# Re: [R] na.action and simultaneous regressions

Date: Wed 03 Jan 2007 - 22:14:35 GMT

No, Bert, lm doesn't produce a list each of whose components is a separate fit using "all" the nonmissing data in the column. It is true that the regressions are independently performed, but when the response matrix is passed from "lm" on to "lm.fit", only the complete rows are passed, i.e. rows with no missing values. I looked at "lm" function, but it was not obvious to me how to fix it.

In the following toy example, the degrees of freedom for y1 regression should be 18 and that for y2 should be 15, but both degrees of freedom are only 15.

> y1 <- runif(20)
> y2 <- c(runif(17), rep(NA,3))
> x <- rnorm(20)
> summary(lm(cbind(y1,y2) ~ x))
Response y1 :

Call:
lm(formula = y1 ~ x)

Residuals:

Min 1Q Median 3Q Max -0.52592 -0.22632 -0.00964 0.25117 0.31227

Coefficients:

Estimate Std. Error t value Pr(>|t|) (Intercept) 0.56989 0.06902 8.257 5.82e-07 *** x -0.12325 0.06516 -1.891 0.078 .

```---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2798 on 15 degrees of freedom
Multiple R-Squared: 0.1926,     Adjusted R-squared: 0.1387
F-statistic: 3.577 on 1 and 15 DF,  p-value: 0.07804

Response y2 :

Call:
lm(formula = y2 ~ x)

Residuals:
Min       1Q   Median       3Q      Max
-0.48880 -0.28552 -0.06022  0.23167  0.54425

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.43712    0.07686   5.687 4.31e-05 ***
x            0.10278    0.07257   1.416    0.177
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3115 on 15 degrees of freedom
Multiple R-Squared: 0.118,      Adjusted R-squared: 0.05915
F-statistic: 2.006 on 1 and 15 DF,  p-value: 0.1771

Ravi.

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Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

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-----Original Message-----
From: r-help-bounces@stat.math.ethz.ch
[mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Bert Gunter
Sent: Wednesday, January 03, 2007 4:46 PM
To: 'Talbot Katz'; r-help@stat.math.ethz.ch
Subject: Re: [R] na.action and simultaneous regressions

As the Help page says:

If response is a matrix a linear model is fitted separately by least-squares
to each column of the matrix

So there's nothing hidden going on "behind the scenes," and
apply(cbind(y1,y2),2,function(z)lm(z~x)) (or an explicit loop, of course)
will produce a list each of whose components is a separate fit using all the
nonmissing data in the column.

Bert Gunter
Genentech Nonclinical Statistics
South San Francisco, CA 94404

-----Original Message-----
From: r-help-bounces@stat.math.ethz.ch
[mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Talbot Katz
Sent: Wednesday, January 03, 2007 11:56 AM
To: r-help@stat.math.ethz.ch
Subject: [R] na.action and simultaneous regressions

Hi.

I am running regressions of several dependent variables using the same set
of independent variables.  The independent variable values are complete, but

each dependent variable has some missing values for some observations; by
default, lm(y1~x) will carry out the regressions using only the observations

without missing values of y1.  If I do lm(cbind(y1,y2)~x), the default will
be to use only the observations for which neither y1 nor y2 is missing.  I'd

like to have the regression for each separate dependent variable use all the

non-missing cases for that variable.  I would think that there should be a
way to do that using the na.action option, but I haven't seen this in the
documentation or figured out how to do it on my own.  Can it be done this
way, or do I have to code the regressions in a loop?  (By the way, since it
restricts to non-missing values in all the variables simultaneously, is this

because it's doing some sort of SUR or other simultaneous equation
estimation behind the scenes?)

Thanks!

--  TMK  --
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917-656-5351	cell

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