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I have a 4x4 contingency table that looks like:

mytable <- xtabs(~df$hair + df$eyes, drop.unused.levels = TRUE)

oddsratio(mytable, log=FALSE) 
lor <- oddsratio(mytable)
summary(lor)

This yields to:

z test of coefficients:

                             Estimate Std. Error  z value  Pr(>|z|)    
black:blonde/blue:brown     -2.346794   0.164453 -14.2703 < 2.2e-16 ***
blonde:brunette/blue:brown   2.568568   0.158240  16.2321 < 2.2e-16 ***
brunette:red/blue:brown     -1.026513   0.190382  -5.3919 6.974e-08 ***
black:blonde/brown:green     0.899755   0.188443   4.7747 1.800e-06 ***
blonde:brunette/brown:green -1.316440   0.187854  -7.0078 2.422e-12 ***
brunette:red/brown:green     1.604794   0.198856   8.0701 7.022e-16 ***
black:blonde/green:other     0.063886   0.138047   0.4628    0.6435    
blonde:brunette/green:other -0.236244   0.144318  -1.6370    0.1016    
brunette:red/green:other    -0.685801   0.149093  -4.5998 4.228e-06 ***

I'm not sure how to interpret the results.

What do the ":" and "/" mean in reading the coefficients?

Moreover if I run a log linear model I can specify it as:

Call:
loglm(formula = ~df$hair + df$eyes, data = mytable)

Statistics:
                      X^2 df P(> X^2)
Likelihood Ratio 566.4536  9        0
Pearson          582.4505  9        0

or

Call:
loglm(formula = df$hair ~ df$eyes, data = mytable)

Statistics:
                      X^2 df P(> X^2)
Likelihood Ratio 1296.951 12        0
Pearson          1462.310 12        0

What is the difference in reading the two different specification?

Thanks for your help

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