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From |
"David M. Drukker, Stata Corp" <[email protected]> |

To |
[email protected] |

Subject |
Re: st: Within and between variances |

Date |
Thu, 15 May 2003 11:16:14 -0500 |

Ineta Sokolowski <[email protected]> wrote: > I wish, there were more details in manual. Me too. I will make some changes to this manual entry. Ineta continued with > > I need the variance components to calculate the ICC (intra class > correlation). I tried different methods to calculate ICC, including > -loneway- and -xtsum-, but it gives very different result. -xtsum- and -loneway- are producing different summaries of your data. -loneway- produces estimates of the variance components and the intraclass correlation. -xtsum- is simply summarizing the within and between transformed variables. If you are interested in estimating the ICC, use the results reported by -loneway-, not -xtsum-. Ineta also asked for more details. My previous posting provides the details of what -xtsum- is doing and [R] loneway provides the details of what -loneway- is doing. Rather than repeat what is available elsewhere, I will attempt to illustrate what -loneway- is doing by comparing it with another other estimator of the ICC. I will use an unbalanced longitudinal dataset on complaints by person over time. The dependent variable, complain, is binary. . clear . set mem 10m (10240k) . use http://www.stata-press.com/data/r8/chicken Now let's use -loneway- to estimate the ICC. . loneway complain person One-way Analysis of Variance for complain: Number of obs = 5952 R-squared = 0.2885 Source SS df MS F Prob > F ------------------------------------------------------------------------- Between person 239.46604 1075 .2227591 1.84 0.0000 Within person 590.52976 4876 .12110947 ------------------------------------------------------------------------- Total 829.9958 5951 .13947165 Intraclass Asy. correlation S.E. [95% Conf. Interval] ------------------------------------------------ 0.13175 0.01204 0.10815 0.15535 Estimated SD of person effect .1355647 Estimated SD within person .3480079 Est. reliability of a person mean 0.45632 (evaluated at n=5.53) -loneway- estimates the ICC without any controls. Thus, another way of estimating the ICC would be to estimate the parameters of random-effects model without any covariates. Recall that a random-effects model on a constant only is y_it = cons + u_i + e_it where y_it are the observations on the dependent variable; cons is a fixed constant to be estimated; u_i are the unobserved individual level effects, the u_i are assumed to be identically and independently distributed (i.i.d.) over the individuals in the sample, E[u_i e_it] = 0; and, e_it are the unobserved idiosyncratic errors which are assumed to be i.i.d. over the entire sample. With unbalanced data, -xtreg- with the -sa- option will produce an estimate of the ICC that is very similar to the one produced by -loneway- but not exactly the same. With balanced data, the estimates will be the same. Until an update in the near future, -xtreg ,sa- does not run with a constant only model. However, we can fit the model by including a manually generated constant, as in the output below. . gen one = 1 . xtreg complain one , i(person) sa Random-effects GLS regression Number of obs = 5952 Group variable (i): person Number of groups = 1076 R-sq: within = 0.0000 Obs per group: min = 3 between = 0.0000 avg = 5.5 overall = 0.0000 max = 8 Random effects u_i ~ Gaussian Wald chi2(0) = 738.70 corr(u_i, X) = 0 (assumed) Prob > chi2 = . ------------------------------------------------------------------------------ complain | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- one | .1685169 .0062002 27.18 0.000 .1563646 .1806691 _cons | (dropped) -------------+---------------------------------------------------------------- sigma_u | .13560089 sigma_e | .34800786 rho | .13181353 (fraction of variance due to u_i) ------------------------------------------------------------------------------ In -xt- terms, the SD of the person effect is the standard deviation of the individual level effect and the SD within person is the standard deviation of the idiosyncratic error. -loneway- and -xtreg, sa- each have a consistent estimator of the standard deviation of the individual level effect, to use the -xt- terminology. In fact, these estimators produce exactly the same estimates from balanced data, but, since they use distinct adjustments for unbalanced data, they produce slightly different estimates from unbalanced datasets. -loneway- and -xtreg , sa- are using the same estimator of the standard deviation of idiosyncratic error. Neither of these estimators explicitly takes account of the binary nature of the dependent variable. I hope that this helps. David [email protected] * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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