Dear R-Helpers,
I posted two days ago on testing significance of random effects in mgcv,
but realize I did not make my overall purpose clear. I have a series of
N short time series, where N might range from 3-10 and short means a
median of 20 time points. The sample data below (PCP) has N = 4 cases
with 9, 13, 16 and 16 observations over time respectively. The data set
contains four variables: PID = case number, SessIDX = time (x axis), DVY
= the outcome (y axis) and TX is treatment is applied = 1 or not = 0.
My goal is to determine (a) is trend present in each case, (b) is it
linear or nonlinear in each case, and (c) does trend vary significantly
over cases (PID), the latter presumably to be measured with a random
effect. I can do the first two (not shown here), but am not sure about
the third. I am using generalized additive models, either mgcv gam or
gamm4. For example, using mgcv gam my syntax is
M1 <- gam(DVY ~ s(SessIDX, bs = "re") + factor(TX),
data = PCP,
family = quasipoisson(link="log"),
method="REML")
summary(M1,all.p=TRUE)
gam.vcomp(M1)
Using gamm4, my syntax is
PCP$fPID <- factor(PCP$PID)
M2 <- gamm4(DVY ~ factor(TX) + s(SessIDX, by = factor(PID)),
data = PCP,
random =~ (1|fPID),
family = poisson (link="log"))
summary(M2$gam)
summary(M2$mer)
It is not clear to me whether either of these gives me what I want. In
generalized linear mixed models, I am accustomed to the HLM approach
(e.g., Raudenbush & Bryk) where each case would have a trend
coefficient, and the random effect would tell me if those four
coefficients varied significantly. So that is what I am looking for, but
adding the nonlinearity modeling of GAM. Is either of these formulations
giving me what I want--a test of whether trend differs significantly
over cases or not.
Thanks for any help you can offer. I have worked very hard to solve this
on my own, and just can't seem to do so.
Will Shadish
> PCP
PID SessIDX DVY TX
1 1 1 4 0
2 1 2 5 0
3 1 3 5 0
4 1 4 8 0
5 1 5 3 1
6 1 6 0 1
7 1 7 0 1
8 1 8 0 1
9 1 9 0 1
10 2 1 2 0
11 2 2 2 0
12 2 3 4 0
13 2 4 4 0
14 2 5 4 0
15 2 6 2 0
16 2 7 3 0
17 2 8 1 1
18 2 9 2 1
19 2 10 3 1
20 2 11 1 1
21 2 12 0 1
22 2 13 0 1
23 3 1 7 0
24 3 2 3 0
25 3 3 2 0
26 3 4 5 0
27 3 5 3 0
28 3 6 4 0
29 3 7 3 0
30 3 8 0 1
31 3 9 3 1
32 3 10 2 1
33 3 11 0 1
34 3 12 0 1
35 3 13 2 1
36 3 14 0 1
37 3 15 1 1
38 3 16 1 1
39 4 1 3 0
40 4 2 1 0
41 4 3 1 0
42 4 4 0 0
43 4 5 1 0
44 4 6 2 0
45 4 7 3 0
46 4 8 0 0
47 4 9 1 0
48 4 10 0 1
49 4 11 0 1
50 4 12 0 1
51 4 13 0 1
52 4 14 0 1
53 4 15 0 1
54 4 16 0 1
>
--
William R. Shadish
Distinguished Professor
Founding Faculty
Mailing Address:
William R. Shadish
University of California
School of Social Sciences, Humanities and Arts
5200 North Lake Rd
Merced CA 95343
Physical/Delivery Address:
University of California Merced
ATTN: William Shadish
School of Social Sciences, Humanities and Arts
Facilities Services Building A
5200 North Lake Rd.
Merced, CA 95343
209-228-4372 voice
209-228-4007 fax (communal fax: be sure to include cover sheet)
wshadish at ucmerced.edu
http://faculty.ucmerced.edu/wshadish/index.htm
http://psychology.ucmerced.edu
