[R] Joint significance of more regressors in summary

Thu Jan 22 00:20:29 CET 2009

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