Measures of depression and anxiety are notorious for their correlation. The Hospital Anxiety and Depression Scale is no such thing, for example. The anxiety and depression scales are so highly correlated that they could be given as evidence of convergent validity.

The high degree of correlation can mean that when you hold one variable constant the other has little remaining variation. A symptom of this happening is that the regression coefficients remain similar but the standard errors rise and the significance (which is effect divided by standard error) declines.

But the main question is what the authors thought anxiety was. Generalised anxiety disorder, a disorder of repetitive cognition, is at least well defined and measurable. At the other end of the quality scale, to the HADS, that is. And even there, there is an overlap between the diagnosis of GAD and depressive disorder.

I actually find this sort of theory-free multivariate modelling somehow depressing. I'd prefer to see a proper phenomenological model any day.

Happy new year though.

Hi Elizabeth, this situation is very common when inclduing anxiety and depression in the same model. I have a few thoughts. First, depression and anxiety are often strongly correlated, so when the variance of one is accoutned for, the other cancels out. When variables are highly correlated, it can be appropriate to run them in separe models. Second, I would caution th authors against using the term "predict" as it appears that these data are cross-sectional. If so, would urge them to use the term "associated with" as prediction is a bit different. Third, I would request efect sizes with cinfidence intervals for the betas. Fourth, I am not sure the correct intepretation is that anxiety and depression predict happiness when the other is not controlled. I think a more accurate response would be to state that both are associated with happiness, but because of their high correlation with each other, they are only assocated in separate models. I hope this makes sense and is helpful.

Cory

Elizabeth -

It would be interesting to see "graphical residual analyses" for each of these separate regression equations, which each do predict happiness. This is not a subject matter field for me, but I understand that you actually do have standard methods for meaningfully quantifying these variables. If you do a graphical residual analysis in each case - predicted/fitted values on the x-axis, and estimated residuals on the y-axis - then you can compare model fit, especially if you put them both on the same scatterplot. (To avoid overfitting to your particular sample, "cross-validation" may be helpful. You can at least rotate a data point out, one after the other, to see if that makes a big difference to the estimate regression coefficient.)

Are you using an intercept term? Many just routinely throw them in, but if you would expect y to be zero IF all variables on the right side were zero, don't use an intercept term, as it just adds noise. Since you have some control variables, which likely aren't zero, that may complicate this consideration in a way in which I haven't dealt or considered, but I would be careful about including an intercept term unless it seemed as necessary as any variable used. (This relates to what Ronán said about theory. Subject matter matters.)

Note that a graphical residual analysis can also indicate heteroscedasticity. Often this appears as a 'fan-shape,' but not necessarily. As long as the density of estimated residual data points in the y-direction for the same y-range is smaller as you move along the x-axis, the sigma for the estimated residuals becomes larger. (That is, for the same range, if there are fewer numbers in one group than another, then the first group has higher variance.) But usually, the points will fan out. Heteroscedasticity is a natural feature associated with the size of predictions. There are other model and data issues which can also impact this. Often, especially with a great deal of data, failing to account for heteroscedasticity will not change predicted values by much, but can impact variance greatly. This may be of interest to a study. The larger cases may have substantially larger sigma which contributes to the estimated variance of the prediction error. (See https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and updates.)

Cheers - Jim