Box-tidwell test

[Malin Lumio]

I am doing a logistic regression analysis with Lyme disease (borrelia) as dependent variable. I wanted to check whether the predictor age, as measured on ratio-scale, is linearly related to the log odds. I used the command Boxtid in stata in order to investigate this. However, since I am beginner in statistics, I am not sure if I have interpreted the results correctly.

I got this result:

. boxtid logistic borrelia age

Iteration 0:  Deviance =   1030.56
Iteration 1:  Deviance =  1030.559 (change =  -.000988)
-> gen double Iage__1 = X^1.9267-22.98836857 if e(sample)
-> gen double Iage__2 = X^1.9267*ln(X)-37.40487309 if e(sample)
(where: X = age/10)

[Total iterations: 1]

Box-Tidwell regression model

Logistic regression                               Number of obs   =       1510
LR chi2(2)      =      32.12
Prob > chi2     =     0.0000
Log likelihood = -515.27909                       Pseudo R2       =     0.0302


borrelia  Odds Ratio   Std. Err.      z    P>z     [95% Conf. Interval]

Iage__1    1.029305   .1032665     0.29   0.773     .8455632    1.252974
Iage_p1    1.001444   .0455013     0.03   0.975      .916119    1.094717

age         .0281323   .0052322      5.377   Nonlin. dev. 0.822   (P = 0.365)
p1    1.926708   1.310557      1.470

Deviance: 1030.559.

I interpret this as: the p-value of 0.365 (non-significant) says that we accept the null hypothesis of linearity. We can therefore say that age is linear to the log odds. Is this correct interpretation?

[Federico Tedeschi]

I interpret this as: the p-value of 0.365 (non-significant) says that we accept the null hypothesis of linearity.

Yes: the test of nonlinearity for the variable age is statistically nonsignificant with p-value =.365.