Haiqing Hua’s Post

Assessing the Efficacy of Logistic Models In statistical modeling, logistic regression serves as a pivotal tool, especially when the dependent variable is dichotomous. The assessment of a logistic model's performance is multifaceted, encompassing various statistical tests and evaluation metrics to ensure its predictive prowess and reliability. The initial step in evaluating a logistic model is to examine its predictive performance. This is commonly done through a confusion matrix, which delineates the number of correct and incorrect predictions made by the model, offering a clear view of its accuracy and precision. A classification report complements this by providing precision, recall, and F1-score, which are critical indicators of the model's predictive quality. Further, the Receiver Operating Characteristic (ROC) curve and the Area Under the Curve (AUC) score are indispensable tools. The ROC curve plots the true positive rate against the false positive rate at various threshold settings, while the AUC score quantifies the model's ability to differentiate between the classes. A model with an AUC close to 1 indicates excellent class separation capacity. Goodness-of-fit tests also play a crucial role. They determine whether the model is an appropriate fit for the observed data. Chi-square tests and analysis of residuals can reveal if there are discrepancies between the expected and observed values, indicating potential issues with the model's fit. Lastly, cross-validation is a robust technique to assess the model's generalizability. By partitioning the data into complementary subsets, the model is trained and tested multiple times, ensuring its performance is consistent across different data samples. In conclusion, a comprehensive assessment of a logistic model involves a blend of predictive performance evaluation, discrimination ability analysis, goodness-of-fit testing, and validation of robustness. Only through a thorough examination can one ensure the model's efficacy and readiness for practical application. #LogisticRegression #ModelAssessment #PredictiveAnalytics #DataScience #MachineLearning #ROC #AUC #CrossValidation #StatisticalModeling #GoodnessOfFit

Day21 Classification Metrics Accuracy : It's the ratio of correct predictions to total predictions. Formula= (True Positives+True Negatives)/Total Predictions Type I and Type II Errors: Type I Error (False Positive): Incorrectly predicting a positive outcome when it is actually negative. Type II Error (False Negative): Incorrectly predicting a negative outcome when it is actually positive. When Accuracy Can Mislead: Accuracy can be misleading in cases of imbalanced datasets. For example, if we're trying to identify terrorists among a large population of normal people, where only a tiny fraction are actual terrorists, a model that predicts everyone as normal could achieve very high accuracy. However, this model fails to identify any terrorists, making it ineffective for our goal. Precision: what proportion of predicted positive is truly positive. useful when the cost of false positives is high. Formula: True Positives/ (True Positives + False Positives) Recall: what proportion of actual positive is correctly classified. important when the cost of false negatives is high. Formula= True Positives / (True Positives + False Negatives) F1 Score: The harmonic mean of precision and recall. It balances precision and recall, especially useful when classes are imbalanced. Formula= 2× (Precision×Recall)/(Precision+Recall) Multiclass Classification:In multiclass classification, we extend these metrics to multiple classes: Macro Precision: Average precision over all classes. Weighted Precision: Average precision over all classes, weighted by the number of true instances for each class. The classification report combines all these metrics, providing a comprehensive evaluation of the model's performance across all classes. It's an essential tool for understanding your model's strengths and weaknesses.

White noise is a concept commonly encountered in time series analysis and signal processing. It refers to a type of stochastic process where each data point in the time series is independently and identically distributed with a constant mean and variance, and there is no autocorrelation between consecutive observations. Key characteristics of white noise include: 1. **Constant Mean**: The mean of the white noise process remains constant over time. 2. **Constant Variance**: The variance of the white noise process is constant across all time points. 3. **Independence**: Each data point in the time series is statistically independent of all other data points. In other words, there are no systematic dependencies or relationships between consecutive observations. 4. **Zero Autocorrelation**: There is no correlation between consecutive observations in the time series. The autocorrelation function (ACF) of white noise is zero for all lags except at lag 0, where it equals 1. White noise is often represented by the symbol \( \varepsilon_t \) and is commonly assumed to follow a Gaussian (normal) distribution with mean zero and constant variance. It serves as a baseline or reference process in time series analysis and is often used to model the random fluctuations or measurement errors present in data. While white noise itself may not have direct practical significance, it serves as an important theoretical concept in time series analysis for several reasons: - It provides a benchmark for comparison when analyzing other time series processes. - Deviations from white noise properties in observed data may indicate the presence of underlying patterns, trends, or serial correlation. - White noise is a fundamental component in many time series models, such as autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models, where it represents the unexplained or residual variation in the data. In summary, white noise is a fundamental concept in time series analysis, representing a stochastic process with constant mean, variance, independence, and zero autocorrelation. It serves as a baseline reference for analyzing and modeling more complex time series data.

I don't rely on Accuracy in multiclass classification settings to measure model improvement 🧩 Consider probabilistic multiclass classification models. Using "Accuracy" as a signal to measure model improvement can be deceptive. It can mislead you into thinking that you are not making any progress in improving the model. In other words, it is possible that we are actually making good progress in improving the model... ...but “Accuracy” is not reflecting that (YET). The problem arises because Accuracy only checks if the prediction is correct or not. And during iterative model building, the model might not be predicting the true label with the highest probability... ...but it might be quite confident in placing the true label in the top "k" output probabilities. Thus, using a "top-k accuracy score" can be a much better indicator to assess whether my model improvement efforts are translating into meaningful enhancements in predictive performance or not. For instance, if top-3 accuracy increases from 75% to 90%, it is clear that the improvement technique was effective: - Earlier, the correct prediction was in the top 3 labels only 75% of the time. - But now, the correct prediction is in the top 3 labels 90% of the time. Thus, one can effectively direct the engineering efforts in the right direction. Of course, what I am saying should ONLY be used to assess the model improvement efforts. This is because true predictive power will be determined using traditional Accuracy. As depicted in the image below: - It is expected that “Top-k Accuracy” may continue to increase during model iterations. This reflects improvement in performance. - Accuracy, however, may stay the same during successive improvements. Nonetheless, we can be confident that the model is getting better and better. For a more visual explanation, check out this issue: https://lnkd.in/dP_h8SFM. -- 👉 Get a Free Data Science PDF (530+ pages) by subscribing to my daily newsletter today: https://lnkd.in/gzfJWHmu -- 👉 Over to you: What are some other ways to assess model improvement efforts?

*** Path Analysis: Explained and Its History *** ~ Path analysis describes the directed dependencies among a set of variables. This includes models equivalent to any form of multiple regression analysis, factor analysis, canonical correlation analysis, discriminant analysis, and more general families of models in the multivariate analysis of variance and covariance analyses (MANOVA, ANOVA, ANCOVA). In addition to being considered a form of multiple regression focusing on causality. ~ Path models consist of independent and dependent variables depicted graphically by boxes or rectangles. Variables that are independent and not dependent are called 'exogenous.' ~ Graphically, these exogenous variable boxes lie at the outside edges of the model and have only single-headed arrows exiting from them. ~ No single-headed arrows point at exogenous variables. ~ Variables that are solely dependent, or are both independent and dependent variables, are termed 'endogenous.' ~ Graphically, endogenous variables have at least one single-headed arrow pointing at them. ~ In the model in the post image, the two exogenous variables (Ex1 and Ex2) are modeled as being correlated, as depicted by the double-headed arrow. These variables have direct and indirect (through En1) effects on En2 (the two dependent or 'endogenous' variables/factors). ~ In most real-world models, the endogenous variables may also be affected by variables and factors stemming from outside the model (external effects, including measurement error). These effects are depicted by the "e" or error terms in the model. ~ Using the same variables, alternative models are conceivable. For example, it may be hypothesized that Ex1 has only an indirect effect on En2, deleting the arrow from Ex1 to En2, and these two models' likelihood or 'fit' can be compared statistically. ~ Wright (1934) proposed a simple set of path-tracing rules for calculating the correlation between two variables to validly calculate the relationship between any two boxes in the diagram. The correlation equals the sum of the contribution of all the pathways through which the two variables are connected. The strength of each of these contributing pathways is calculated as the product of the path coefficients along that pathway. The rules for path tracing are: 1. You can trace backward up an arrow and then forward along the next or forwards from one variable to the other, but never forward and back. 2. You can pass through each variable only once in a given chain of paths. 3. No more than one bi-directional arrow can be included in each path-chain. Again, the expected correlation due to each chain traced between two variables is the product of the standardized path coefficients, and the total expected correlation between two variables is the sum of these contributing path chains. --- B. Noted

You don't need to know 20+ regression models! Learn these top 4 that you can apply in 80% of real-world problems👇 📕 𝗢𝗟𝗦 𝗥𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 This is a great starter model for inference and prediction of Y that is continuous. It's my default model for establishing a baseline for model performance and explaining the relationship between X and Y. 📘 𝗟𝗼𝗴𝗶𝘀𝘁𝗶𝗰 𝗥𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 If you are doing binary classification or inference, give this model a go. It's easy and quick to train, and it provides a high level of interpretability in terms of statistical significance, confidence and prediction intervals. 📗 𝗣𝗼𝗶𝘀𝘀𝗼𝗻 𝗥𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 This model is great for count-based data where the range is from 0 to +infinite on the Y. I've used this model for survival modeling as a consultant at the Pentagon. 📙 𝗠𝘂𝗹𝘁𝗶𝗹𝗲𝘃𝗲𝗹 𝗥𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 The first three models explain variation at an individual subject level. But, there is variability with respect to the groups that the subject belongs to. Think of assessing the performance of employees (level 1) across multiple stores (level 2). Multilevel regression is helpful when you want to measure outcomes at multiple levels. 👉 Which model have you used before?👇

Evaluating model improvements with Accuracy can be misleading 🧩 The efficacy of a model improvement step is best determined using performance metrics. However, improving probabilistic multiclass-classification models using "Accuracy" as a signal can be deceptive. In other words, it is possible that we are actually making good progress in improving the model... ...but “Accuracy” is not reflecting that (YET). The problem arises because Accuracy only checks if the prediction is correct or not. And during iterative model building, the model might not be predicting the true label with the highest probability... ...but it might be quite confident in placing the true label in the top "k" output probabilities. Thus, using a "top-k accuracy score" can be a much better indicator to assess whether my model improvement efforts are translating into meaningful enhancements in predictive performance or not. For instance, if top-3 accuracy increases from 75% to 90%, it is clear that the improvement technique was effective: - Earlier, the correct prediction was in the top 3 labels only 75% of the time. - But now, the correct prediction is in the top 3 labels 90% of the time. Thus, one can effectively direct the engineering efforts in the right direction. Of course, what I am saying should ONLY be used to assess the model improvement efforts. This is because true predictive power will be determined using traditional Accuracy. So make sure you are gradually progressing on the Accuracy front too. As depicted in the image below: - It is expected that “Top-k Accuracy” may continue to increase during model iterations. This reflects improvement in performance. - Accuracy, however, may stay the same during successive improvements. Nonetheless, we can be confident that the model is getting better and better. For a more visual explanation, check out this issue: https://lnkd.in/dP_h8SFM. -- 👉 Get a Free Data Science PDF (550+ pages) with 320+ posts by subscribing to my daily newsletter today: https://lnkd.in/gzfJWHmu -- 👉 Over to you: What are some other ways to assess model improvement efforts?

*** Path Analysis: Explained and Its History *** Path analysis describes the directed dependencies among a set of variables. This includes models equivalent to any form of multiple regression analysis, factor analysis, canonical correlation analysis, discriminant analysis, and more general families of models in the multivariate analysis of variance and covariance analyses (MANOVA, ANOVA, ANCOVA). In addition to being considered a form of multiple regression focusing on causality. ~ Path models consist of independent and dependent variables depicted graphically by boxes or rectangles. Variables that are independent and not dependent are called 'exogenous.' ~ Graphically, these exogenous variable boxes lie at the outside edges of the model and have only single-headed arrows exiting from them. ~ No single-headed arrows point at exogenous variables. ~ Variables that are solely dependent, or are both independent and dependent variables, are termed 'endogenous.' ~ Graphically, endogenous variables have at least one single-headed arrow pointing at them. ~ In the model in the post image, the two exogenous variables (Ex1 and Ex2) are modeled as being correlated, as depicted by the double-headed arrow. These variables have direct and indirect (through En1) effects on En2 (the two dependent or 'endogenous' variables/factors). ~ In most real-world models, the endogenous variables may also be affected by variables and factors stemming from outside the model (external effects, including measurement error). These effects are depicted by the "e" or error terms in the model. ~ Using the same variables, alternative models are conceivable. For example, it may be hypothesized that Ex1 has only an indirect effect on En2, deleting the arrow from Ex1 to En2, and these two models' likelihood or 'fit' can be compared statistically. ~ Wright (1934) proposed a simple set of path-tracing rules for calculating the correlation between two variables to validly calculate the relationship between any two boxes in the diagram. The correlation equals the sum of the contribution of all the pathways through which the two variables are connected. The strength of each of these contributing pathways is calculated as the product of the path coefficients along that pathway. The rules for path tracing are: 1. You can trace backward up an arrow and then forward along the next or forwards from one variable to the other, but never forward and back. 2. You can pass through each variable only once in a given chain of paths. 3. No more than one bi-directional arrow can be included in each path-chain. Again, the expected correlation due to each chain traced between two variables is the product of the standardized path coefficients, and the total expected correlation between two variables is the sum of these contributing path chains. --- B. Noted

*** Path Analysis: Explained and Its History *** Path analysis describes the directed dependencies among a set of variables. This includes models equivalent to any form of multiple regression analysis, factor analysis, canonical correlation analysis, discriminant analysis, and more general families of models in the multivariate analysis of variance and covariance analyses (MANOVA, ANOVA, ANCOVA). In addition to being considered a form of multiple regression focusing on causality. ~ Path models consist of independent and dependent variables depicted graphically by boxes or rectangles. Variables that are independent and not dependent are called 'exogenous.' ~ Graphically, these exogenous variable boxes lie at the outside edges of the model and have only single-headed arrows exiting from them. ~ No single-headed arrows point at exogenous variables. ~ Variables that are solely dependent, or are both independent and dependent variables, are termed 'endogenous.' ~ Graphically, endogenous variables have at least one single-headed arrow pointing at them. ~ In the model in the post image, the two exogenous variables (Ex1 and Ex2) are modeled as being correlated, as depicted by the double-headed arrow. These variables have direct and indirect (through En1) effects on En2 (the two dependent or 'endogenous' variables/factors). ~ In most real-world models, the endogenous variables may also be affected by variables and factors stemming from outside the model (external effects, including measurement error). These effects are depicted by the "e" or error terms in the model. ~ Using the same variables, alternative models are conceivable. For example, it may be hypothesized that Ex1 has only an indirect effect on En2, deleting the arrow from Ex1 to En2, and these two models' likelihood or 'fit' can be compared statistically. ~ Wright (1934) proposed a simple set of path-tracing rules for calculating the correlation between two variables to validly calculate the relationship between any two boxes in the diagram. The correlation equals the sum of the contribution of all the pathways through which the two variables are connected. The strength of each of these contributing pathways is calculated as the product of the path coefficients along that pathway. The rules for path tracing are: 1. You can trace backward up an arrow and then forward along the next or forwards from one variable to the other, but never forward and back. 2. You can pass through each variable only once in a given chain of paths. 3. No more than one bi-directional arrow can be included in each path-chain. Again, the expected correlation due to each chain traced between two variables is the product of the standardized path coefficients, and the total expected correlation between two variables is the sum of these contributing path chains. --- B. Noted

#LinearRegression Linear Regression is one of the most important tools in a Data Scientist's toolbox. Here's everything you need to know in 3 minutes. 1. OLS regression aims to find the best-fitting linear equation that describes the relationship between the dependent variable (often denoted as Y) and independent variables (denoted as X1, X2, ..., Xn). 2. OLS does this by minimizing the sum of the squares of the differences between the observed dependent variable values and those predicted by the linear model. These differences are called "residuals." 3. "Best fit" in the context of OLS means that the sum of the squares of the residuals is as small as possible. Mathematically, it's about finding the values of β0, β1, ..., βn that minimize this sum. 4. Slopes (β1, β2, ..., βn): These coefficients represent the change in the dependent variable for a one-unit change in the corresponding independent variable, holding other variables constant. 5. R-squared (R²): This statistic measures the proportion of variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. 6. t-Statistics and p-Values: For each coefficient, the t-statistic and its associated p-value test the null hypothesis that the coefficient is equal to zero (no effect). A small p-value (< 0.05) suggests that you can reject the null hypothesis. 7. Confidence Intervals: These intervals provide a range of plausible values for each coefficient (usually at the 95% confidence level).