# Questions tagged [total-least-squares]

A technique to estimate parameters $\beta$ of the linear model $Y=X\beta$ when both $Y$ and $X$ are subject to measurement error. Includes Orthogonal and Deming regression as special cases.

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### Variance Component Estimation of Weighted Total Least Squares

Note: I'd like to make the cited document accessible to everyone but I am unsure how to do this. I am a bit confused by this 2014 article "Variance components in errors-in-variables models: ...
1 vote
48 views

### Derivative of Linear Model with respect to Residual

I am looking at two sections on the wikipedia page for total least squares, specifically: #Allowing_observation_errors_in_all_variables and #Example I have two questions, the first is how does one ...
1 vote
18 views

### How to estimate a feasible Generalized Error-in-Variable Model (combine deming regression/TLS and f-generalized least squares)

I have observational data with spatial structure. A hypothetical dataset could be brain mass for 100 species of birds and body mass for those same species. The data has spatial structure because ...
47 views

### 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 ...
1 vote
7 views

### Has the generalized Deming model been developed?

I am familiar with Deming regression and wonder if anyone has generalized it to other error families and links beyond Gaussian and identity.
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1 vote
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### Comparing Deming/Orthogonal Regression to Null Hypothesis

I have some data of with the relationship Y=commonFactor+error1 and X=Alpha+Beta*commonFactor+error2 I want to test the hypothesis that Beta is non-zero, or that there is a significant relationship ...
11 views

### X and Y are correlated, errors in both X and Y but error variances unknown; How to predict X|Y or Y|X? Deming, bivariate gaussian ellipses, other?

Seeking relationships between two variable, both with random gaussian errors; ratio of error variances is unknown, no correlation of errors in X and Y, but another unknown variable Z (unmeasured) may ...
167 views

### Applications of total least squares and related pitfalls (in biology/ecology)

I recently discovered TLS for a bio-statistical (ecological) problem I am working on. However, I was not able to find a lot of (ecological) literature that uses TLS in their analysis. From other ...
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1 vote
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### Mixed-level Deming regression?

Is there an implementation of Deming regression that also handles random intercepts and slopes in the sample? We have a situation where we have compelling theoretical reason to believe that one ...
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140 views

### 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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130 views

### 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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