Joint significance of more regressors in summary
try
install.packages('car')
?car::linear.hypothesis
hth,
Kingsford Jones
On Wed, Jan 21, 2009 at 4:20 PM, Roberto Patuelli
<roberto.patuelli at lu.unisi.ch> wrote:
Dear All, I was wondering if it is possible to generate a regression summary (it does not matter at this stage if from an lm or for example a glm estimate) in which to obtain the joint significance of a set of regressors? Examples could be looking at the joint significance level of a polynomial, or of a set of exogenous variables of which is of interest the linear combination suggested by the regression parameters. With regard to the latter, it would also be cool to visualize directly the linear combination of such group of variables, which will obviously have a regression coefficient of 1. The standard error and significance level, though, are less obvious. I would expect - please correct me if I'm wrong - that a simple ANOVA comparison between two models with and without this set of variables would give the significance level. But what if there are two sets of variables included in the model for which to find joint significance (that is, set by set)? I hope someone can help. As an example, please see the regression output below, from a quasipoisson estimation. I have two large set of eigenvector decomposition variables, one marked by "_o" and one by "_d". For these two sets of variables, I would like to have, in the regression summary, only two lines, with Estimate, Std. Error, t-value and Pr(>|t|). Obviously I can do this by hand, constructing the linear combinations, rerunning the model, and therefore obtaining a standard error and a p-value for each set. But the degrees of freedom of the model would in reality be different... Thanks in advance for any help! Cheers Roberto Patuelli Post-doc researcher Institute for Economic Research (IRE) University of Lugano Email: roberto.patuelli at lu.unisi.ch Homepage: http://www.people.lu.unisi.ch/patuellr *****************************
dep.qglm <- glm(dep ~ lndist + com_lang + contig + history + fta + lnarea_i + lngdppc_i + lngdp_i + island_i + landl_i + lnarea_e + lngdp_e + lngdppc_e + island_e + landl_e
+ + e1_o + e3_o + e4_o + e5_o + e7_o + e8_o + e9_o + e10_o + e11_o + e12_o + e13_o + e14_o + e15_o + e17_o + e18_o + e19_o + e20_o + e21_o + e22_o + e23_o + e24_o + + e1_d + e2_d + e4_d + e5_d + e7_d + e8_d + e9_d + e10_d + e12_d + e13_d + e14_d + e16_d + e17_d + e18_d + e19_d + e20_d + e22_d + e23_d + e24_d + e25_d + e26_d + e27_d + e28_d + e29_d + e30_d, family = quasipoisson (link = log))
summary(dep.qglm)
Call:
glm(formula = dep ~ lndist + com_lang + contig + history + fta +
lnarea_i + lngdppc_i + lngdp_i + island_i + landl_i + lnarea_e +
lngdp_e + lngdppc_e + island_e + landl_e + e1_o + e3_o +
e4_o + e5_o + e7_o + e8_o + e9_o + e10_o + e11_o + e12_o +
e13_o + e14_o + e15_o + e17_o + e18_o + e19_o + e20_o + e21_o +
e22_o + e23_o + e24_o + e1_d + e2_d + e4_d + e5_d + e7_d +
e8_d + e9_d + e10_d + e12_d + e13_d + e14_d + e16_d + e17_d +
e18_d + e19_d + e20_d + e22_d + e23_d + e24_d + e25_d + e26_d +
e27_d + e28_d + e29_d + e30_d, family = quasipoisson(link = log))
Deviance Residuals:
Min 1Q Median 3Q Max
-137.3970 -4.3775 -1.8095 -0.6143 195.3221
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -29.311658 0.243063 -120.593 < 2e-16 ***
lndist -0.608668 0.009603 -63.386 < 2e-16 ***
com_lang 0.162357 0.021064 7.708 1.34e-14 ***
contig 0.578563 0.023609 24.506 < 2e-16 ***
history 0.176760 0.023113 7.647 2.15e-14 ***
fta 0.411314 0.018823 21.851 < 2e-16 ***
lnarea_i -0.137816 0.008402 -16.404 < 2e-16 ***
lngdppc_i 0.003957 0.018315 0.216 0.828937
lngdp_i 0.816396 0.010770 75.801 < 2e-16 ***
island_i 0.118761 0.030618 3.879 0.000105 ***
landl_i -0.337145 0.040638 -8.296 < 2e-16 ***
lnarea_e -0.054909 0.006349 -8.649 < 2e-16 ***
lngdp_e 0.808997 0.009182 88.111 < 2e-16 ***
lngdppc_e 0.012582 0.012363 1.018 0.308837
island_e -0.202474 0.029096 -6.959 3.55e-12 ***
landl_e -0.226312 0.041144 -5.501 3.84e-08 ***
e1_o 0.685095 0.130636 5.244 1.59e-07 ***
e3_o -1.204244 0.140884 -8.548 < 2e-16 ***
e4_o -1.311745 0.433108 -3.029 0.002460 **
e5_o -1.539045 0.278576 -5.525 3.34e-08 ***
e7_o 1.722945 0.145778 11.819 < 2e-16 ***
e8_o 1.286667 0.124809 10.309 < 2e-16 ***
e9_o 0.359851 0.111494 3.228 0.001251 **
e10_o 3.783921 0.288042 13.137 < 2e-16 ***
e11_o 0.429692 0.138996 3.091 0.001995 **
e12_o -0.707160 0.087880 -8.047 9.00e-16 ***
e13_o -2.231826 0.225201 -9.910 < 2e-16 ***
e14_o -0.256754 0.108398 -2.369 0.017865 *
e15_o -0.408286 0.158939 -2.569 0.010212 *
e17_o 0.297300 0.125250 2.374 0.017623 *
e18_o -0.969633 0.357462 -2.713 0.006683 **
e19_o -1.201774 0.116932 -10.278 < 2e-16 ***
e20_o -1.508240 0.151872 -9.931 < 2e-16 ***
e21_o 0.551079 0.269277 2.047 0.040720 *
e22_o -1.692244 0.145631 -11.620 < 2e-16 ***
e23_o -0.383306 0.104032 -3.685 0.000230 ***
e24_o 0.521337 0.102742 5.074 3.93e-07 ***
e1_d 1.782647 0.200351 8.898 < 2e-16 ***
e2_d 1.810030 0.228498 7.921 2.48e-15 ***
e4_d -1.614327 0.407554 -3.961 7.49e-05 ***
e5_d -2.177586 0.288719 -7.542 4.83e-14 ***
e7_d 0.685296 0.150117 4.565 5.03e-06 ***
e8_d 0.581178 0.129893 4.474 7.71e-06 ***
e9_d 0.383017 0.136256 2.811 0.004944 **
e10_d 1.057013 0.302056 3.499 0.000467 ***
e12_d -1.715899 0.098873 -17.355 < 2e-16 ***
e13_d -2.186354 0.306954 -7.123 1.10e-12 ***
e14_d -0.644178 0.186572 -3.453 0.000556 ***
e16_d 0.432474 0.128943 3.354 0.000798 ***
e17_d 0.411581 0.141766 2.903 0.003698 **
e18_d -2.096561 0.417727 -5.019 5.24e-07 ***
e19_d -0.828071 0.139642 -5.930 3.08e-09 ***
e20_d -1.403737 0.162520 -8.637 < 2e-16 ***
e22_d -2.012591 0.114711 -17.545 < 2e-16 ***
e23_d -0.510387 0.163163 -3.128 0.001762 **
e24_d 1.139063 0.145660 7.820 5.56e-15 ***
e25_d -0.512741 0.175212 -2.926 0.003433 **
e26_d 1.931725 0.224658 8.599 < 2e-16 ***
e27_d -1.184863 0.114861 -10.316 < 2e-16 ***
e28_d 1.022568 0.147280 6.943 3.96e-12 ***
e29_d -1.403916 0.224753 -6.246 4.29e-10 ***
e30_d 0.769500 0.231363 3.326 0.000883 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for quasipoisson family taken to be 217.7894)
Null deviance: 40268568 on 18631 degrees of freedom
Residual deviance: 2453593 on 18570 degrees of freedom
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