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Rewrite your linear predictor $\eta(x_1,x_2)=\beta_0+\beta_1 x_1 + \beta_2 x_2$ as $\eta(x_1, X_2)=\beta_0+\beta(x_1+x_2)+(\beta_2-\beta) x_2$. In this model you test the null hypothesis $H_0\colon \beta_2-\beta=0$ versus the alternative $\beta_2-\beta <0$.
In practice, I would do that fitting the full model and making a confidence interval based on ...
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How can I test for a systematic increase in Y as a function of X in data modeled by a sigmoid curve?
You could use a mixed-effects logistic regression, with R synatx such a model could be
lme4::glmer( correct ~ x + (1 | Subject), family=binomial(link="log"),
data=your_data_frame, ... )
with a random intercept for each Subject, or if you want also random slopes
lme4::glmer( correct ~ x + (1 + x | Subject), family=binomial(link="...
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Whether you use the standard "rule of thumb" of 10-20 minority-class cases per predictor or the more refined approaches described in the paper linked by @Chl in a comment, you will find that having only 22 events will severely limit your ability to "find the association" between the event and your approximately 20 candidate predictors. ...
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Accuracy is, always, the number of correct guesses out of the total number of guesses. If you guess the right category when there are two categories, you had an accurate prediction. If you guess the wrong category when there are ten categories, you had an inaccurate prediction. Think of it like your score on a multiple choice test.
However, Cross Validated ...
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For simplicity, let's say you have a (binary) logistic regression model where you regress the binary outcome variable $Y$ on the predictors $X_1$ and $X_2$. $Y$ takes the value 1 for the event of interest (e.g., student is admitted into the program) and 0 otherwise (e.g., student is not admitted into the program).
The (binary) logistic regression model is ...
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Both of these methods require satisfaction of Conditional Independence Assumption, so as long there are unobserved confounders (i.e. selection variables), or other endogeneity problems, both methods are invalid and biased.
These two methods base on different model: regression models outcome, propensity score models selection. If it is more easy/difficult to ...
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Without much more information we can't give you guaranteed advice here.
You can remove rows of data. However, this will cause problems if they are not randomly missing. For instance, the fact that they are missing may indicate something about them (such as they are not an engaged customer).
You can impute values if you have a means to do so.
You can remove ...
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I don't have enough reputation to comment. But let me give you my view.
Ordinal data is related to information organized in a particular order without indicating a specific relationship between each item. Items may be greater than or less than other items. The order of items is often defined by assigning numbers to them to show their relative position.
...
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Let me answer your second question, why they switched to the logistic function.
The Elo rating system comes from the Chess world. The initial Elo's premise was a normal distribution, but since more chess statistics became available, FIDE (The World Chess Federation) realized that it was better to consider the logistic function.
Have a look here for a ...
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You are right. You can take the 10-th root of the odds ratio (relative change of the odds) for a step of size 1, in order to get the odds ratio for a step of size 0.1
The reason is because a logistic model is modeling the logarithm of the odds as a linear function of the parameter/predictor. And this makes the odds an exponential function of the parameter/...
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Overview
The rules/formulae themselves have been published in several locations. Here's an accessible version (framed in terms of SAS, but the equations are under the heading "Combining Inferences from Imputed Data Sets" on page 5.)
https://stats.idre.ucla.edu/wp-content/uploads/2016/02/multipleimputation.pdf
Caveats
As noted by Amparo, for ...
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