Dear Michael,My previous response was inaccurate: First, linearHypothesis() *is* able to accommodate aliased coefficients by setting the argument singular.ok = TRUE:
> linearHypothesis(minimal_model, "bt2 + csent + bt2:csent = 0", + singular.ok=TRUE) Linear hypothesis test: bt2 + csent + bt2:csent = 0 Model 1: restricted model Model 2: a ~ b * c Res.Df RSS Df Sum of Sq F Pr(>F) 1 16 9392.1 2 15 9266.4 1 125.67 0.2034 0.6584Moreover, when there is an empty cell, this F-test is (for a reason that I haven't worked out, but is almost surely due to how the rank-deficient model is parametrized) *not* equivalent to the t-test for the corresponding coefficient in the raveled version of the two factors:
> df$bc <- factor(with(df, paste(b, c, sep=":")))
> m <- lm(a ~ bc, data=df)
> summary(m)
Call:
lm(formula = a ~ bc, data = df)
Residuals:
Min 1Q Median 3Q Max
-57.455 -11.750 0.439 14.011 37.545
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 20.50 17.57 1.166 0.2617
bct1:unsent 37.50 24.85 1.509 0.1521
bct2:other 32.00 24.85 1.287 0.2174
bct2:sent 17.17 22.69 0.757 0.4610 <<< cf. F = 0.2034, p
= 0.6584
bct2:unsent 38.95 19.11 2.039 0.0595 Residual standard error: 24.85 on 15 degrees of freedom Multiple R-squared: 0.2613, Adjusted R-squared: 0.06437 F-statistic: 1.327 on 4 and 15 DF, p-value: 0.3052In the full-rank case, however, what I said is correct -- that is, the F-test for the 1 df hypothesis on the three coefficients is equivalent to the t-test for the corresponding coefficient when the two factors are raveled:
> linearHypothesis(minimal_model_fixed, "bt2 + csent + bt2:csent = 0")
Linear hypothesis test:
bt2 + csent + bt2:csent = 0
Model 1: restricted model
Model 2: a ~ b * c
Res.Df RSS Df Sum of Sq F Pr(>F)
1 15 9714.5
2 14 9194.4 1 520.08 0.7919 0.3886
> df_fixed$bc <- factor(with(df_fixed, paste(b, c, sep=":")))
> m <- lm(a ~ bc, data=df_fixed)
> summary(m)
Call:
lm(formula = a ~ bc, data = df_fixed)
Residuals:
Min 1Q Median 3Q Max
-57.455 -11.750 0.167 14.011 37.545
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 64.000 25.627 2.497 0.0256
bct1:sent -43.500 31.387 -1.386 0.1874
bct1:unsent -12.000 36.242 -0.331 0.7455
bct2:other -11.500 31.387 -0.366 0.7195
bct2:sent -26.333 29.591 -0.890 0.3886 << cf.
bct2:unsent -4.545 26.767 -0.170 0.8676
Residual standard error: 25.63 on 14 degrees of freedom
Multiple R-squared: 0.2671, Adjusted R-squared: 0.005328
F-statistic: 1.02 on 5 and 14 DF, p-value: 0.4425
So, to summarize:
(1) You can use linearHypothesis() with singular.ok=TRUE to test the
hypothesis that you specified, though I suspect that this hypothesis
probably isn't testing what you think in the rank-deficient case. I
suspect that the hypothesis that you want to test is obtained by
raveling the two factors.
(2) There is no reason to use deltaMethod() for a linear hypothesis, but there is also no intrinsic reason that deltaMethod() shouldn't be able to handle a rank-deficient model. We'll probably fix that.
My apologies for the confusion, John -- John Fox, Professor Emeritus McMaster University Hamilton, Ontario, Canada web: https://www.john-fox.ca/ On 2023-09-26 9:49 a.m., John Fox wrote:
Caution: External email. Dear Michael, You're testing a linear hypothesis, so there's no need to use the delta method, but the linearHypothesis() function in the car package also fails in your case: > linearHypothesis(minimal_model, "bt2 + csent + bt2:csent = 0")Error in linearHypothesis.lm(minimal_model, "bt2 + csent + bt2:csent = 0") :there are aliased coefficients in the model. One work-around is to ravel the two factors into a single factor with 5 levels: > df$bc <- factor(with(df, paste(b, c, sep=":"))) > df$bc [1] t2:unsent t2:unsent t2:unsent t2:unsent t2:sent t2:unsent [7] t2:unsent t1:sent t2:unsent t2:unsent t2:other t2:unsent [13] t1:unsent t1:sent t2:unsent t2:other t1:unsent t2:sent [19] t2:sent t2:unsent Levels: t1:sent t1:unsent t2:other t2:sent t2:unsent > m <- lm(a ~ bc, data=df) > summary(m) Call: lm(formula = a ~ bc, data = df) Residuals: Min 1Q Median 3Q Max -57.455 -11.750 0.439 14.011 37.545 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 20.50 17.57 1.166 0.2617 bct1:unsent 37.50 24.85 1.509 0.1521 bct2:other 32.00 24.85 1.287 0.2174 bct2:sent 17.17 22.69 0.757 0.4610 bct2:unsent 38.95 19.11 2.039 0.0595 Residual standard error: 24.85 on 15 degrees of freedom Multiple R-squared: 0.2613, Adjusted R-squared: 0.06437 F-statistic: 1.327 on 4 and 15 DF, p-value: 0.3052 Then the hypothesis is tested directly by the t-value for the coefficient bct2:sent. I hope that this helps, John -- John Fox, Professor Emeritus McMaster University Hamilton, Ontario, Canada web: https://www.john-fox.ca/ On 2023-09-26 1:12 a.m., Michael Cohn wrote:Caution: External email. I'm running a linear regression with two categorical predictors and their interaction. One combination of levels does not occur in the data, and asexpected, no parameter is estimated for it. I now want to significance test a particular combination of levels that does occur in the data (ie, I wantto get a confidence interval for the total prediction at given levels of each variable). In the past I've done this using car::deltaMethod() but in this dataset that does not work, as shown in the example below: The regression model gives the expected output, but deltaMethod() gives this error: error in t(gd) %*% vcov. : non-conformable arguments I believe this is because there is no parameter estimate for when the predictors have the values 't1' and 'other'. In the df_fixed dataframe,putting one person into that combination of categories causes deltaMethod()to work as expected. I don't know of any theoretical reason that missing one interaction parameter estimate should prevent getting a confidence interval for adifferent combination of predictors. Is there a way to use deltaMethod() orsome other function to do this without changing my data? Thank you, - Michael Cohn Vote Rev (http://voterev.org) Demonstration: ------ library(car) # create dataset with outcome and two categorical predictors outcomes <- c(91,2,60,53,38,78,48,33,97,41,64,84,64,8,66,41,52,18,57,34) persontype <- c("t2","t2","t2","t2","t2","t2","t2","t1","t2","t2","t2","t2","t1","t1","t2","t2","t1","t2","t2","t2") arm_letter <- c("unsent","unsent","unsent","unsent","sent","unsent","unsent","sent","unsent","unsent","other","unsent","unsent","sent","unsent","other","unsent","sent","sent","unsent") df <- data.frame(a = outcomes, b=persontype, c=arm_letter) # note: there are no records with the combination 't1' + 'other' table(df$b,df$c) #regression works as expected minimal_formula <- formula("a ~ b*c") minimal_model <- lm(minimal_formula, data=df) summary(minimal_model)#use deltaMethod() to get a prediction for individuals with the combination'b2' and 'sent' # deltaMethod() fails with "error in t(gd) %*% vcov. : non-conformable arguments." deltaMethod(minimal_model, "bt2 + csent + `bt2:csent`", rhs=0)# duplicate the dataset and change one record to be in the previously emptycell df_fixed <- df df_fixed[c(13),"c"] <- 'other' table(df_fixed$b,df_fixed$c) #deltaMethod() now works minimal_model_fixed <- lm(minimal_formula, data=df_fixed) deltaMethod(minimal_model_fixed, "bt2 + csent + `bt2:csent`", rhs=0) [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
