Now that I have my full complement of subjects (*N *= 64), I'm able to re-run logistic regression analyses and investigate the degree to which confidence is predictive of accuracy as a function of *remember*, *know*, or *guess*. I'll present two regression models. The first is just the effects of confidence on accuracy as a function of *remember*, *know*, or *guess*:

The regression equations for the figure above (Model 1) are:

For

*remember*, log odds = -1.125 + .031*c*, where*c*is confidence (0-100)For

*know*, log odds = -1.999 + .031*c*For

*guess*, log odds = -2.104 + .031*c*

And here's what the prediction curves look like when we through in the interaction term (i.e., confidence *x* remember/know/guess). Let's call this Model 2.

For

*remember*, log odds = -2.946 + .053*c*For

*know*, log odds = -1.895*c*For

*guess*, log odds = -1.043 + .005*c*

Because logistic regression is not my strong suit, I am researching the best way to evaluate these global models. Right now I am not convinced that the model with the interaction term is doing that much better predicting accuracy. One thing I'm reading about is how we can use signal detection theory to compare models. Here's one way of taking a look:

Model 1:

*HR*= .805,*FAR*= .402,*d'*= 1.11Model 2:

*HR*= .778,*FAR*= .337,*d'*= 1.19

So as you can see, not a huge improvement in discrimination (prediction) going from Model 1 to Model 2.

Now, this is the global analysis. I suppose the next step is getting the subject-level equations.

What can we draw from all of this? A possible observation, which we get from Model 2, is that there really perhaps *is *a difference in the predictiveness of confidence as a function of *remember/know/guess*. This is helpful because some of the analyses I presented last week suggested that there wasn't one. But what we show here is that one increase in a point of confidence is worth twice as much, in terms of log odds, when one is *remembering *as opposed to when one is *knowing*. And when people say they're guessing, they really are, regardless of confidence rating. They hover around what I think is chance (i.e., 33% accuracy). This is really neat.

Of course, these analyses are leaving out something rather important: "new" responses, because we never collect *remember/know/guess* judgments for "new" responses. We need to characterize those responses another day, but you could always turn to DeSoto and Roediger (2014) for one look at this issue.

Here's the data (and the formulae) used to make the figures above, if you're interested.