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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13 views

How to handle nondifferentiable points of the objective function in the geometric circle fit?

We a given measured points in $(x_i,y_i) \in \mathbb{R}^2$, $i=1,..,n$. The geometric circle fit is the circle with center (a,b) and radius $r$ that minimizes the squared Euclidean distances between ...
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Errors only in variables model, and polynomial fitting

I have a bunch of data points $(x, y)$, and I know that they fit well to a model of the form $y = a + bx + c x^2$, with $a \approx 0.01, \ b \approx 1\ \textrm{and}\ c \lesssim 0.1$. I'd like to fit ...
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55 views

Use of ordinary least squares line in correlation analyses

I want to study and plot the correlation between two variables, X,Y. Both are measured, so they have comparable noise. Correlation (and not regression) is the correct analysis here. In a paper, I ...
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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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1answer
40 views

Linear regression with normally distributed data and model with arbitrary covariance

Consider the linear regression problem $$(A+\Delta A)x = b + \Delta b.$$ If $\Delta A = 0$ and $\Delta b$ is identically and independently distributed, then ordinary least-squares gives a good (BLUE) ...
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29 views

Which is more correct to calculate least squares (errors) during nonlinear curve fitting, calculating after transformation or in the original form?

I am studying curve fitting and linear regression. I am supposed to find a and b in the equation $$ P=ae^{bh} $$ so I transformed it to $$ lnP=ln a +bh $$ then $$ Y=c+bX $$ after that I solved it to ...
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Identifying an algorithm described as 'Tukey approach' for ignoring outliers?

MVTec's machine vision library Halcon has an operator fit_line_contour_xld for robustly fitting lines to 2D points. Here's the documentation entry for that operator:...
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508 views

Including model uncertainty in non-linear least squares minimization

The problem I have experimental data $Y$ with heteroscedastic and normally distributed uncertainties characterized by covariance matrix $C_{exp}$. I want to fit the data using model $F(X, \beta)$ ...
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Standardizing regression coefficients in the case of Total Least Squares Regression

So I know that there exits a method to standardize regression coefficients by simply multiplying them with the ratio of the standard deviations of the two variables. I'm wondering if this holds true ...
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61 views

Difference between estimating parameters for prediction and estimating parameters for their own sake

In a 1989 paper on orthogonal regression, Ammann and Van Ness write: An important caveat should be noted. The errors-variables-model is useful when the primary goal is to estimate the model ...
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186 views

Statistical library for orthogonal distance regression with a ridge penalty?

There are many libraries in R and python for doing orthogonal distance regression and for doing ridge regression separately. Is there one for doing them at the same time?
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559 views

Difference between “orthogonal distance regression” and “total least squares”

I'm trying to figure out the difference(s) between total least squares (TLS) and orthogonal distance regression (ODR). Both techniques are used when there is error in the dependent variable. Per this ...
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least absolute deviation version of deming [closed]

Based on what I know, deming minimizes the sum of square of perpendicular distance to the regression line. Is there a package in R that can run regression that minimize the sum of absolute value of ...
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515 views

Why my Deming Regression line change so much when switching variables? If they seem to be a linear relationship betwen them?

I am trying to fit a line that best predicts the production of energy Y given the speed of wind X, a typical Y = xm + b , using deming regression. I am looking for the slope and the intercept of that ...
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38 views

Correct way to fit a line in 3D (x-position vs y-position vs other quantity)

I have measured the position of light spots $(x,y)$ in an arbitrarily chosen basis and I compare that to some other measured quantity, say the brightness of each spot $B$. Now, in theory all the ...
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253 views

Deming regression prediction interval using jackknife resampling

I am trying to write a custom Deming function following the maths in Linnet (1993): https://www.ncbi.nlm.nih.gov/pubmed/2281234 Using jackknife resampling I calculate the standard error for the ...
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329 views

Standard error of coefficient estimates for model II regression

I'm working with time series data that has error in both the dependent and independent variables, so I'm analyzing each half hour of data with model II linear regression, specifically geometric mean ...
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86 views

Selecting appropriate likelihood during non-linear regression

When performing regression to fit a function, $f (x,{\bf \beta})$, to a set of observed data, $y_i(x_i)$, we are seeking to optimize the parameters, $\beta$, of the fitting function, to minimize some ...
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Can total least squares be used to account for uncertainty due to measurement timing?

Suppose we have a dataset in which we wish to perform regression analysis, and where the response/dependent variable is a measurement at time T. But due to pragmatic sampling we do not have ...
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54 views

Regression to estimate parameters

I would like some suggestions to tackle the following problem. Given a system $y = X\beta$ where $y \in \mathcal{R}^m$, $X \in \mathcal{R}^{m \times n}$, $m\geq n$, and $\beta \in \mathcal{R}^n$, ...
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199 views

Orthogonal polynomials + cross validation: should subsetting be done prior or after constructing the orthogonal polynomials?

So, just to start... I've just learned of orthogonal polynomial regression today. I've gone through the master's-level linear models courses, and we did not cover that topic. I was always under the ...
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847 views

Why does the total least squares line in 2D pass through the average across all data points?

I have $N$ data points $\mathbf{m_k}$ and I want to fit a line through them with minimal error $$J = \sum_k^N ||\mathbf{m_k^*} - \mathbf{m_k}||^2 = \sum_k^N ||\mathbf{m_0} + a_k\mathbf{e} - \mathbf{...
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Advantage of orthogonal polynomials

What is the sense or background of orthogonal polynomials (regarding using mixed models)? I would like to know why they shall or should be orthogonal. Is it to build independent sample points? On Is ...
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523 views

Least Squares Derivation

I come from physics and would like to derive the chi-square function given by the Particle Data Group: \begin{equation} \chi^2 (\boldsymbol\theta) = (\boldsymbol y-\boldsymbol\mu(\boldsymbol \...
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Deming regression implementation: force intercept to 0

I implemented Deming Regression in a known programming language, using the algorithm from here: https://en.wikipedia.org/wiki/Deming_regression However, the algo does not specify what to do in case we ...
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What's the shape of confidence interval for linear regression estimated through TLS (total least squares)?

So, we know the shape of confidence intervals for vanilla linear regression estimated through OLS (ordinary least squares): Shape of confidence interval for predicted values in linear regression. In ...
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When to use Deming regression

I am currently working on a way to transform two different phosphorus test values into each other. Background There exist many (extraction) methods to measure plant available phosphorus in soil. ...
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Generating Random Data Sets for Linear Regression with Random Slope and Error Term in R

I want to test the effects of sample size on Deming regression using simulated paired data in R. As the data are paired, the expected slope value should be 1 and the intercept 0. The code I have ...
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Specifying the Error Ratio in Deming Regression

We use Deming Regression for method validation in our clinical ELISA laboratory. As we run clinical trials this needs to be performed if we get a new reagent batch, batch of plates, new plate reader ...
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488 views

How to compare two Deming regressions?

I have two small data sets. For each data set, I performed a Deming regression. Hence, I have, for each data set, the relationship between X and Y in the form of slope+intercept coefficients. Now, I ...
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small sample approach to simple linear regression with errors-in-variables (measurement errors)

I seek to estimate $b_1$ and $b_0$ from data of the form: $$y_i = b_1x_i + b_0 + e_i, \quad i\in\{0,1,...,N-1\}$$ given $\{y_i\}$ and $\{\tilde{x}_i\}$ where $\tilde{x}_i=x_i + n_i$ (i.e., error-in-...
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Regression of dataset with many x values per y value

I am performing a total least squares regression in which I have many x observations for a given y observation. The x observations are normally distributed. I am aware I could do some sort of ...
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391 views

why regress a y variable on a vector of just ones

I am trying to understand some code somebody has written. I have a y vector which is a factor say book to price for 500 companies. Then I also have a x vector of the same shape which is just ones. ...
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375 views

Find best fit diagonal matrix for error minimization

I want a set of input values to be as similar to the output values as possible. I have an input matrix X (m*n) that has m data points and n dimensions for each data point. I also have an output matrix ...
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553 views

What weights for weighted Total Least Square (TLS) regression?

I have a dataset with known errors in both the X and Y and want to perform a simple linear regression. From reading other posts, it seems I want to TLS over OLS due to the presence of error in both ...
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Multiple errors-in-variables regression with collinearities

I have a $[k \times N]$ matrix of predictors / independent variables and a $[k \times N]$ matrix of predictands / dependent variables. I have uncertainty estimates for each predictor and each ...
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$X$ and $Y$ at different scales in total least squares?

As this section of the Wiki article says, the best (in total least squares sense) matrix $B$ that projects $X$ to $Y$ is given by $$B=-V_{XY}V_{YY}^{-1},$$ where $V_{XY}$ and $V_{YY}$ come from the ...
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123 views

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 ...
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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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Regression when each point has its own uncertainty in both $x$ and $y$

I made $n$ measurements of two variables $x$ and $y$. They both have known uncertainties $\sigma_x$ and $\sigma_y$ associated with them. I want to find the relation between $x$ and $y$. How can I do ...
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Introductory references about total least squares

I am an engineering student and I've been recently told about the Total Least Square (TLS) method. I am interested in applying it to topographic measurements and in comparing the results with the ...
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988 views

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 ...
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110 views

Total least squares minimization

I've seen some lecture notes about the Total Least Squares, which state the following: Suppose we have a linear system $Y=XB$, which may be inconsistent. Now change this system to $$(Y+\Delta)=(...
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How to calculate confidence/prediction bands for Deming regression

Revised question: My fundamental question seems to be: "I have data with error both in y and x. How do I estimate a value of true x so that y evaluated at that x will be distinguished from y(0) say, ...
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403 views

Is it possible to make a regression with known standard error on y

I want to compare estimate with standard error in function of a continuous variable and a categorial variable . Here an example of what my data look like. ...
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Is it possible to calculate R-squared on a total least squares regression?

I am using the Deming function provided by Terry T. on this archived r-help thread. I am comparing two methods, so I have data that look like this: ...