Dia 1

1

• 5nd meeting
• Multilevel modeling Summary Extras
• Subjects for today
• How to do multilevel analysis a 5-step-approach
• Interaction, cross-level interactions, mean
  centering
• Influential cases in multilevel modeling
• New developments I generalized multilevel
  models in SPSS 19
• New developments II Missing data substitution

2

• During this course we discussed several steps in
  multilevel modeling. Here is a summary that may
  be followed
• Calculate the higher level variances (often level
  2), the intra class correlation and test whether
  it is significant (in linear models use
  difference in -2 loglikelihood, in logistic
  models use t-test).
• When there is level 2 variance, include relevant
  level 1 variables to test hypotheses on indidual
  level, but also to take into account
  compositional effects (notable as a change in the
  level 2 variance, which in many cases will
  decrease).
• After including all relevant level 1 indicators
  you may include relevant level 2 variables
  (preferably not all at once but one by one or
  cluster by cluster)._____________________
• When you are after crosslevel interactions (you
  may think that level 1 effects are conditional
  upon level 2 variables or that level 2 effects
  are conditional upon level 1 variables), first
  set relevant level 1 variables random.

2
3

• You may be are after crosslevel interactions. You
  may think/hypothesize that level 1 effects are
  conditional upon level 2 variables or that level
  2 effects are conditional upon level 1 variables.
  First set relevant level 1 variables random.
• Even when you find no random variantion I advice
  to test the cross-level interaction because
  random variance may be quite low and
  non-significant while a test on an interaction
  may very well be significant. So, include the
  interaction between X on level 1 and X on level 2
  and test whether the interaction is significant
  (use level 2 df)
• For the interpretation of interaction mean
  centering may come in handy (also may prove
  benificial when model does not converge (see
  later slides).
• NEXT SLIDE an example of a Table with steps 2 -
  5

3
4
4
5
Interactions once more! DATA again fake and
stored in TOPGEAR.sav Why interactions? Because
we like to test whether effects DIFFER ACROSS
GROUPS or CATEGORIES Suppose we estimated the
effect of education on watching Top Gear. This
tv-show is about fast cars. Top Gear therefore
might just be more interesting for men than for
women. This eventually means that it might not be
a very good idea to model the educational effect
equal for men and women. So the regression
model Top Gear a b1 education e might be
wrong here. Even Top Gear a b1 education
b2 gender e is wrong because we only added to
the model that women might differ in viewing Top
Gear but the educational effect still is the same.
5
6
First solution just split the file sort cases
by gender. split file by gender. REGRESSION /DEPEN
DENT topgear /METHODENTER educat. split file
off.
6
7
7
8
Second solution just estimate one model so we
can statistically test whether the educational
effects differs between men and women Top Gear
a b1 education b2 gender b3 gender
education Now for females (coded 0 on gender)
the model can be re-written Top Gear a b1
education b2 0 b3 0 education ?? Top
Gear a b1 education For males (coded 1) we
get Top Gear a b1 education b2 1 b3
1 education ?? Top Gear a b1 education
b2 b3 education ?? Top Gear (a b2)
((b1 b3) education) So b2 is the increase of
the intercept in case you are a man B3 is the
ADDITIONAL effect for education when you are a
man, which can be tested with a t-test
8
9
9
10
10
11
In multilevel we can incorporate interactions as
well. Whenm they are on the same level then there
is no difference with the previous slides If the
interaction is between variables from different
levels there something extra. Let us go back to
the Math test and the relation with homework
11
12
It helps when interpreting the main effects in an
interaction model. Suppose you have homework
black on a school.Then you get someting like
this Homework .10 blacks -.20 Interaction
homework blacks .01. What does it say 1)
When blacks 0, the effect of homework is
.10 2) When Homework 0, the effect of blacks
is -.20 3) When blacks 1, the effect of
homework is .11 4) When homework 1, the effect
of blacks is -.19 So as blacks increases in a
classroom, the effect of homework becomes
stronger As the hours spent on homework increase,
the effect of blacks is less strong
12
13
We know that the co-variance is at x0 (the
intercept) but if we mean center the variable
homework the co-variance changes (let us
substract 2 we get
0
So the co-variance dependents upon where you put
intercept! Is this important, well yes. 1) It
helps in the estimation procedure (interation
proces, converging problems
13
14
The problem of influential cases at higher levels
(more at http//www.ru.nl/methodenentechnieken/ic
/downloads/
60 landen
volunteers
With the 3 datapoints (Uganda, Tanzania
Zimbabwe) correlation .43, Without these 3
countries it is .2!
church attendees
15
15
16
Be aware of non-linear relations The correlation
is -.6, BUT it is far from being linear. When we
log transform both variables we get -.9
16
17
New developments I generalized multilevel models
in SPSS 19 Since SPSS 19 there are multiple
ways to link the dependent variable with
x-variables in mixed models. New developments
II Missing data substitution In MLwiN there
is an additional add on called REAL COM to do
miising data substition, a short manual is
provided on this web site.
17