Hi,

Could anybody tell me the difference between these three models (summary of models at the end of the message)?

"inf" is a binary response, "fs" and "ib" are both categorical variables with two levels (0 or 1), "col" (for colony) is factorial, with each colony allocated to one (and only one) particular combination of "fs" and "ib". Finally, "samp" is continuous (repeated sampling over time at each "col"). "fs" and "ib" are the main experimental factors (hence fixed), and I am not really interested in the effect of "col" (hence random).

m1 <- lmer(inf~fs*ib*samp+(1|col),family=binomial)
m2 <- lmer(inf~fs*ib*samp+(samp|col),family=binomial)
m3 <- lmer(inf~fs*ib+(samp|col),family=binomial)

Even with the help of internet and two books I have trouble to figure it out... The only thing I think I have understood is that "samp|col" would mean repeated measures analysis. But I am far from being certain.

Many thanks.

G


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m1 <- lmer(inf~fs*ib*samp+(1|col),family=binomial)

Generalized linear mixed model fit by the Laplace approximation 
Formula: inf ~ fs * ib * samp + (1 | col) 
   AIC   BIC logLik deviance
 166.2 192.6 -74.09    148.2
Random effects:
 Groups Name        Variance Std.Dev.
 col    (Intercept) 2.0048   1.4159  
Number of obs: 139, groups: col, 31

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)  
(Intercept)   -3.3297     1.4521  -2.293   0.0218 *
fs1            1.8935     1.7651   1.073   0.2834  
ib1            0.7643     2.1850   0.350   0.7265  
samp           1.1800     0.4818   2.449   0.0143 *
fs1:ib1       -4.5125     2.8772  -1.568   0.1168  
fs1:samp      -0.9691     0.5775  -1.678   0.0933 .
ib1:samp      -0.6088     0.8580  -0.710   0.4780  
fs1:ib1:samp   2.2149     1.0452   2.119   0.0341 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Correlation of Fixed Effects:
            (Intr) fs1    ib1    samp   fs1:b1 fs1:sm ib1:sm
fs1         -0.823                                          
ib1         -0.665  0.547                                   
samp        -0.852  0.701  0.566                            
fs1:ib1      0.505 -0.613 -0.759 -0.430                     
fs1:samp     0.711 -0.840 -0.472 -0.834  0.516              
ib1:samp     0.478 -0.394 -0.843 -0.562  0.640  0.469       
fs1:ib1:smp -0.393  0.464  0.692  0.461 -0.854 -0.552 -0.821


m2 <- lmer(inf~fs*ib*samp+(samp|col),family=binomial)

Generalized linear mixed model fit by the Laplace approximation 
Formula: inf ~ fs * ib * samp + (samp | col) 
   AIC BIC logLik deviance
 169.7 202 -73.87    147.7
Random effects:
 Groups Name        Variance Std.Dev. Corr  
 col    (Intercept) 0.808349 0.89908        
        samp        0.048877 0.22108  1.000 
Number of obs: 139, groups: col, 31

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)  
(Intercept)   -3.2619     1.3799  -2.364   0.0181 *
fs1            2.0143     1.6498   1.221   0.2221  
ib1            1.0153     2.0774   0.489   0.6251  
samp           1.1893     0.5013   2.372   0.0177 *
fs1:ib1       -4.8953     2.7404  -1.786   0.0740 .
fs1:samp      -1.0523     0.5978  -1.760   0.0783 .
ib1:samp      -0.7595     0.8904  -0.853   0.3937  
fs1:ib1:samp   2.4646     1.0805   2.281   0.0226 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Correlation of Fixed Effects:
            (Intr) fs1    ib1    samp   fs1:b1 fs1:sm ib1:sm
fs1         -0.836                                          
ib1         -0.664  0.556                                   
samp        -0.829  0.694  0.551                            
fs1:ib1      0.504 -0.602 -0.758 -0.418                     
fs1:samp     0.695 -0.811 -0.462 -0.839  0.488              
ib1:samp     0.467 -0.390 -0.832 -0.563  0.631  0.472       
fs1:ib1:smp -0.385  0.449  0.686  0.464 -0.839 -0.553 -0.824

m3 <- lmer(inf~fs*ib+(samp|col),family=binomial)

Generalized linear mixed model fit by the Laplace approximation 
Formula: inf ~ fs * ib + (samp | col) 
   AIC   BIC logLik deviance
 182.2 202.7  -84.1    168.2
Random effects:
 Groups Name        Variance Std.Dev. Corr   
 col    (Intercept) 0.73161  0.85534         
        samp        1.18386  1.08805  -1.000 
Number of obs: 139, groups: col, 31

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)  
(Intercept)  -1.2445     0.6513  -1.911    0.056 .
fs1           0.3539     0.8194   0.432    0.666  
ib1          -0.2006     0.9780  -0.205    0.837  
fs1:ib1      -0.4762     1.2414  -0.384    0.701  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Correlation of Fixed Effects:
        (Intr) fs1    ib1   
fs1     -0.795              
ib1     -0.666  0.529       
fs1:ib1  0.525 -0.660 -0.788


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