[R] t-test for regression estimate
Fox, John
jfox at mcmaster.ca
Wed Jun 29 22:51:48 CEST 2016
Dear Steven,
> -----Original Message-----
> From: Steven Yen [mailto:syen04 at gmail.com]
> Sent: June 29, 2016 9:48 AM
> To: Fox, John <jfox at mcmaster.ca>
> Cc: R-help <r-help at r-project.org>; Sandy Weisberg (sandy at umn.edu)
> <sandy at umn.edu>
> Subject: Re: [R] t-test for regression estimate
>
> Also,
> Is there a way to get the second command (hypothesis defined with externally
> scalars) below to work? Thanks.
>
> linearHypothesis(U,"0.5*eq1_DQ+0.3*eq2_DQ",verbose=T)
> w1<-0.5; w2<-0.3
> linearHypothesis(U,"w1*eq1_DQ+w2*eq2_DQ",verbose=T) # does not work
You can specify the hypothesis matrix (a vector in the 1-df case). E.g.,
----------------- snip ---------------------
> library(car)
> mod <- lm(prestige ~ income + education, data=Duncan)
> one <- 1
> minus.one <- -1
> linearHypothesis(mod, c(0, one, minus.one)) # 0 * the intercept
Linear hypothesis test
Hypothesis:
income - education = 0
Model 1: restricted model
Model 2: prestige ~ income + education
Res.Df RSS Df Sum of Sq F Pr(>F)
1 43 7518.9
2 42 7506.7 1 12.195 0.0682 0.7952
----------------- snip ---------------------
John
>
>
> On 6/29/2016 12:38 PM, Steven Yen wrote:
>
>
> Thanks John. Yes, by using verbose=T, I get the value of the hypothesis.
> But tell me again, how would I get the variance (standard error)?
>
>
> On 6/29/2016 11:56 AM, Fox, John wrote:
>
>
> Dear Steven,
>
> OK -- that makes sense, and there was also a previous request
> for linearHypothesis() to return the value of the hypothesis and its covariance
> matrix. In your case, where there's only 1 numerator df, that would be the
> value and estimated sampling variance of the hypothesis.
>
> I've now implemented that, using (at least provisionally)
> attributes in the development version of the car package on R-Forge, which you
> should be able to install via install.packages("car", repos="http://R-Forge.R-
> project.org" <http://R-Forge.R-project.org> ). Then see ?linearHypothesis for
> more information.
>
> Best,
> John
>
>
> -----Original Message-----
> From: Steven Yen [mailto:syen04 at gmail.com]
> Sent: June 28, 2016 3:44 PM
> To: Fox, John <jfox at mcmaster.ca>
> <mailto:jfox at mcmaster.ca>
> Cc: R-help <r-help at r-project.org> <mailto:r-help at r-
> project.org>
> Subject: Re: [R] t-test for regression estimate
>
> Thanks John. Reason is I am doing linear
> transformations of many coefficients
> (e.g., bi / scalar). Of course I can uncover the t-statistic
> from the F statistic and
> then the standard error. Simply scaling the estimated
> coefficients I can also
> transform the standard errors. I have since found
> deltaMethod from library
> "car" useful. Its just that, if linearHypothesis had
> provide the standard errors
> and t-statistics then the operation would have been
> easier, with a one-line
> command for each coefficient. Thank you again.
>
>
> On 6/28/2016 6:28 PM, Fox, John wrote:
>
>
> Dear Steven,
>
> The reason that linearHypothesis() computes a
> Wald F or chisquare
> test rather than a t or z test is that the (numerator) df
> for the linear hypothesis
> need not be 1.
>
> In your case (as has been pointed out) you can
> get the coefficient
> standard error directly from the model summary.
>
> More generally, with some work, you could
> solve for the the SE for a 1
> df linear hypothesis in terms of the value of the linear
> function of coefficients
> and the F or chisquare. That said, I'm not sure why you
> want to do this.
>
> I hope this helps,
> John
>
> -----------------------------
> John Fox, Professor
> McMaster University
> Hamilton, Ontario
> Canada L8S 4M4
> Web: socserv.mcmaster.ca/jfox
>
>
>
> -----Original Message-----
> From: R-help [mailto:r-help-
> bounces at r-project.org] On Behalf
> Of Steven Yen
> Sent: June 28, 2016 9:27 AM
> To: R-help <r-help at r-project.org>
> <mailto:r-help at r-project.org> <mailto:r-help at r-
> project.org> <mailto:r-help at r-project.org>
> Subject: [R] t-test for regression
> estimate
>
> test option for linearHypothesis in
> library(car) include "Chisq"
> and "F". I prefer
> a simple t-test so that I can retrieve
> the standard error.
> Any options other than
> linearHypothesis to test the linear
> hypothesis (with 1
> restriction/degree of freedom)?
>
> > summary(ols1)
>
> Coefficients:
> Estimate Std. Error t value
> Pr(>|t|)
> (Intercept) -0.20013 0.09199 -2.176
> 0.0298 *
> age 0.04054 0.01721 2.355
> 0.0187 *
> suburb 0.01911 0.05838 0.327
> 0.7435
> smcity -0.29969 0.19175 -1.563
> 0.1184
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01
> ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> > linearHypothesis(ols1,"suburb")
> Linear hypothesis test
>
> Hypothesis:
> suburb = 0
>
> Model 1: restricted model
> Model 2: polideo ~ age + suburb +
> smcity
>
> Res.Df RSS Df Sum of Sq F Pr(>F)
> 1 888 650.10
> 2 887 650.02 1 0.078534 0.1072
> 0.7435
>
>
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>
>
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