## St with shared frailty only

*April 2, 2009 at 10:05 am* *gabrielrossman* *
1 comment *

| Gabriel |

Several Stata commands in the xt family allow you to specify a random model (i.e., structured error terms) with no fixed model (i.e., independent variables). For instance:

xtreg y, re i(clustervar) xtmixed y || clustervar: gllamm y, i(clustervar)

This is very useful if the only thing you’re interested in is rho, the proportion of variance clustered within groups. To take a classic example of multilevel modeling, you might have test score data on students by classroom and you may be interested simply in how much good performance clusters by classroom (rho) before you get to independent variables like whether teacher credentials or class size matter.

In the [st] syntax, shared frailty is closely analogous to random effects (and strata are analogous to fixed effects). However unlike most xt commands, the st syntax expects there to be independent variables and it chokes if it doesn’t get them. Fortunately this is not a limitation of the model, only the syntax parsing, and you can trick Stata by feeding it a constant. It drops the constant from the model and estimates only the shared frailty. For instance, this model shows only the extent to which radio station adoptions of a particular song clustered by the stations’ corporate owners:

. gen x1=1 . streg x1, shared(owner_n) distribution(exponential) Note: frailty(gamma) assumed. failure _d: add analysis time _t: (fpdate-origin) origin: time firstevent id: station_n note: x1 dropped because of collinearity Fitting exponential model: Iteration 0: log likelihood = -260.2503 Iteration 1: log likelihood = -252.85211 Iteration 2: log likelihood = -246.83872 Iteration 3: log likelihood = -246.28281 Iteration 4: log likelihood = -246.10157 Iteration 5: log likelihood = -246.10117 Iteration 6: log likelihood = -246.10117 Exponential regression -- log relative-hazard form Number of obs = 171 Gamma shared frailty Number of groups = 46 Group variable: owner_n No. of subjects = 171 Obs per group: min = 1 No. of failures = 164 avg = 3.717391 Time at risk = 3739 max = 58 F( 0, .) = . Log likelihood = -246.10117 Prob > F = . ------------------------------------------------------------------------------ _t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- -------------+---------------------------------------------------------------- /ln_the | -1.792063 .4458721 -4.02 0.000 -2.665956 -.9181693 -------------+---------------------------------------------------------------- theta | .1666161 .0742895 .0695329 .3992493 ------------------------------------------------------------------------------ Likelihood-ratio test of theta=0: chibar2(01) = 15.60 Prob>=chibar2 = 0.000

Entry filed under: Uncategorized. Tags: random variables, st, Stata.

1.Shufflevar « Code and Culture | October 26, 2009 at 5:14 am[…] of my current radio work to understand how much corporate clustering we’d expect to see in the diffusion of pop songs under the null hypothesis that radio corporations don’t actually practice central […]