SPSS Multinomial logistic regression (1 of 2) Video Lecture - SPSS

the multinomial logit model first
question is do you need this model well
this model is typically taught at the
graduate level so if you an undergrad
then this may not be applicable to you
or you might not have to go as far as
looking at this model if you've
collected data from a survey this model
could well be useful if you've come
across the logit model the binomial
logit model then this is pretty much
similar recall that in the binomial
logit or just a logit model that your
response variable has one of two
outcomes okay where those outcomes
there's no natural ordering so their
nominal one silly example I did of this
video I did of this was a date does a
person get to date another person yes or
no so that's what I mean
so multinomial logit is an extension to
the binomial logic because now your
response variable has more than two
outcomes I'm going to focus here on
interpreting the coefficients because
remember at the end of the day we are
interested in either using the model for
prediction or interpreting the
coefficients to link the explanatory
variables see what the explanatory
variables have to say about the
dependent variable the response we're
going to focus on interpreting
coefficients so I'm not interested in
coming up for strategy to build a
suitable model for the data okay so
what's the date look like here's an
example taken from the SPSS example
files so you can follow it so pretend
I'm a marketing company I have three
products cereal product a breakfast bar
and an O
your thing and I want to kind of see
what factors influence people's choices
of which kind of bar they go for
so my response variable is here be fast
and you've got cereal breakfast bar
oatmeal so here we've got three choices
so we're supposing an individual can
pick one of three but not more than one
all right okay and then we've got some
expander variables notice that they are
all qualitative or categorical they are
not continuous so my interpretation of
the coefficients in this case will be
for qualitative explanatory variables
okay let's just show it's been coded
we'll look at this value label so I
press this that should show us the codes
used like that toggle back all right so
I'm going to kind of look at that how
gender see where the gender got the
interpretation of the coefficient gender
on the breakfast bar so I'm going to ask
question does your gender influence your
choice of the kind of breakfast bar X
our breakfast choice you go for okay so
how do we do it okay we know we can't
fit a standard regression model because
my response variable is not continuous
just said nor can I fit the normal logit
model because it has more than two
outcomes three outcomes okay because
that's an important point let's just say
this first person chooses cereal over
bread when they've given a choice of Co
breakfast note meal the second person
here who is aged in this group 46 to 60
and it's a male person who is married
and not active goes for the breakfast
bar kick breakfast bar just breakfast
bar and one more let's do one more fifth
one oh okay just happens to be also in
46
60 group also mail married inactive as
well
goes for the oatmeal okay right and
notice as I said their note each person
he only goes for one choice can't pick
them on one it can't be a kind of can't
be kind of greedy and go for more than
one so we'll ask each person what is
your preferred what the question it
would be like what it would be your
preferred choice
oatmeal breakfast bar or cereal pick one
only that's it say stuff like that in
the survey okay
so we have to fit a multinomial as the
name suggests multi means and many many
no meal like nominal so these are
nominal outcomes they're not ordered
can't say cereal is better than
breakfast we can say oatmeal is better
than the cereal so on okay right okay
now so let's do it without any bells and
whistles we'll just go analyze
regression and then we look for
multinomial logistic click our window
pops up and I'll just reset it because I
run this through earlier so we'll face
with something like this
a dependent box that is my choice my
response variable so that's going to be
the label be fast for breakfast take
that over there now the factors here any
kind of qualitative things where it's
cool there it's the kind of continuous
things
alright continued your success these are
categorical X's we're just going to have
gender that's it and we're not looking
anything else we'll just press ok as
usual of SPSS you get a whole load of
stuff dumped we're interested solely on
the parameters this or is it the bottom
there you go let's look at it notice the
box consists what within it of two sub
tables
what goes down here is the choice now
notice that one choice is missing
remember had cereal breakfast by oatmeal
cereal has been left out oh why
well idea is that we're going to compare
all these other choices relative to
cereal so if you think about dummy
variables when we did dummy variables
remember that if you have K group
categories then K categories you setup K
minus-1 dummies so here we've got a
choice of three we sell two dummies
something like that and likewise for the
explanatory variable so we'll look at
each of these boxes each of these boxes
will be comparing that choice to the
thing left out cereal so this here box
we're saying comparing people's choice
of breakfast bar relative to cereal and
this one would be oatmeal relative to
cereal okay let's just take the first
one so now what we see inside here is
we've got gender 0 gender 1 so let's go
back to the we need to know what is what
here so we click on this tab right so we
get mail is 0 right and female is 1
that's how it's coded go back to the
output male male better to write this
down otherwise - that forget right so
male is 0 right male is 0 ok nail is 0
okay now because gender has two
categories so K is 2 we leave out one as
a reference category so that's why you
see that here is the at gender equals 0
that has a number that's the coefficient
but gender one that is set to zero and
then you go superscript B which tells
you that this parameter set to zero
because it's redundant in other words
it's um there's
set the gender' one which is female here
to set as the reference category alright
so gender just to recap gender is
categorical variable has two categories
because of that we we set up just one
dummy variable because of the rule a
dummy rule and if you have K categories
you set up K minus one dummies so this
coefficient tells us then we'll compare
males to females and tell us something
about how likely a male is compared to
female to go for this option the
breakfast bar
relative to cereal the interpretation is
a bit like the binomial Lockett so let's
just recap that here so if this
coefficient on gender is a we need to
consider three cases bigger than zero
equal to 0 or less than 0 if it is
bigger than 0 it would mean that males
compared to females more likely to go
for the breakfast bar rather than cereal
if it is equal to 0 then males and
females are equally likely to go for the
breakfast bar relative to the cereal and
if it was less than 0 and males it
compared to females are less likely to
go for the breakfast bar relative to
cereal okay and instead of looking at a
B we can look at the exponential of the
B which gives us the odds ratio I think
it's a good idea to write this down let
me try and write this down let me lay it
out ok so we've got here am i saying
we've got the gender coefficient
let's call it let's just call it B so
I'd like to write again again and then
we've got the odds ratio which is given
so this categorical variable here as e
to the coefficient value B alright and
we've said there are three cases so a
result I say conclusion conclusion right
it can be bigger than zero it can be
equal to zero it can be less than zero
but if it's bigger than 0 if you take e
to the number bigger than zero that's
going to be bigger than one if B is 0 e
to the 0 is 1
you try some calculator not just and if
B is less than 0 if you put that into
here e to the negative number is going
to be less than 1 but positive ok the
conclusion here then is to say that
nails compared to females are more
likely to go for the breakfast bar and
cereal cereal likewise here males
females equally likely to go for the
breakfast bar blah blah blah let's go up
a breakfast button cereal and here it's
going to be males compared to females
less likely
to go for the breakfast bar and the
cereal okay right so let's see what
we've got here in this output what we
have got here is got got we've got the
coefficient of negative all right so
let's first all get the direction right
so negative that tells us if we go back
here the coefficient is negative it
tells us then males compared to females
are less likely to go for the breakfast
button cereal simple as that
okay how about if you wanted to say
something more precise well in that case
you can report the odds ratio 0.864
okay that tells us let's write this odds
ratio 0.864 odds ratio that's going to
be odds for the male group divided by
odds for the female group is equal to
not 0.864 okay
now if this figure going back to this
here is equal to one you can see the
odds of the male is the same as odds
females going for the breakfast bar
compared to the cereal since this is
less than one you just do multiply both
sides take the sky multiply both sides
by odds of female we're going to get
odds male equals not 0.864 odds female
okay and this tells us that the odds for
males is 14 about approximately 14%
lower than odds for females to take
breakfast bar and cereal okay that last
point there you might just want to kind
of think why that is but this may not be
important to precise nature so long as
you get the direction right which is
which is more likely to happen
I just want to point out the
interpretation here is for my expansive
arable which is categorical okay so
let's just pause a bit so that let that
sink in before move on