SPSS for newbies Interpreting the coefficients of a logistic regression

hi everyone Phil from Statistics mentor
here today we're going to talk about
logistic regression now logistic
regression is applicable when our
dependent variable is not continuous or
scale parable but a binary variable so
it takes only one of two values let's
look an example here we've got data from
the Titanic we've got the variable
survived which survived yes or no so
it's binary we've got a dummy variable
Vijender that's a female who's coded 0
of its male 1 if it's female we've got
age of each passenger and then we've got
like the class that that passenger paid
for was traveling on ok now
the dependent variable here is survival
yes or no that's what we're interested
in and the other ones female age and
classes they are the Ivy's now let's
have a look at the scatter plot of the
DV survived and age which is continuous
here you go now recall that for the
usual type of regression we've seen the
standard regressions a scatter plot
doesn't look something strange as this
is has just got two horizontal lines one
at this is vertical axis is surviving
IDB and it is on a scale from 0 to 1 but
look at the dots they're either 1 or 0
they are not like with accustomed seeing
dots maybe like that around here like
that so we can draw a straight line
right through the dots or going down the
other way so can draw a negative sloping
line here you've got two horizontal
lines and which explains why the
standard regression model
ain't so great anymore okay so each of
these dots represents the coordinate of
age and whether they survived or not so
if I point to dot over here this dot
here that's saying that the age of that
person was just short of 80 years old
that they survived yes because one here
is coded for survived and zero is could
it not survive so that's why we get to
horizontal lines with nothing in between
now if you think about drawing a
straight line through these two over
these these dots then that's how to
imagine isn't it that we might do that
you might have a line going like that's
very hard to say isn't it okay so now we
could fit a standard regression model
but there are many disadvantages of
doing that they're more advantages
running something a model that is
specifically formulated to deal with
cases where the dependent variable is
coded binary 0 & 1 then not happen or it
did happen
okay so that motivates the use for
logistic regression okay so let's go
back now I'm going to kind of fit the
going to regress survived on age version
then we're going to interpret the
coefficient
you're going to fit a logistic
regression of survived on age and do an
interpretation of the coefficient on age
so to run it we go analyze regression we
go to binary logistic binary because
your dependent variable has one of two
outcomes supposed to multinomial
logistic where the DV has more than two
outcomes okay binary logistic now what
we do is transfer into the deep end
variable box survived will transfer into
the covariance box which is another word
for ib age and then we just press click
enter okay now compared to standard
regression the logistic regression is
that you have a lot more output so
that's why I'm going to just focus on
interpretation here because at the end
of the day we either use the model for
prediction or for interpreting the
coefficients we're going to interpret
the coefficients so we go a lot of stuff
coming out of this we're looking let's
zoom in and what we're actually
interested in this is what we're
interested in variables in the equation
now age is the i-iv that's the
coefficient - naught point naught naught
5 and the exponential of that
coefficient is 0.99 five now this is the
one where you want okay in logistic for
the interpretation we go to the
exponential of the coefficient that just
means we take if you use the calculator
exponential of this figure here e 2 this
will give you point 995
okay so we're going to interpret this
coefficient on age 0.995 with the
exponential of the coefficient now this
takes us onto the jargon of odds and
odds ratio and the many ways to write
down explain what this point 995 is
telling us so I've just listed them we
could say the odds of surviving is lower
for an older person this is equivalent
to saying implies that the probability
of surviving is lower for an older
person we could also say for that but
this first statement is very gently it
doesn't take account of the actual
number just rather than number is bigger
than or less than one next one for an
additional year of in age the odds of
surviving is lower by a factor of 0.995
another way of saying it is for an
additional year in age the odds of
surviving is lower by half a percent so
that's expressing that the same this is
a second statement in terms of percent
how do we turn into a percent take that
figure the exponential of the
coefficient times by 100 subtract 100
okay another way of to explain the
coefficient is the odds ratio is not
point 995 for additional year of age so
here I'm using
new jargon here odds odds ratio now we
are more problem we're more comfortable
talking about probabilities than in odds
so let's take this odds ratio and
explain what it means in terms of
probability odds ratio looking at three
cases it's evil to one bigger than 1
less than 1 it is equal to 1 it tell
interpreter is saying that the
probability of the event occurring in
this case that you survive on the
titanic between the two situations are
the same so if we're looking at the
Corvair age it means that that's what I
mean by two situations it means
whether you are at the original age of
your the traditional year older so this
is saying if that all schemes to one
then the probability of surviving is the
same whether you are age X or if you're
older by one year than age X if the odds
ratio is bigger than one in terms
probability that says that probability
of the event occurring with unit
increase in the IV is higher than the
original value of IV so in this context
it would mean that if my odds ratio for
age is bigger than 1 then the
probability of surviving on the Titanic
increases with age
finally odds ratio less than 1 in terms
of probability it means that the
probability of an event occurring with
unit increase in IV is lower than the
original IV so the probability in this
context probability of surviving on the
Titanic will will fall okay with age so
in this case the odds ratio is point 995
so we can actually see that it's going
to with age the chances of surviving
Falls how much does it fall by it falls
by compared to person who is one year
younger your chances of surviving is
lower by half a percent repeat again
side on that your odds of surviving is
lower by half a percent we can say that
the probability of surviving is lower
than half a percent note that so odds
and probability are different things
so the best way to get around this is
just read through each of the statements
which are all kind of saying this saying
something about the coefficient and try
and understand it and then apply it to
your model so to summarize for a
dependent variable which is one of two
outcomes standard regression although
applicable has several disadvantages
compared to the logistic regression
which is designed specifically for
dealing with dependent variables which
have one of two outcomes the
coefficients in terms of interpreting
the coefficients we look at the
exponential of the coefficient on the IV
and then we can interpret in terms of
odds or odds ratio finally just to say
that a model that is similar to the
logistic is the probit which we will you
will find in SPSS as well analyze linear
regression binary logistic so I mean
analyze regression probit we moved it
down here so binary logistic and probit
basically they are designed to handle
dependent variables which is one of two
outcomes the interpretation for the
probit model coefficient probit model is
different to the logistic model which
one you use it doesn't really matter it
depends on what field of application
subject area that you're dealing with
you see some in some subject areas they
prefer one mole to another for example
in economics and econometrics they tend
to use the probe it was in something
like psychology they tend to use a
logistic okay that's all for now