Can the items measure one underlying construct?

Question

For an assignment I am asked to test whether different items (all dichotomous) can actually measure one concept. The items:

Please tell me whether or not you think it should be possible for a pregnant woman to obtain a legal abortion . . . A. If the woman's own health is seriously endangered by the pregnancy? B. If there is a strong chance of serious defect in the baby? C. If she became pregnant as the result of a rape? D. If the family has a very low income and cannot afford any more children? E. If she is not married and does not want to marry the man?

The results of my latent-class analysis are that:

• The model with two and three classes do not have an acceptable model fit:

2-class: X² = 492.485; L² = 337.1439; df = 20; p = .000; AIC = 297.1439; BIC = 195.7409
3-class: X² = 170.096; L² = 26.4617; df = 14; p = .0226; AIC = -1.5383; BIC = -72.5204

• There is a clear pattern in the estimated classes. One group agreeing on all items X1, one agreeing on only the medical/ethical reasons (health, defect and rape) , one never agreeing X3 (exept sometimes for the health item, I think because this is a balance between killing the baby or killing the mother, so both answers are not pro-life).

X. are the three classes, the first horizontal line of numbers are the proportions of the sample in each class, and then the probabilities of those classes to say yes (=1) or no (=2) to the different item.

I was wondering if the simple answer is: the items can not measure one construct because the model does not have an acceptable fit.

Or is the structure of the latent classes more informative to answer this question? I know that putting constraints on the model could lead to an acceptable model fit, so in that way my criterium to base my statement on seems flawed. (something like: they can not measure one construct, but when we put constraint on the model, they can)

Answer 1

The questions clearly measure one construct. One way to see this is to look at the correlations between them. Since all the variables are dichotomous, use the tetrachoric correlation. If these are all close to 0 in your data, then you have a very strange sample of people!

As you note, these question also form a graded series. That is, you could look at the proportion of people endorsing each item and it is likely that it declines; furthermore, most people endorsing the last item will endorse all the earlier ones. If it was not a single construct, it is hard to see how this pattern could be maintained.

Then you could do factor analysis, again using the tetrachoric correlations as input. If all the items load on one factor (and I strongly suspect they will) then that is further evidence of a single construct.

I don't know what models you ran to get the results you did, could you tell us?