# Questions tagged [leverage]

Leverage is a measure used in regression to highlight observations which are outlying in the space of the predictors.

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### Cooks Distance for multiple observations

I would like to determine the combined influence of a group of observations on a linear regression model, but I am not entirely sure how to compute the Cook's Distance for that. I know that for a ...
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### Simple Linear Regression: Hat-Value $h_i$

I'm trying to finish proving that in simple-regression analysis, $h_i = \frac{1}{n} + \frac{(X_i - \bar{X})^2}{\sum_{j=1}^{n}(X_j - \bar{X})^2}$, where $h_i := h_{ii} = \sum_{j=1}^nh_{ij}^2$, the ...
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### Individual significance of data points in correlation

In this question on stackoverflow, I asked about how it is possible to find the individual significance of each correlation coefficient of each node. I answered the question myself later stating that ...
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### Proof about the diagonal element of the hat matrix

I'd really appreciate it if you could help me find the proof for the following formula: $$h_{ii}=1/n + \frac{(x_{i}-\bar{x})^2}{\sum(x_{j}-\bar{x})^2},$$ where $j=1,\ldots,n$. I don't really know ...
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### Outliers and influential observations in elastic net logistic regression

My dataset has many biomarkers and the boxplots of these variables show the presence of many outliers. However, these 'outliers' are real data and not misread observations. I want to use elastic net ...
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### Bounding residual variance with distance from mean

For a linear regression $Y = X\beta + \varepsilon$ with $\varepsilon \sim \mathcal N(0,\sigma^2 I)$, we have $\hat Y = H Y$ for $H = X(X^TX)^{-1}X^T$. This means that $Var(Y - \hat Y) = \sigma^2(I-H)$ ...
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### Inferences about leverage score and Mahalanobis distance [duplicate]

I have some inference given below: Given the design matrix $\textbf{X}$, the leverage score is defined as $\textbf{H}_{ii}$ where $\textbf{H} = \textbf{X} (\textbf{X}^T \textbf{X})^{-1} \textbf{X}^T$ ...
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### Leverage and Influence

Is it possible that an outlier is neither influential nor does it have high leverage? Or can it happen that an observation with high leverage is not an outlier and is neither influential?
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### How to find influance on correlation of single value

I need to find possible errors or outliers in my data sets. I want to find most affecting values of my pearson correlation. For example let say we got two data sets for X and Y: ...
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### Why would standard errors around each individual point of an ARIMA model converge to a single value?

I am using an AR(1) model to determine if a new data point is beyond some expected range. Typically, you could use a prediction interval, which would just be the predicted value, +/- some multiple (e....
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### How outliers influence your results? and what are good and bad leverage points? [duplicate]

I am confused between outliers and leverage points. And the difference between good and bad leverage points in time series analysis. Can somebody help me?
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### Numerically Distinguish Between Real Correlation and Artifact

I'm looking at correlation for a large number of vectors, and many (about 3000) of these pairwise comparisons appear to have a significant correlation even after Bonferroni correction. Plotting these ...
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### Why divide by 1-leverage?

I'm reading about resampling methods, and specifically leave-one-out cross-validation. I understood the method, and how to calculate the estimate of the test MSE (Mean squared error): In the setup ...
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### Why uncentered hat matrix can be used to measure the distance from the center of data?

This question is motivated from here :Why leverage measure the distance of the ith observation from the center of the x space? which is the question related to the wonderful answer of this link :...
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Sample data ...
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### Influential observations and Outliers in Linear Regression model

What is the difference between influential observations and outliers in linear regression model?
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### Is there a specific standard error for an individual residual?

On page 97 of Introduction to Statistical Learning book, there is a paragraph on studentized residuals within the context of looking for outliers. But in practice, it can be difficult to decide how ...
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### News Impact curve shift

I computed the NIC for both vanilla GARCH and EGARCH model specifications (with t(4)-student distributed innovations). As we can see from the plot, no asymmetries are present, but the curve has ...
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### How to solve a well fitted model - Model Misspecification

I am currently writing a paper, analysing the impact of goldprice movements on the capital structure of gold mining firms. My basic model is a simple OLS model with (y=leverage and x=ln(goldprice)). ...
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### Sensitivity Measures for GEE Model

Is there any method (e.g. like Cooks D) implemented in R to identify leverage points for GEE Models? I used geepack to fit my models and would like to do a sensitivity analysis now. However, I don't ...
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### Leverage formula/derivation and Hat matrix

1) So I know that $h_{ii}$ is just the ith row ith column of $H=X(X^TX)^{-1}X^T$. Intuitively, why is this the case? I understand that H is the projection matrix and leverage is measuring how far away ...
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### Cook's distance vs. hat values

What exactly does Cook's distance measure? And how is this different from what hat values measure? I know hat values measure how distant a point it form its corresponding fitted point. I also know ...
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### Leverage Statistic - equation explanation

I came across this equation for the leverage statistic in ISL. Does the denominator translate to the summation of all the squares of $(x_i - mean(x))^2$ excluding the current observation of x? In ...
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### Influence function for glm?

I would like to calculate the influence of each sample on the coefficient under a logistic regression model. The R built-in function influence() is suppose to do ...
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### How to extract/compute leverage and Cook's distances for Generalised Additive models

Similar to the following question, How to extract/compute leverage and Cook's distances for linear mixed effects models Is there any method in R to determine influential points in a GAM?
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### What is .hat in regression output

The augment() function in the broom package for R creates a dataframe of predicted values from a regression model. Columns created include the fitted values, the ...
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### leverage.plot() R - CAR package

I'm trying to complete a homework regarding added-variables and leverage plots using the CAR package. In the documentation of the ...
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### How to identify outliers and do model diagnostics for an lme4 model?

I need to identify outliers and high leverage points, and perform model diagnostics, in an lme4 model. For outliers and high leverage points, simply making a plot ...
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### Multiple regression - High adjusted R^2 but the residuals are high

I used the multiple regression models to derive the outcomes after using AIC pairwise comparison and deleted the outliers, high leverage points. And it seems good, the adjusted R^2 acheived 0.9543, ...
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### R not plotting observations with leverage one

I am building a really simple linear model. I want to test if the frass I got over 3 days from butterfly larvae depend upon the food they ate (diet), the butterfly family (the mother line) and ...