Comparing two models

[Masoumeh Sanagou]

Dear Statalist,

I have the following variable:

 
kVp
Freq.
Percent
Cum.

80
20
0.03
0.03

90
30
0.05
0.08

100
11,999
18.03
18.1

110
1,202
1.81
19.91

120
45,807
68.83
88.74

130
5,049
7.59
96.32

135
1,037
1.56
97.88

140
1,411
2.12
100

Total
66,555
100

I looked at its effect in two ways:
as a continues variable:

xtset SurveyID_code
xtgee CTDI  kVp   ,  corr(exchangeable) vce(robust)

as a discrete variable:

xtset SurveyID_code
xtgee CTDI  i.kVp   ,  corr(exchangeable) vce(robust)

How can I compare these two models and find out which one is the correct one?

[Clyde Schechter]

I would, for each model, separately use -predict- to get the model predicted values and then make a scatter plot of those predicted values against the observed values. A visual comparison of the two graphs may make it obvious which model is superior. (It is highly unlikely that either model is "correct.")

So a sequence something like this:

xtgee CTDI kVp, corr(exch) vce(robust)
predict pred_continuous
label var pred_continuous "Continuous kVp"

xtgee CTDI i.kVp, corr(exch) vce(robust)
predict pred_discrete
label var pred_discrete "Discrete kVp"

graph twoway scatter pred_* CTDI || line CTDI CTDI

A perfectly fitting model would fall exactly along the diagonal line.

This might give a clear sense of which model fits the data better. If neither model is obviously better fit than the other, then you might want to consider other factors. For example, if other values of kVp besides the ones you have in your data are possible, the continuous model would extend by interpolation (or with much less reliability, by extrapolation) to those, whereas the discrete model has nothing to offer. The continuous model is also simpler.

[Masoumeh Sanagou]

Thanks for the reply. I'm sure other values of kVp are not possible.

I will have a look at scatter plots.

[Masoumeh Sanagou]

.