My special thanks to Chunhao Tu for the suggestions about testing significance
of two locations.
I used logistic models to describe relationships between Y and X at two
locations (A & B). And within each location, I have four groups
(N,E,S,W)representing directions. So the test data can be arranged as:
Y X dir loc
0.6295 0.8667596 S A
0.7890 0.7324820 S A
0.4735 0.9688875 S A
0.7805 1.1125239 S A
0.8640 0.9506174 E A
0.9445 0.6582157 E A
0.8455 0.5558860 E A
0.9380 0.3304870 E A
0.4010 1.1763090 N A
0.2585 1.3202890 N A
0.3750 1.1763090 E A
0.3855 1.3202890 E A
0.3020 1.1763090 S A
0.2300 1.3202890 S A
0.3155 1.1763090 W A
0.8890 0.6915861 W B
0.9185 0.6149019 W B
0.9275 0.5289258 W B
0.8365 0.9507088 S B
0.7720 0.8842165 N B
0.8615 0.8245123 N B
0.9170 0.7559687 W B
0.9590 0.6772720 W B
0.9900 0.5872023 W B
0.9940 0.4849064 W B
0.7500 0.9560776 W B
The data is grouped using:
>LAST<-groupedData(Y~X|loc/dir, data=test)
I then used logistic models to define the relationship between Y and X, and got
fm1, fm2, and fm3 as follows:
--------------------------
>fm1 <- nlme(DIFN ~ SSlogis(SVA, Asym, R0, lrc),data = LAST,fixed = Asym + R0 +
>lrc ~ 1,random = Asym ~ 1,start =c(Asym = 1, R0 = 1, lrc = -5))
>fm2 <- update(fm1, random = pdDiag(Asym + R0 ~ 1))
>fm3 <- update(fm2, random = pdDiag(Asym + R0 + lrc ~ 1))
>anova(fm1,fm2,fm3)
------------------------------------------------------------
ANOVA showed:
>anova(fm1,fm2,fm3)
Model df AIC BIC logLik Test L.Ratio p-value
fm1 1 7 -1809.913 -1774.304 910.9564
fm2 2 9 -1805.774 -1758.295 910.8871 1 vs 2 0.1386696 0.9999
fm3 3 12 -1801.822 -1742.473 910.9109 2 vs 3 0.0475543 0.9666
** question: do the results show that fm1 could represent the results of fm2
and fm3?
>coef(fm1)
Asym R0 lrc
AB/E 0.9148927 1.389432 -0.3009858
AB/N 0.8775250 1.389432 -0.3009858
AB/S 0.9247592 1.389432 -0.3009858
AB/W 0.8479180 1.389432 -0.3009858
BC/E 0.8791908 1.389432 -0.3009858
BC/N 0.8414229 1.389432 -0.3009858
BC/S 0.9169323 1.389432 -0.3009858
BC/W 0.8817838 1.389432 -0.3009858
** question: how could I know if any of the models is significantly different
from the other ones? (eg. AB/E is different from the AB/S)?
> summary(fm1)
Nonlinear mixed-effects model fit by maximum likelihood
Model: DIFN ~ SSlogis(SVA, Asym, R0, lrc)
Data: LAST
AIC BIC logLik
-1809.913 -1774.304 910.9564
Random effects:
Formula: Asym ~ 1 | loc
Asym
StdDev: 2.303402e-05
Formula: Asym ~ 1 | dir %in% loc
Asym Residual
StdDev: 0.03208693 0.1741559
Fixed effects: Asym + R0 + lrc ~ 1
Value Std.Error DF t-value p-value
Asym 0.8855531 0.015375906 2783 57.59355 0
R0 1.3894322 0.009418047 2783 147.52869 0
lrc -0.3009858 0.012833066 2783 -23.45393 0
Correlation:
Asym R0
R0 -0.440
lrc -0.452 0.150
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-4.1326757 -0.6117037 0.1082112 0.6575250 3.3297270
Number of Observations: 2793
Number of Groups:
loc dir %in% loc
2 8
I have marked all the codes and questions(**). Any answers and suggestions are
appreciated.
Have a good day!
Jenny
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