lh_test mishandling joint tests?

[macartan]

Correct behavior for a joint test:

data <- data.frame(X1 = rnorm(10), 
                   X2 = rnorm(10), 
                   X3 = rnorm(10),
                   Y = rnorm(10)) 

lm(Y ~ X1+X2+X3, data = data) %>%
car::linearHypothesis(c("X1", "X2")) 

Produces a single test of the joint hypothesis:

> lm(Y ~ X1+X2+X3, data = data) %>%
+ car::linearHypothesis(c("X1", "X2")) 
Linear hypothesis test

Hypothesis:
X1 = 0
X2 = 0

Model 1: restricted model
Model 2: Y ~ X1 + X2 + X3

  Res.Df  RSS Df Sum of Sq    F Pr(>F)
1      8 4.86                         
2      6 4.68  2     0.178 0.11   0.89

However lh_robust produces:

> lh_robust(Y ~ X1+X2+X3, data = data, 
+           linear_hypothesis = c("X1", "X2")) 
$lm_robust
            Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper DF
(Intercept)     0.24        0.3    0.79      0.5     -0.5      1.0  6
X1              0.01        0.2    0.05      1.0     -0.6      0.6  6
X2              0.11        0.1    0.74      0.5     -0.2      0.5  6
X3             -0.08        0.2   -0.35      0.7     -0.6      0.5  6

$lh
   Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper DF
X1   0.0125      0.243  0.0514    0.961   -0.581    0.606  6
X2   0.1091      0.147  0.7439    0.485   -0.250    0.468  6

• The issue appears to be that return_lh_robust re-calculates a series of separate tests from attr(car_lht, "value")) and sqrt(diag(attr(car_lht, "vcov")) even if these are not requested.

• May be enough to flag in documentation that printed output is for single hypotheses and not for joint hypotheses when these are requested; (as noted) the original output is available as an attribute on the lh object.

[nfultz]

May be enough to flag in documentation that printed output is for single hypotheses and not for joint hypotheses when these are requested; (as noted) the original output is available as an attribute on the lh object.

IIRC (one of) the original intent was to make it easier to test different pairs of levels in a factor w/o having to refit, which usually takes the form

lh_robust(Y ~ X1+X2+X3, data = data, linear_hypothesis=c("1*X1- 1*X2 = 0"))

I generally feel confident about that use case.

But it is definitely worth making the documentation clearer that the omnibus tests that car::linearHypothesis prints out by default are basically ignored, and literally yields one test per row of linear_hypothesis.

And to illustrate why/how it is different, for example:

> lm(Y ~ X1+X2+X3, data = data) %>% car::linearHypothesis(c("X1=0", "X2=0"))
Linear hypothesis test

Hypothesis:
X1 = 0
X2 = 0

Model 1: restricted model
Model 2: Y ~ X1 + X2 + X3

  Res.Df        RSS Df Sum of Sq       F  Pr(>F)
1      8 11.3058701                             
2      6  8.6222509  2 2.6836192 0.93373 0.44356
> lm(Y ~ X1+X2+X3, data = data) %>% car::linearHypothesis(c("X1+X2=0"))
Linear hypothesis test

Hypothesis:
X1  + X2 = 0

Model 1: restricted model
Model 2: Y ~ X1 + X2 + X3

  Res.Df        RSS Df Sum of Sq       F  Pr(>F)
1      7 11.2911837                             
2      6  8.6222509  1 2.6689328 1.85724 0.22187
> lh_robust(Y ~ X1+X2+X3, data = data, linear_hypothesis= "X1+X2=0")
$lm_robust
                 Estimate   Std. Error       t value     Pr(>|t|)     CI Lower     CI Upper DF
(Intercept) -0.4563304929 0.5034293555 -0.9064439488 0.3996380783 -1.688177749 0.7755167633  6
X1          -0.2313394433 0.5478439885 -0.4222724866 0.6875394457 -1.571865391 1.1091865047  6
X2          -0.4277196300 0.4822974013 -0.8868379320 0.4093025385 -1.607858857 0.7524195971  6
X3          -0.2169584712 0.6851843731 -0.3166424684 0.7622420790 -1.893544234 1.4596272917  6

$lh
          Estimate Std. Error   t value  Pr(>|t|)  CI Lower  CI Upper DF
X1+X2=0 -0.6590591  0.3989217 -1.652101 0.1496022 -1.635185 0.3170671  6

Also, this comment gives me pause: https://github.com/DeclareDesign/estimatr/blob/b734297abfbf51cef3c0e271fbffc1a81ed8e06f/R/estimatr_lh_robust.R#L81