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POdegrees of freedom, t-statistic, and f-values of combined multiply imputed data
 

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    <p>I am a novice R user. I installed Zelig version 4.1-3 and Amelia II version 1.7. I am puzzled on how I can obtain the degrees of freedom, t-statistic, and f-values of combined multiply imputed data using R packages and functions. </p> <p>First, I loaded Amelia and Zelig:</p> <pre><code>require(Amelia) require(Zelig) </code></pre> <p>Then, I loaded the sample data that came with Amelia:</p> <pre><code>data(freetrade) </code></pre> <p>I created 5 imputations for this dataset using the amelia function. </p> <pre><code>a.out &lt;- amelia(freetrade, m = 5, ts = "year", cs = "country") </code></pre> <p>Then, to combine imputations, I used the zelig function:</p> <pre><code>z.out.imp &lt;- zelig(tariff ~ polity + pop + gdp.pc + year + country, data = a.out$imputations, model = "ls" ) </code></pre> <p>However, I got coefficients that appeared to be coefficients of individual imputations, and not those of the combined set when I used this code:</p> <pre><code>summary(z.out.imp) </code></pre> <p>They were as follows:</p> <pre><code>Coefficients: Value Std. Error t-stat p-value (Intercept) 2.766176e+03 6.670110e+02 4.1471215 0.0003572868 polity 1.645011e-01 3.078134e-01 0.5344183 0.5938286336 pop -6.079963e-08 6.518429e-08 -0.9327345 0.3774275934 gdp.pc -4.246794e-04 1.945866e-03 -0.2182470 0.8319093062 year -1.335563e+00 3.519513e-01 -3.7947390 0.0009787456 countryIndonesia -7.000319e+01 4.646330e+01 -1.5066343 0.1700377061 countryKorea -8.643855e+01 4.671629e+01 -1.8502870 0.0926657863 countryMalaysia -8.815182e+01 5.389486e+01 -1.6356256 0.1393312364 countryNepal -8.215250e+01 5.475828e+01 -1.5002753 0.1702129176 countryPakistan -4.349869e+01 5.149729e+01 -0.8446791 0.4238033944 countryPhilippines -8.088975e+01 5.320694e+01 -1.5202857 0.1673234716 countrySriLanka -7.668840e+01 5.695485e+01 -1.3464771 0.2161986616 countryThailand -7.400481e+01 5.186395e+01 -1.4269026 0.1903428838 </code></pre> <p>The Amelia manual shows what some of the coefficients for the combined multiply imputed dataset should be although there is no explanation on how to obtain all of them using R (see page 46 of <a href="http://cran.r-project.org/web/packages/Amelia/vignettes/amelia.pdf" rel="nofollow">http://cran.r-project.org/web/packages/Amelia/vignettes/amelia.pdf</a>)</p> <pre><code>Complete DF = 167 DF: min = 10.36 avg = 18.81 max = 37.62 F( 2, 10.4) = 15.50 Prob &gt; F = 0.0008 Value Std. Error t-stat p-value polity -0.206 0.39 -0.53 0.61 pop -3.21 e-08 8.72e-09 3.68 0.004 gdp.pc -0.0027 0.000644 -4.28 0.000 Intercept 32.7 2.66 12.29 0.000 </code></pre> <p>Because the amelia function uses monte carlo simulations, we can expect small differences between runs. However, the huge difference in the intercept was a clue that the zelig function returned regression statistics for something else than the combined set. </p> <p>The Amelia manual provides this code:</p> <pre><code>&gt; b.out &lt;-NULL &gt; se.out &lt;-NULL &gt; for(i in 1:a.out$m){ + ols.out &lt;- lm(tariff ~ polity + pop + gdp.pc, data = a.out$imputations[[i]]) + b.out &lt;- rbind(b.out, ols.out$coef) + se.out &lt;-rbind(se.out, coef(summary(ols.out))[,2]) + } &gt; combined.results&lt;-mi.meld(q=b.out, se = se.out) &gt; combined.results </code></pre> <p>I tried using it. The returned results are very close to the values and standard errors shown on page 46:</p> <pre><code>$q.mi (Intercept) polity pop gdp.pc [1,] 33.17325 -0.1499587 2.967196e-08 -0.002724229 $se.mi (Intercept) polity pop gdp.pc [1,] 2.116721 0.276968 6.061993e-09 0.0006596203 </code></pre> <p>However, they do not include the t-statistic, degrees of freedom, or f-values. </p> <p>Are there open-source packages or functions available in R so that I can obtain the degrees of freedom, t-statistic, and f-values without having to do manual calculations?</p> <p>Thanks.</p>
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