[R] NLME questions -- interpretation of results

[Jenny Sun]

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