logistic | vectorized implementation of a logistic regression | Machine Learning library

Facing a couple logistical issues in PowerShell - clearly I'm missing a basic concept:

Setup: Create the menu.ps1 file (shown below), launch PowerShell 7.2.2 and call the file locally.

Issues:

1. The first time you choose option 1 for the ArrayList ($psArrayList), it does not display (although we see from the initial screen load that the items are populated). If you return to the menu and choose option 1 again, it will display on the second pass. ($psArray does load fine on first try, so is this is a type issue.?)
2. When the script ends, $psArrayList and $psArray are still in the current session variables, as indicated by: Get-Variable psArray*. Even if I instantiate them with $script:psArrayList = [System.Collections.ArrayList]@() and $script:psArray = @() they seem to stay within the session scope. Is there a "right" way to clear them when the ps1 ends?

menu.ps1 contents:

For my master's thesis I have to work with a database in order to make a logistic regression model. One of the variables of my model is NEWS, This should be a dummy variable that is equal to 1 if a company had to publish a negative net income (bad news) in a given year, which belongs to the time period of this study (2017, 2018 and 2019), while it still had a positive net income the year before (good news). The dummy is equal to 0 otherwise. Now my professor said that I had to make a dummy that is equal to one when a company had a negative net income during one of the three years, O otherwise. That part I understand. But then she also said that I had to use a LAG function in order to find out if the company had a positive net income the year before the negative net income. And that part I don't understand. I don't really understand how i should do this with the help of SPSS. Below you can find a small part of the data I have to work with.

In GridSearchCV, I want to try different combinations of parameters to tune hyperparameter but some can't be use with another such as lbfgs can be used with only l2 in logistic regression.

Below is common way that I use currently,

Let's consider the data following:

I am currently attempting to estimate the parameters of a logistic regression model "by hand" on the iris dataset via minimisation of cross-entropy. Please note, when I say iris dataset, it has been changed such that there are only two classes - Setosa and Other. It was also normalised via the scale function:

I've trained a pretty complex (random intercept and slope) mixed logistic model which I'm then using to predict new data. My predictions were way off so I compared the predicted values for my original data and noticed that they are very different from my fitted.values(). E.g. taking just the first data point, the fitted value is 0.359, the predicted value (predict(model, newdata=data, type="response") is 0.0585. I'm pretty sure the issue relates to the random effects, because if I predict the same data point with only fixed effects I get 0.707, which is what I'd expect, and random effects only gives 0.0252 which is very wrong.

You can see the different random effect groups by plotting fitted vs predicted (below) This also shows how the gradients within groups are the same so it looks like a problem with the intercepts rather than the slopes.

Any help would be really appreciated!

EDIT: In case it helps, the formula basically looks like this:

The rows of data frame "pars" hold the two parameters defining logistical curves:

What im looking to achieve is pulling a csv file from a workorder app that we use. Then convert it using pandas and remove unnecessary columns. Then post this info into slack using a webhook. I dont have access to the slack API. So far this is what i came up with but am finding it hard to get the data into a format that i can send.

I am trying code from this page. I ran up to the part LR (tf-idf) and got the similar results

After that I decided to try GridSearchCV. My questions below:

1)