Obs per group: min = 1 Family: binomial avg = 4.6 Correlation: exchangeable max = 12 Wald chi2(2) = 30.23 Scale parameter: 1 Prob > chi2 = 0.0000
union Coef. Std. Err. z P>|z| [95% Conf. Interval]
age .0045624 .0013959 3.27 0.001 .0018264 .0072984
not_smsa -.1440246 .0318838 -4.52 0.000 -.2065156 -.0815336
_cons -.8770284 .0479603 -18.29 0.000 -.9710288 -.7830279

xtgee options

The xtgee command allows these options:

Families
  • Bernoulli/binomial
  • gamma
  • Gaussian
  • inverse Gaussian
  • negative binomial
  • Poisson
Links
  • cloglog
  • identity
  • log
  • logit
  • negative binomial
  • odds power
  • power
  • probit
  • reciprocal
Correlation structures
  • independent
  • exchangeable
  • autoregressive
  • stationary
  • nonstationary
  • unstructured
  • user-specified

Assume an independent correlation structure that ignores the panel structure of the data. Under this assumption, xtgee will produce answers already provided by Stata’s nonpanel estimation commands. Examples of situations when xtgee provides the same answers as an existing command are given in the table shown to the right.

Note 1

These methods produce the same results only for balanced panels.

Note 2

For cloglog estimation, xtgee with corr(independent) and cloglog will produce the same coefficients, but the standard errors will be only asymptotically equivalent because cloglog is not the canonical link for the binomial family.

Note 3

For probit estimation, xtgee with corr(independent) and probit will produce the same coefficients, but the standard errors will be only asymptotically equivalent because probit is not the canonical link for the binomial family. If the binomial denominator is not 1, the equivalent maximum-likelihood command is bprobit.

Note 4

Fitting a negative binomial model using xtgee (or glm) will yield results conditional on the specified value of alpha. nbreg, however, estimates that parameter and provides unconditional estimates.

Note 5

xtgee with corr(independent) can be used to fit exponential regressions, but this requires specifying scale(1). As with probit, the xtgee-reported standard errors will be only asymptotically equivalent to those produced by streg, dist(exp) nohr because log is not the canonical link for the gamma family. xtgee cannot be used to fit exponential regressions on censored data.

Using the independent correlation structure, the xtgee command will fit the same model as the glm, irls command if the family–link combination is the same.

Note 6

If the xtgee command is equivalent to another command, using corr(independent) and the vce(robust) option with xtgee corresponds to using vce(cluster clustvar) option in the equivalent command, where clustvar corresponds to the panel variable.

Family Link Correlation Equivalent Stata command
gaussian identity independent regress
gaussian identity exchangeable xtreg, re (see note 1)
gaussian identity exchangeable xtreg, pa
binomial cloglog independent cloglog (see note 2)
binomial cloglog exchangeable xtcloglog, pa
binomial logit independent logit or logistic
binomial logit exchangeable xtlogit, pa
binomial probit independent probit (see note 3)
binomial probit exchangeable xtprobit, pa
nbinomial nbinomial independent nbreg (see note 4)
poisson log independent poisson
poisson log exchangeable xtpoisson, pa
gamma log independent streg, dist(exp) nohr (see note 5)
family link independent glm, irls (see note 6)

If you choose to model the intracluster correlation as an identity matrix (by specifying the name of an existing identity matrix in the option corr), GEE estimation reduces to a generalized linear model, and the results will be identical to estimation by glm.

. glm union age not_smsa, family(gauss) link(identity) Iteration 0: log likelihood = -10713.086 Generalized linear models No. of obs = 19226 Optimization : ML Residual df = 19223 Scale parameter = .1784791 Deviance = 3430.904127 (1/df) Deviance = .1784791 Pearson = 3430.904127 (1/df) Pearson = .1784791 Variance function: V(u) = 1 [Gaussian] Link function : g(u) = u [Identity] AIC = 1.114749 Log likelihood = -10713.08631 BIC = -186185.1
OIM
union Coef. Std. Err. z P>|z| [95% Conf. Interval]
age .0018369 .0004926 3.73 0.000 .0008714 .0028024
not_smsa -.0648492 .0067672 -9.58 0.000 -.0781126 -.0515858
_cons .1950571 .0158061 12.34 0.000 .1640777 .2260365
. xtgee union age not_smsa, family(gauss) link(identity) corr(indep) Iteration 1: tolerance = 6.230e-15 GEE population-averaged model Number of obs = 19226 Group variable: idcode Number of groups = 4150 Link: identity Obs per group: min = 1 Family: Gaussian avg = 4.6 Correlation: independent max = 12 Wald chi2(2) = 103.63 Scale parameter: .1784513 Prob > chi2 = 0.0000 Pearson chi2(19226): 3430.90 Deviance = 3430.90 Dispersion (Pearson): .1784513 Dispersion = .1784513
union Coef. Std. Err. z P>|z| [95% Conf. Interval]
age .0018369 .0004926 3.73 0.000 .0008715 .0028023
not_smsa -.0648492 .0067666 -9.58 0.000 -.0781116 -.0515869
_cons .1950571 .0158049 12.34 0.000 .1640801 .2260341

We could fill up lots of space demonstrating other ways that the xtgee command is equivalent to other commands, but the real power is in using it for its intended use and modeling the correlation that exists in the panels.

The Stata Blog: Not Elsewhere Classified Find us on Facebook Follow us on Twitter LinkedIn Google+ Watch us on YouTube