# 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 this regression model valid X/Z = B0 + B1*X + B2*Z? [closed]

In other terms can I explain a variable with the others variables that are used to compute this variables? What are the implication for my model?
1answer
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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 ...
0answers
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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 $X\sim N(0,1), \epsilon\sim N(0,1)$ ...
2answers
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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 $e_t, u_t$ ...
0answers
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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 ...
0answers
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### Interpolating between poorly-defined stratification levels - modeling with very large errors-in-variables

I'm trying to estimate the mean response error associated with a measurement device (Device A) for concentration of a chemical in solution. The measurement device uses a disposable component whose ...
2answers
312 views

### 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 ...
1answer
143 views

### 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 ...
0answers
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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 ...
0answers
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### Errors-in-variables with correlated latent variable

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 ...
1answer
228 views

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### Model selection: OLS vs TLS

I have two sets of real-valued data and I am interested in their correlation. From my perspective, there appear to be errors both variables, so I am inclined to perform a regression with TLS (Total ...
1answer
245 views

### Fit error-in-variables polynomial regression using mle2 (R)

I need to fit a polynomial regression that accounts for measurement errors. I found out how to do it with a mcmc model (using RJags) and I would like to do it with a Maximum Likelihood Estimator (...
1answer
1k views

### Total least squares with weights [duplicate]

I am looking for a way to perform weighted total least squares in R. I know one can use PCA for this as described nicely in the following post. How to perform orthogonal regression (total least ...
0answers
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### linear regression accounting for standard errors of variables

I am trying to figure out what is the best way to estimate beta why accounting for the uncertainty in x and y. For example, I have ...
0answers
36 views

### Signing the inconsistency of a control functions estimator with an incomplete set of instruments

I've got a model of the form $$y = 1\left(\alpha+\delta x+\beta_1\tilde v+\tilde\epsilon>0\right)$$ $x$ is endogenous, and $\tilde v$ is a control function residual:  \tilde v = x-Z'^{inc}\...
4answers
2k views

### Systematic/measurement error on a linear regression

Suppose I have a set of data ${(x_i,y_i)}$ in which the uncertainty in the measurements ${(\Delta x_i,\Delta y_i)}$ (which come from the propagation of systematic errors from the measurement apparatus)...
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### Total least square intuition

I have yet to find a good intuitive explanation of TLS. Online resources tend to focus on the vertical vs. perpendicular square error pictures (I don't need to see perpendicular lines to understand ...
0answers
612 views

### Errors-in-variables multivariate polynomial regression (R)

(EDIT: the question has been modified just a little bit to be more specific) I want to fit a multivariate polynomial regression that accounts for measurement errors (an Error-in-Variables model). ...
1answer
902 views

### Biased estimator for regression achieving better results than unbiased one in Error In Variables Model

I am working on some syntatic data for Error In Variable model for some research. Currently I have a single independent variable, and I am assuming I know the variance for the true value of the ...
0answers
272 views

### Deming Regression/Errors-in-Variables with replicates

I have a question about a model related to Deming regression and would appreciate some help and/or publications to further study this model. Statistical Model: \begin{align} X_{i,j}&=\mu_{X,i}+\...
0answers
204 views

### Estimating variances in orthogonal regression

In orthogonal regression it is assumed that both variables have noise. I'm interested in the simplest possible case. That is, I have a very large number of data points $(X_1,Y_1), ..., (X_n,Y_n)$. ...
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### Errors-in-Variables model for logistic regression

Simple question: I am familiar (though don't have tons of experience) with errors-in-variables regression. From what I have seen, this mostly is used with continuous outcomes in a linear model. A) Is ...
1answer
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### Intuitive meaning of error-in-variables

I understand the explanation of the example of error-in-variables used wikipedia. What I do not understand is how could we explain intuitively the error-in-variables problem? One way would be to say ...
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### Linear regression with estimates of error in predictor

I have data with two different kinds of measurements at the same set of $S$ sites. One of these (call it $X$) returns m estimates at each site, which are not necessarily independent of one another. So ...