okay in this video I'm going to review a
couple of macros that you can download
from the web for use with SPSS in order
to carry-out
regression analysis using robust
standard errors basically when you run
regression analysis through the standard
approach just a standard linear
regression it doesn't take into account
the possibility that you might have
heteroscedasticity in terms of your
residuals and if that is the case and
what that can do it may not it won't
bias your regression coefficients but it
can lead to biases in terms of the
standard errors and ultimately your
significance tests and confidence
intervals so this is basically a major
reason why we care about this particular
issue so what I'm going to do is I'm
going to review two macros in particular
the first one is Andrew Hayes macro he
has it on his website basically on his
book website it looks like there's a new
book out regression analysis and linear
models and at this particular downloaded
spot you can download a zip file
containing the R ALM macro and you can
install it to SPSS and then be able to
run it straight from there so in order
to do that if you just download it from
there you'll just go to extensions go to
utilities install custom dialog and I
basically have my I have it saved under
a certain folder here if you click on
this folder here go down to our LM macro
and click on it there's there's the
macro click on open it'll install it to
your program and so you can see it's
it's installed right here as as our LM
macro by Andrew Hayes so that's the
first one I'm going to demonstrate the
second one actually comes from this
website right here and I just happened
upon it by when I
ran across this YouTube video explaining
it and the nice thing about this
particular macro is it also allows you
to generate robust standard errors for
your regression analysis but it also
incorporates the brush of pagan test and
the cannot connect or test which are
basically utilized in the evaluation of
the homoscedasticity of variance
assumption so our constant variance
assumption so the basic idea is that if
you find statistical significance for in
terms of these tests right here that
would be an indicator that you have
heteroscedasticity which would call into
question perhaps the use of the standard
least squares regression that does not
make any kind of adjustments to the
standard errors and so that's so with
this program though you can also ask for
heteroscedasticity adjusted standard
errors so making them essentially robust
standard errors so I'm gonna walk
through both of these programs right
here are macros so and I've it installed
that pretty much doing the same thing
that did with Andrew Hayes's and you'll
see the under regression I've got it
right here heteroscedasticity test and
so at this point we'll run those
analyses I also have on here Andrew
Hayes is older macro the H basically
it's an older approach to giving robust
standard errors and that is actually
coming from this macro down here so you
might find it HC reg this is just a much
more drilled drilled down version of
what you would get with respect to this
particular macro so as he says on his
website it's becoming obsolete with the
release of the R LM so but I will just
kind of show that as a point of contrast
so you can see what it looks like so for
starters let's start with Andrew Hayes's
macro so we're going to go to animal
as good a regression rlm macro by Andrew
Hayes now first of all really quickly
the the basic model that we're going to
be looking at we have a dependent
variable which will be achieved and we
have a set of independent variables
right here so gender something matter
interest mastery goals and anxiety and
so I'm gonna move achieve which is going
to be my dependent variable to this box
and move the remaining variables over to
the regressors box I can ask for
standardized coefficients I can ask for
you know a number of different things
one of the kind of cool things about
this particular macro is you can even
get all subsets regression that's really
pretty slick and if you want regression
Diagnostics you know basically cut you
know in the same way that you might get
if you're running the analysis through
regression just standard regression
module and click on safe you know you
can ask for various things like
Mahalanobis and cooks D and and things
like that you can get some of that
through this macro as well so basically
will do so create a new file that would
incorporate some of those those
diagnostic indicators so so you don't
actually have to do it I'm just saying
that you you know it is available to you
so I'm gonna I'm just gonna stick with
this right here notice the confidence
interval is already defaulted at 95%
there are other options if you want it
and down here where it says covariance
estimator
HC so if I click on this there are
various adjustments to the standard
errors and I'm going to pivot off of a
haze in Kies 2007 article where they
actually recommended using either the HC
3 or HC 4 estimators so I'm going to use
HC 3 so I'm going to click on this go
down to HC 3 and at this point I'll
click on OK and so you can see we've got
several you know a number of pieces of
information we have the multiple are
right here the r-square value the f-test
and you know there's our p-value for
testing the significance related to our
square down here where it says
regression model you can see we have the
efficients and then a column containing
SC and so these are the robust standard
errors using that particular adjustment
that means that them that the t-value
p-values and confidence intervals are
all going to be reflecting the
adjustment to the standard errors so if
you scroll down a little bit further you
can see we've got we also asked for
those standardized assessments including
the correlation simple correlation
between each of the end of the
independent variables and the dependent
variable semi partial correlations and
then partial correlations right here and
then these would be your standard as
regression weights or you know basically
we call them beta weights so at any rate
that's you know that's what we have
right there if we want to compare this
just against what you would get in terms
of the standard errors we just run our
analysis I'm going to take these off run
our analysis without the adjustment you
can see the difference the for the
standard error is the standard error for
model one well for our model that for
the intercept is thirty three point nine
seven eight you can see it's forty seven
point nine one nine for gender it's one
point eight forty nine versus two point
one then 0.195 for the for the next one
is versus point one nine oh so you can
see that these standard errors in this
in this column right here tend to be a
little bit larger than those that we
have when we don't adjust for the
possibility of heteroscedasticity so at
any rate there you go
so that's kind of the difference that
you that you get right there let me just
show you one more time let's just I'll
show you what to get if you click on
regression Diagnostics will click on
okay and what you'll see it's just going
to be the same output but now it
generates a new file that contains all
of our variables as well as Diagnostics
and so you can see you know here we've
got the fitted values residuals hella
novus distance Kooks D and so forth
that's that's essentially Andrew Hayes's
macro
the new one the old one by the way it
looks like this if we want to use that
one the H see we're Greg regression when
basically you can see right here we
would just be putting our T variable
into the dependent box gender and
through anxiety into the predictors box
you can click on HC method and I've
already got set for HC three and so
that's the difference right there so
it's quite a difference in terms of
what's printed out but you see that we
have our F test right here the standard
errors the robust standard errors the
the T tests and the p-values all those
reflecting the adjustments for any kind
of heteroscedasticity they may be
present okay so that that takes care of
Andrew Hayes's version now we're going
to go to this one right here what we're
going to look at that and and again the
nice thing about this particular macro
is it does incorporate tests for
heteroscedasticity the brush pagan and
conic er test and and basically to carry
out that analysis once you've installed
it we're gonna go to analyze go to
regression and here it is so
heteroscedasticity test will click on it
and I'm just gonna reset it and just
kind of you know sometimes it's just
nice nice to have a visual walkthrough
so I'm just gonna put my independence in
the explanatory box outcome and the
achieve and the outcome box you can see
you've got the robust standard error
options hc3 I'm gonna click on OK and so
now you can see that here we've got the
standard least squares regression output
there's our R square value you can see
as before all of our regression
coefficients are exactly the same
whether we're using the default OLS
versus the heteroscedasticity robust
standard errors but you see the
differences lie in the column four
standard errors right here versus here
so we basically were able to generate
both of those using
and replaces macros and and then also
juxtaposing those against the standard
errors from the standard least squares
regression so then we have our T values
down here significance levels 95 percent
confidence intervals all down here in
this area adjusted for or after we've
adjusted the standard errors well scroll
down and you'll see that we have the
ANOVA summary table down here this looks
like this maybe from the standard least
squares regression priority any kind of
adjustments so that's something to kind
of note there when you look at Andrew
Hayes's F value that's printed out up
here you can see it's nine point zero
307 the FA from this macro is printed
out as far as it out there is nine point
five to four if we compare that with our
previous regression earlier on you can
see it's a nine point five to four so
that's where I'm getting that
supposition from okay so with the brush
pagan and Conacher tests I hope I'm
pronouncing that right I probably am not
but you can see down here that with
respect to those tests in this little
area we've got the the test results and
you've got the boys pagan test and the
concur tests these are the tests values
using a Lagrange multiplier test we have
significance levels right here and the
Pete you know basically if your p-values
are are greater than say 0.05
conventional alpha then we would assume
that the assumption of homoscedasticity
is met in other words the constant error
assumption is met if it's less than 0.05
then we would maybe infer that that we
violated that particular assumption just
keep in mind that these kinds of tests
are impacted by sample size and
you know the drill that the larger the
sample size the greater likelihood of
rejecting the null so just keep that in
mind as you're evaluating whether or not
you've violated or whether we violated
the assumption and can't use the
standard least squares regression if
it's so in this particular case it looks
like based on these tests or there's
evidence that we would not have violated
that assumption if we were using the
standard least squares regression so
that would call into question the need
to utilize adjusted standard errors or
robust standard errors in the way that
we have but you know also keep in mind
that this is like I said this is a
significance test it's probably not a
bad idea to also you know look at
residuals plots and so forth to further
evaluate whether the assumption is met
so at any rate that that pretty well
light lays it out for you and I hope you
find this useful that like I said these
are two really neat macros that are
available to you you know the nice thing
about Andrew Hayes macro the first one
is it does contain a lot more options in
terms of you know different types of
output and it does incorporate that nice
little aspect of the all subsets
regression if you choose to go with the
latter approach the nice thing is is
that you do get significance tests
related to you know testing the
assumption of constant variances but you
don't get quite as much in the way of
the individual output in other areas so
at any rate just uh I hope this I hope
you find this useful and good luck with
your research
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