Ordered Logistic Regression in Jupyter Notebook

A statistical method used to predict the probability of a categorical outcome, where the outcome has ordered categories. For example, predicting a team's ranking based on their win-loss record.

A measure of a team's winning potential, calculated using the ratio of a team's score for to their score against, raised to a specific exponent (usually 2).

A variable that represents a binary state, either 1 or 0, indicating whether a team played a game at home or away.

The process of preparing data for analysis, often including cleaning, transforming, and encoding variables. Often involves creating new variables or modifying existing ones.

Combining multiple data sets or data frames into a single data structure. Essential for merging different sources of information for analysis.

A key step in data preparation where values in a column are numerically sorted to create a sequential order.

Calculating cumulative statistics for a group of individuals or teams. The cumulative value includes the sum of values up to a particular point.

Reading and displaying the initial data to verify its structure, content, and understand its potential for analysis. This is often done to identify any issues or missing data.

A Python library specifically designed for fitting ordered logistic regression models.

The parameters in an ordered logistic regression model that represent the thresholds defining the boundaries between different categories of the outcome variable.

The estimates for the relationship between each predictor variable and the outcome variable in an ordered logistic regression model. They indicate how much the log odds of an outcome change for each unit increase in a predictor.

A measure representing the predicted log odds of each outcome category for a specific combination of predictor values.

A process of transforming the linear product (log odds) back into probabilities for each outcome category, making it easier to interpret the results.

Predicting the most likely outcome category based on the calculated probabilities, using the ordered logistic regression model.

The way outcome categories are numerically encoded in the dataset, often using consecutive integers to represent the order.

The success rate of a fitted model is calculated by comparing the predicted outcomes with the actual outcomes. It represents the proportion of correctly predicted outcomes.

Ordinal regression models attempt to predict an outcome variable with ordered categories. For example, a sports game can have outcomes of 'win', 'draw', or 'loss'.

An independent variable is a factor that we believe has an influence on the outcome variable. In sports, examples could be home advantage, player skill, or team performance.

A dummy variable represents a categorical variable with two values, often '0' and '1'. It's used to incorporate categorical information into the analysis, like 'home' or 'away' in a sports game.

Regression coefficients are numerical values associated with each independent variable in a model. They quantify the impact of each independent variable on the outcome variable.

Thresholds, in an ordinal regression model, are cut-off points that separate the different outcome categories. For example, a threshold might define the point at which the probability of winning becomes higher than the probability of drawing.

The fitted probabilities, in an ordinal regression model, are the estimated likelihoods of each outcome category based on the model's prediction. These probabilities range from 0 to 1.

The fitted outcome is the final prediction from the ordinal regression model, based on the highest fitted probability. It represents the model's best guess for the outcome category.