10 votes

Linear regression's (OLS) coefficient interpretation with heteroscedasticity

Heteroscedasticity makes it so that the OLS estimator is not the best linear unbiased estimator of the regression slopes and makes it so that the usual standard errors (and the quantities based on ...
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  • 21.9k
8 votes

QQ plot result doesn't correspond to normality test

Your Q-Q plot does not show that the data is normally distributed. In fact, it shows that the distribution diverges from Gaussian (values lower than -1 and higher than 1.5 diverge from the diagonal ...
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  • 113k
6 votes
Accepted

How to assess normality under the OLS assumptions?

The first two are totally wrong but are common misconceptions about the normality assumption in OLS regression (when we choose to make such an assumption, which we don’t have to do). There is no ...
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  • 31.1k
5 votes

Exists an option to avoid reference categories in logistic regression?

This question has nothing to do with logistic regression per se, the problem and answers is the same for all generalized linear regression models. If you have only one categorical variable, just leave ...
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4 votes

QQ plot result doesn't correspond to normality test

Just on first look, this distribution looks very short tailed, as you can see it looks kind of like this simulation with a uniform distribution
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4 votes

Exists an option to avoid reference categories in logistic regression?

Normally, with three categories, you will obtain an intercept, reflecting the log odds of the outcome in the reference category, and two effect terms, indicating how the log odds for the other two ...
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  • 4,691
4 votes

Interpreting interaction effects for categorical reference group in regression

@EdM makes valid points - read those first. Just for reference, you could get the effects of interest along with their confidence intervals using the emmeans package. For example: ...
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  • 3,110
4 votes

Interpreting interaction effects for categorical reference group in regression

First, with the default R treatment coding of your categorical predictors, the individual coefficients for things like Story Vision are their associations with ...
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  • 62.3k
3 votes

Different Meanings of "Clusters" in Statistics

From the Merriam-Webster Dictionary: a number of similar things that occur together The two uses of the term that you describe have to do whether you are trying to discover a cluster in a data set ...
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  • 62.3k
3 votes
Accepted

Logistic regression simulation with respect to event occurrence (prevalence)

You have an array of explanatory variables $(x_1, x_2, \ldots, x_n)$ ($n=20000$) and a model that assigns a probability to each $x_i.$ You seek a subarray of these variables that has a mean ...
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  • 287k
2 votes

What is the impact of duplicate data on the variance of regression coefficient?

The coefficients themselves will no change. Imagine you perform the analysis on the first dataset, and plot the regression line with the datapoints around the regression line. Now what would happen if ...
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  • 570
2 votes

Forecasting using regression coefficients

Your first question: Yes, this is a valid approach. If you only want to do prediction and you think a linear dependency is appropriate, this is a valid approach. Your second question: Of course, you ...
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  • 2,958
2 votes

Cox Proportional Hazards : Why not "Cox Proportional Survival"?

Proportional survival rates depend on the overall prevalence of events, proportional hazards do not. Suppose you have two groups with different hazard rates, one where events occur in 10% of the ...
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2 votes
Accepted

What does it mean when there is a pattern in residuals related to the dependent variable?

It usually means nothing -- and that's why we don't ordinarily look at this plot. A regression model fits values $\hat y$ to responses $y.$ We can analyze the response into the sum of the fitted ...
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  • 287k
2 votes
Accepted

Gauss-Markov theorem explanation (linear regression)

The vector $\ell$ is whatever you want it to be. That is, if you want to estimate some linear combination of the true coefficients $\beta$, the same linear combination of the estimated coefficients $\...
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2 votes

Correct loss function and metric for regression of count data in neural network

The Poisson distribution is one integer-valued distribution among many alternatives. You can experiment with alternative losses. The model's predictions for the Poisson model is the conditional ...
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  • 78.2k
1 vote

Ideal Settings for Longitudinal Models?

There is a simple counterexample to your suggestion. Imagine a case where some units are affected by large measurement error, while others have only small measurement error. It is more statistically ...
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  • 4,691
1 vote

How do I increase accuracy with Keras using LSTM

This is an old question, but I will answer for anyone who has the same issue and finds this question. The issue is that you use the wrong metric. Accuracy metric is used for classification problems. ...
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  • 11
1 vote

Why do fixed effects in a logistic regression model differ depending on the presence of a random slope?

Fixed effects change You do get that the fixed effects change when you add a random effect. With your example both the intercept and slope change. Below is an example of the situation. black line: ...
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1 vote

How to tell if data has homgenous variance?

For an ANOVA model like this, you have 1 mean value estimate for each of 3 groups. The residuals are the differences of each individual observation from its corresponding group mean. Roughly, the ...
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  • 62.3k
1 vote

Applications of "Dose Response" Outside of Biostatistics?

A major class of what you might consider "dose-response models" has roots going back to the mid 19th-century. The 4-parameter logistic curve described in the package you cite for dose-...
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  • 62.3k
1 vote

How to assess economic significance in a log-log OLS model?

Statistical and economic significance are not the same concept. Broadly speaking, statistical significance in a regression tells you if a variable has an effect on the outcome variable (depending on ...
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1 vote

Find a linear scale factor and offset that minimizes total variance between two observed data sets

You could consider your two datasets $D_1, D_2$ as samples from two different probability density functions (pdfs) $p_1, p_2$, resp. And then the question is how to transform $p_1$ to obtain some new ...
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  • 2,958
1 vote

Is it possible to derive the joint probability distribution of squared OLS residuals under the classical linear regression assumptions?

I've managed to come up with an answer to my question as follows. Bivariate Case Let ${(U_1,V_1),\ldots,(U_k,V_k)}$ be an independent random sample of size $k$ from a bivariate normal distribution ...
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1 vote

How do I interpret the coefficients of a mixed effects multilevel logistic regression differently from regular logistic model?

@Robert Long what would it mean if a variable was significant in the regular logistic regression, but no longer significant after a random effect is added in the mixed-effect model? What does that say ...
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  • 41
1 vote

"Survival" vs. "Hazard" : When to Use Which?

Hazard models are highly flexible methods that produce summary measures of differences in the time to event. Using the hazard function, we can create multivariable regression models with independent ...
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  • 1,743
1 vote

Testing difference between coefficients of nonlinear regression models

I feel a bit bad by overcrowding the comments section with pedantic notes and questions about the origins of the noise in the data. So I will make up for it with an answer that is a bit more decent ...
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