# 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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### 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 ...
29 views

### Method comparison: removing double-zeros before orthogonal regression, deming or passing-bablock?

I am comparing two pieces of equipment / methods which are supposed to measure the same information over time. I looked into the literature and decided Passing-Bablock seemed like the right approach (...
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### Model selection when dealing with orthogonal columns

Let $L$ be a subset of indices referring to orthogonal columns $X_i$. Let $RSS_L:=\lVert y-H_L y\rVert^2$. I have shown that the relative projection matrix $H_L$ is given by $H_L=\sum_{i \in L} H_i$. ...
49 views

### How to estimate the covariance matrix of total least squares parameters

The slope(s) and intercept(s) of a total least squares regression can be obtained by principal component analysis, as explained in this old post. How does one obtain the covariance matrix of the fit ...
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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 ...
117 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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### Usiing Deming regression within structural equation modeling?

Is it valid to use Deming regression within structural equation modeling? If so, how would I go about doing that?
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### Is quantile regression a better option than total least squares RMA in this case

I have paired cobalt concentrations in bird blood and feathers. Blood levels give me an idea of how recent the cobalt exposure was (<30days), feather give the 6 month accumulated total. Previous ...
589 views

### Confidence/prediction intervals for total least squares regression

I am learning the ropes of total least squares regression and I found this thread How to perform orthogonal regression (total least squares) via PCA? where the answer by @amoeba, together with some R ...
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