[R] t-test for regression estimate

[Steven Yen]

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

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"). 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>
>>> Cc: R-help<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>
>>> 		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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>


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