Hello,
I am a relative novice at both using regression analysis and at using R in
general (and at object oriented programing). A colleague convinced me that
binary logistic regression is the most appropriate analysis for the data that I
have though, so I've been trying to muddle through.
I'm currently stumped on how to interpret/compute odds ratios for two and three
way interactions when a variable has more than 2 factors.
The study design is an examination of the use of past tense by 3 subject
populations in 3 different sentence types and 2 locations within each sentence.
I have been treating subject and main/subordinate verbs as random factors and
group (age, sli, mlu) and condition (and, that, when) and clause order
(first/second) as fixed factors. In each case it is worth noting that the
first factor is the reference group. I would like to be able to clearly
interpret the interactions because specific hypotheses hinge on the results.
Two other points that may be relevant: 1) The original design was balanced, but
the current results are unbalanced because of data loss (e.g. children failing
to respond) and this is not randomly distributed across groups. 2) There is
some colinearity between the conditions (corr between subord/when = .44) and
between the groups (corr between SLI/MLU =.48). This is somewhat logical given
the targets, but is not easily reduced.
The syntax I'm using for the analysis is:
clauseOPCyesI <- lmer(OPCorrect == "past" ~ group*Cond* Clause.Order + (1|SUBJ)
+ (1|sub.V) + (1|main.V), subset(a), family="binomial")
And the results I obtain are:
Generalized linear mixed model fit by the Laplace approximation
Formula: OPCorrect == "past" ~ group * Cond * Clause.Order + (1 | SUBJ) + (1
| sub.V) + (1 | main.V)
Data: subset(a)
AIC BIC logLik deviance
5673 5817 -2816 5631
Random effects:
Groups Name Variance Std.Dev.
main.V (Intercept) 0.056843 0.23842
SUBJ (Intercept) 1.248441 1.11734
sub.V (Intercept) 0.085521 0.29244
Number of obs: 6827, groups: main.V, 47; SUBJ, 38; sub.V, 36
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.19570 0.35057 6.263 3.77e-10 ***
groupm 0.67645 0.52638 1.285 0.1988
groups -0.59218 0.47534 -1.246 0.2128
Condsubord 0.27588 0.23297 1.184 0.2363
Condwhen -0.17839 0.20278 -0.880 0.3790
Clause.Ordersecond -0.10066 0.19965 -0.504 0.6141
groupm:Condsubord 0.38856 0.52295 0.743 0.4575
groups:Condsubord -0.07662 0.29406 -0.261 0.7944
groupm:Condwhen -1.82957 0.31892 -5.737 9.65e-09 ***
groups:Condwhen -1.42286 0.26601 -5.349 8.85e-08 ***
groupm:Clause.Ordersecond -0.29247 0.33645 -0.869 0.3847
groups:Clause.Ordersecond -0.53254 0.26494 -2.010 0.0444 *
Condsubord:Clause.Ordersecond -0.60703 0.28965 -2.096 0.0361 *
Condwhen:Clause.Ordersecond 1.64044 0.34265 4.788 1.69e-06 ***
groupm:Condsubord:Clause.Ordersecond -2.95511 0.60007 -4.925 8.45e-07 ***
groups:Condsubord:Clause.Ordersecond -0.04796 0.38893 -0.123 0.9019
groupm:Condwhen:Clause.Ordersecond -0.36423 0.48229 -0.755 0.4501
groups:Condwhen:Clause.Ordersecond 0.05882 0.41775 0.141 0.8880
While I know to talk about odds ratios I need to raise e to the estimate of the
coefficient for main effects, I am less clear about interactions terms.
So for instance, if I would like to say that the SLI group was X% less likely
to produce a correct past tense for in the second clause than in the first
clause do I add the estimates
(groups+Clause.Ordersecond+groups:ClauseOrdersecond = -1.22538) and then
compute the OR 0.293646094? "The odds of the SLI group producing a past tense
form in the second clause was approximately 29% as compared to their
productions in the first clause" Or since the reference group is their age
matched peers would I need to say "The odds of the SLI group producing a past
tense form in the second clause was approximately 29% as compared to the
age-matched groups productions in the first clause of the target sentences".
(Note that the second sentence is much less useful to me than the first).
Similarly if I would like to talk about the fact that Condwhen is relatively
poorer for the MLU/SLI groups than the age matched-coordinate but I get muddled
by the fact that there is improvement in the Cond when, second clause (as
compared to condwhen-first clause-age-matched, right?). Again, my trouble is
with what to use as the reference group and how to separate that out in terms
of computing percentages.
Thanks so much for any assistance you can lend.
Amanda
Amanda J. Owen PhD CCC-SLP
Assistant Professor
Dept of Communication Sciences and Disorders
University of Iowa
319-335-6951 (office)
amanda-o...@uiowa.edu
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