- this is a very basic thing
- that's all there is to it
because although it is a basic thing to you, it's not a basic thing to someone who hasn't spent the same time studying all the concepts beforehand.
This is generally why you have to take a class to grok stats rather than just read some reference material and definitions.
It's similar to programming environments when the senior dev says some thing that requires a lot of context is just really simple.
Monads are Simply Just monoids in the category of endofunctors, after all, they are really Simple, that's all there is to it! (what the subject hears: This is so simple to me, why aren't you smart enough to get this simple concept? You should know this already—I shouldn't even have to make this comment! Why haven't you been properly educated, like I have? )
also, mansplaining generally refers to assuming people (women, usually) have less pre-existing knowledge than they actually do.
1) agree with others comments that stating with 'very basic' ain't going to work
2) logistic regression actually isn't a common topic in an undergraduate statistics course. I cover it on the second to last day as an 'here is where you can extend it'
3) this isn't a very effective explanation.
4) a big background factor is the misconceptions about statistics that are ingrained in human beings. Learning statistical tests is hard, especially for many engineers and similar STEM types because it is typically the first (and sometimes only) class that deals with concepts of error and variance. Everything else presents an absolute theoretical model. On average, it breaks their brain...
(i.e. > 0.5 equals 1, and < 0.5 equals 0).
This seems to be a "rarely-questioned assumption".
Is there a reason why this is considered reasonable? And is there a name for the cut-off (i.e., if I were to want to change the cut-off, what keyword should I search for inside the software's manual?)?
Almost all statistical models give you probabilities and it is up to the domain to determine the cutoff. You can clearly see this in logistic regression it's giving you a probability not a 1 or 0.
When a clinician gives me a dataset I build the model and leave it to them to do the cut off. It is not my domain or expertise to tell them where the cut off is. Plus it gives away the responsibility. I'm not responsible for it unless they don't know and are asking me for a reasonable cut off.
An example is people opting for artificial in semenation because of problem. I believe the cut off is above 60% because of the trade off.
You can read more about it in Regression Modeling Strategies by Dr. Frank Harrell.
In the software, you can get classification models to output class probabilities instead of class labels. You can then use whatever threshold you like for to transform those probabilities to labels.
You may see it refered to as "discrimination threshold". Varying that threshold is how ROC curves are constructed.
The idea behind binary regression ( Y is 0 or 1) is that you use a latent variable Y* = beta X + epsilon.
X is the matrix of indenpent variables, beta is the vector of coefficients and epsilon is an error term that sums the rest of what X can't explain.
Y thus becomes 1 if Y* >0 and 0 otherwise.
Seeing how Y is binary, we can model it using a Bernoulli distribution with a success probability P(Y=1) = P(Y* >0) = 1 - P(Y* <=0) = 1 - P(epsilon <= -beta X) = 1 - CDF_epsilon(-beta X)
Technically you can use any function that maps R to [0, 1] as a CDF. If its density is symmetrical then you can directly write the above probability as CDF(beta X). The two usual choices are either the normal CDF which gives the Probit model or the Logistic function (Sigmoid) which gives the Logit model. With the CDF known you can calculate the likelihood and use it to estimate the coefficients.
People prefer the Logit model because the coefficients of the model are interpretable in terms of log-odds and all and the fucntion has some nice numerical properties.
That's all there is to it really.