SPSS Introduction to loglinear analysis for multiway contingency tables

a very brief introduction to log linear
analysis for multi way contingency
tables that's a mouthful
the topic is log linear analysis and for
designing to make this video I did think
of jumping straight in and showing you
an example
but then they're just so many issues
involved here I thought mm let's kind of
just do a really really general
introduction so here it is so these are
questions I'm going to kind of answer as
best as I can so first one what is log
linear analysis useful okay
recall that that in crosstabs we study
about whether there's an association
between two categorical variables you
know is an association between a and B
or is there a relationship between a and
B or a and B independent where those a
and B's are factors qualitative
variables categorical variables for
example is there a relationship between
between smoking and lung cancer
log-linear analysis is a generalization
of of of crosstabs because in crosstabs
you the question is is the association
between a and B so in other words just
between two things two qualitative
factors in locally in the analysis you
extend that because you can study it to
weigh more than two things between three
four five six any number of things
because if some of you have done
crosstab to a more advanced level you've
in a master's course you probably even
seen it for a three variable case that's
when you do across tabs of two factors
controlling for a third one well lovely
analysis takes care of that but it can
go higher and higher and higher all
right
so that brings us onto multi-way
contingency table what is what is meant
by multi-way contingency table let me
show you an example here here I've got
data categorical data on whether a
person uses alcohol whether they smoke
cigarettes whether they use marijuana
and this is aggregated data so for
people who do not use alcohol do not
kind of drink alcohol smoke cigarette
and smoke marijuana three people okay so
this is aggregated data now if I were to
kind of just get a table for the
we've got factors here alcohol
cigarettes and let's put marijuana as
well so now this is like you know this
is like three variables then what I want
to do is I go to model okay I'm going to
go to custom and I can build terms and
what I'm going to do is going to put all
the main effects and then let me just
add an interaction of alcohol and
cigarettes in other words and this is
how I do it but that's the usual
it's got the x button there to alcohol
time cigarettes that's an interaction
term then get the output now go to
options undelete all these things I
don't cutter up the output
I just want estimates
the whole point I'm doing this is I'm a
trunk answering a question how can I
tell the interaction term is significant
and where can I find the trench term in
the output
okay parameter estimates is just like
regression so we've got constant that's
like the intercept term here and let's
run down here the multiplication signs
these are the interactions okay and
forget about those zeros walk see is
that out of all these interactions only
one has a number so we look at that
that's the estimate we run along there
look at significance it is significant
okay just like the usual you know
dislike just the usual kind of t-test
only it's not the t-test it's called the
z-test t-test but it does the same thing
testing significance of the interaction
the null hypothesis is there is no
interaction that will be the same for
all these kind of models all these
parameters of the interaction terms the
null hypothesis the interaction term is
not significant we reject so we say that
that is present in this case strong
evidence of presence of interaction okay
so that's how I find it an interaction
means that there's an association so
here you go next point
significant interaction terms means that
there is an association so just by
looking we don't even have to delve into
knowing what it means at the moment or
can say is that there is a relationship
between cigarette a smoking and alcohol
drinking and the nature of the
relationship can be can be described in
terms of odds ratios just as for
crosstabs okay so that's the interaction
term the main effects right the main
effects are not much used to us that
they're not interesting so let's go back
to my output again alright I said that
the components of a load linear model
are the main effects and the
interactions suppose I put them all in
so here this block consists of
interactions because they've got the
stars by each of these terms here all
these other guys upstairs
these are main effects okay and they are
not useful because the interaction terms
tell about whether there's association
yes or no and were able to kind of
interpret in terms of the odds by
looking the parameters and that's all we
need we don't need the stuff up there
all right next log linear analysis
versus cross tabs okay I said earlier on
I was going to demonstrate to you that
you get the same results say we'll have
two variables using cross tabs as we're
going to get using log lid analysis so
let's let's do that so you can see you
know make it concrete your mind that the
two things I'm pretty much doing the
same thing let's test the null
hypothesis using cross tabs where
there's an association between alcohol
use and cigarette smoking null
hypothesis will be no association
between cigarette smoking and alcohol
analyzed descriptive study statistics
this is some revision for you it's
really care
take that marijuana controlling for
marijuana so just a straightforward
analysis alright I just want to look at
the chi-square test here we have the
Pearson's chi-square value for 51.4 and
the p-value is really tiny a p-value
P stands for probabilities between zero
and one low p-value means we reject the
null here it is pretty much its low all
right less than naught point naught 5
even less than not but not 1 what does
that mean it means that there is very
strong evidence of a relationship
between cigarette smoking and alcohol
use in other words there's some kind of
pattern in this table we don't need to
go into that what I want to show you now
is that I can get the same result by
running this like a log linear analysis
now before I do that
you might be asking well if you can do
it using if crosstabs and log linear
analysis are doing the same thing why
don't you just use cross tabs all the
time well remember a log linear analysis
can handle cases of many many many many
variables much more easily than cross
tabs because with cross tabs the tables
just get massively big and complicated
and you'll be very hard to kind of
interpret what's going on
okay so log linear analysis I run it now
I'll just do the same thing as that
cross tabs what I do this time is I take
away that interaction term you don't
have to understand exactly why I'm doing
this guys and how I just set that model
we just wanna look at in coefficients
here okay goodness of fit tests we're
testing same null hypothesis no
relationship between cigarette smoking
and alcohol juice Pearson chi-square for
51.4 now was that what we had with the
cross temps let's have a look for 51.4
indeed it is p-value less than 0.01 same
so it's that exactly identical what the
log-linear table gives you that cross
tabs doesn't is this parameter estimates
box I know those of you who have to
report odds and odds ratios and cross
tabs and they're lazy to do so you can
actually kind of get them more easily by
running a log as if it was log linear
analysis on it and interpreting these
coefficients which can be converted into
odds ratios okay so now we know what a
log linear analysis is is it's an
extension of cross tabs we can use it
for only makes sense to use of two or
more variables but usually when we have
two variables we'll just run cross tabs
on it but and if you have many many many
that's when you use log linear analysis
buttons in SPSS for log linear analysis
okay let's now quick overview of what
is available in SPSS for log linear
analysis we go analyze log linear
alright
the three menus well first I've chosen
the first one the general is like when
you want to set up a model and you want
to control what's in your model you want
to control what the main effects are and
what the interaction effects are through
all this stuff okay second option run on
the second option we're going straight
to my full selection is because if you
have a model with loads and loads of
variables
I've got maximum three variables but
beside many many many variables what you
can do is just like in regression where
you have this automated stepwise
procedures like backwards elimination
and forward selection procedures that
kind of statistically select the best
model you can do the same thing with
this model selection procedure so you
can see your model building can use
backward elimination and single step so
how you could use this is to if you had
a big big lots of variables is to run
this thing first just to kind of get an
idea a starting point as to what the
model should be and then go to general
and run that model so you can get more
output for it and maybe think of it if
you need to okay final option log it
okay well this kind of falls into my
final issue
notable issues in log linear analysis I
left this to the end because usually I
think when you learn about crosstab yawn
you can be told about this until the end
of the course if at all in load Li now
analysis we've assumed so far that our
variables are nominal as opposed to
ordinal
can remember nominal means that there's
no
kind of natural ranking you can't say
like for example for the alcohol that
yes they smoke alcohol is better than no
they don't smoke alcohol and simple
cigarettes in marijuana
so that's nominal as opposed to ordinal
ordinal is like a simple example like is
a customer satisfaction how satisfied or
how satisfied are you of this video I've
made very satisfied not satisfied at all
I'm very satisfied satisfied satisfied
no Center sir or satisfied and so on
that's got natural ranking that that's
ordinal so when we have ordinal
variables the thing is that you can run
log-linear
but there will be we can improve upon
the results by taking account that we
have ranking just like in crosstab you
can take account fact that you have
ranking
so that's a very brief introduction I
don't know how brief that was but now
you can get an idea that I have the
length of this video is that there's a
is quite a number of issues here