# Questions tagged [errors-in-variables]

Errors in variables are measurement errors which increase the estimation variance (error in the dependent variable) or bias the regression coefficients towards zero (error in the independent variables).

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### Is reduced major axis regression a special case of total least squares?

Edit: It seems the answer to my first question is that the website has a typo. $\lambda = V_{y}/V_{x}$, NOT $\lambda = V_{x}/V_{y}$. But I'm still stumped on the second question about why it cannot be ...
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### What is the Likelihood Formula for an Error in Variable Model?

I am comparing different models ability to explain my joint observation of (X,Y) with AIC for which I need the likelihood. How can I calculate the likelihood of (X,Y) for the error in variable model ...
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### Asymmetric errors on cluster size distributions

I have a question that might seem simple, but I'm unsure how to address it. For an analysis on pixel detectors, I am extracting a histogram similar to the ones attached, focusing on the cluster size ...
1 vote
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### Errors-in-variables regression with sample size weighting?

Very belated follow-up to a previous question: I have some pretty simple linear models predicting a rate (continuous response var) from certain features of the distribution of some measured value. The ...
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### A lot of variables in a Quadratic Discriminant Analysis

I'm trying to make a Quadratic Discriminant Analysis in R, but appears the follow mistake: "some group is too small for 'qda'". I was reading about it and I concluded that I have more ...
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### Error-in-Variables regression p-value?

I ran an EIV model in r and I was wondering if there is something else besides the R-adjusted to see if the fit of the model is good? I noticed that eivreg function ...
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### Calculate the average of absolute values of a measurement with a measurement error

I have a few parameters; each is measured imprecisely with a known but unique random measurement error. We can assume that the error is normally distributed, with mean 0 and known variance (different ...
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### What is the best linear regression method when the errors in the variables x and y are unknown?

I have pairs of observations $(X_i,Y_i)$ with errors in both variables and I need to find the line that best fits the data. I have found some methods, but it is essential to know the standard ...
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### Hypothesis testing using samples with different measurement errors/intervals

Are there generalizations of common hypothesis tests (e.g. t-test, mann-whitney) that can take into account different confidences in the sample measurements? For example, if I have two sets of ...
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### When calculating the statistical power of a t-test, do I need to consider the uncertainty of the single values?

I have a question regarding calculating the power for a statistical test that includes data which are estimated by a model (means they have an uncertainty): I want to find out if two piles of stones ...
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### Linear Regression but the Variables have errors

I have received this confusing task: You have two variables 𝑥 and 𝑦, where y is a response variable which can be written as an explicit linear function of 𝑥. However, the technique used for ...
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### What does Deming regression estimate?

Least squares regression estimates conditional means. Least absolute regression estimates conditional medians. Quantile regressions estimate conditional quantiles (a special case of which is the ...
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### What is the name of this regression model?

I am wondering how I can map this problem to something known. Let us start with a standard linear regression framework, and suppose we want to reconstruct an observed signal $y$ from single known ...
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### How to test for correlated errors in regression

I understand that one assumption that must hold for regression is for there to be no correlation in the error structure. Put another way: The residuals should be impossible to predict above chance. ...
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### How to compare distributions with errors on the data points?

Here's a mock set-up of my problem: I have two non-normal probability density distributions (PDFs), $A$ and $B$. Distribution $A$ has error measurements for each data point while distribution $B$ ...
1 vote
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### MLE on Structural VAR

I have a simple model that I wish to fit using data. The model is of the form below. \begin{gather} y_t = -\lambda r_t + \theta a_t + \varepsilon_1 \\ \\ \pi_t = \pi_{t-1} + w y_t + \varepsilon_2 \\ \\...
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### Removing the bias from some unknown measurement error

Imagine I have two variables X and Y which have a statistical relationship. However I cannot observe X. I can only observe X* = X + U where U is some 0-centered random noise. I don't know U but I ...
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### Linear least-square fitting of two variables with uncertainty on both

I am trying to find an R function to calculate the linear least-square fitting of two variables when both have an error (expressed as standard deviation). I have found this problem referred to in half ...
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### Interview question (incomplete): extension of linear regression (errors in variable)

Here is a interview question I head from others, but I think the information may be not complete and correct. Could anyone help me to modify it? Question: Suppose $X\sim N(0,1), \epsilon\sim N(0,1)$ ...
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### If the $\varepsilon$ in $Y = \beta_0 + \beta_1 X + \varepsilon$ does not represent measurement error in $Y$, then what does it represent?

The classical simple linear regressoion model is $$Y = \beta_0 + \beta_1 X + \varepsilon. \tag{1}$$ On page 3 of these slides, the author says if there are measurement errors in the outcome then we ...
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### In reality, there is almost always measurement error in the independent variable(s), so why is this ignored in almost every linear regression model?

In the vast majority of cases, linear regression models are used in practice as opposed to the more complicated errors-in-variables models. For the sake of example, consider modelling height $Y$ vs ...
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### Regression problem with "error in variables"

Suppose that there is a deterministic relation $y_t=ax_t$ where $x_t,y_t$ are real sequences or real functions and $a$ a constant. But only $X_t=x_t+e_t$ and $Y_t+u_t$ can be observed, with $e_t, u_t$ ...
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### How to do Error in Variables regression with known standard errors

I need some help with EiV regression and comparison of two methods. I have used two different methods to estimate the size of the same population and would like to find out how good method 1 is ...
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### Inverse Regression vs Reverse Regression

I'm aware there's a great number of questions which deal with the mathematical difference between the two, but I'm still confused as to best practice. Basically I'm looking at a situation where we ...
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### Big outlier in dependent variable

I have my data from the official statistics office of my country and I rechecked multiple times already. I have a big outlier skewing all my glm (poisson) modells to the extreme (like 5 times the ...
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### What kind of statistical analysis is required to compare two methods for regression

I want to do comprehensive study of errors in variables and compare the results with regression for selected parameter estimation problems in my domain where it is expected to perform better in terms ...
Suppose I have data generated as follows: $\tilde{X} = k \cdot X + u$, where X is an unobserved latent variable (say the temperature of the room) and X_tilda is the observed variable (say temperature ...