Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [deming-regression]

22 questions
31
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3 answers

How to perform orthogonal regression (total least squares) via PCA?

I always use lm() in R to perform linear regression of $y$ on $x$. That function returns a coefficient $\beta$ such that $$y = \beta x.$$ Today I learned about total least squares and that princomp() function (principal component analysis, PCA) can…
Dail
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1 answer

Errors-in-variables regression: is it valid to pool data from three sites?

I recently had a client come to me to do a bootstrap analysis because an FDA reviewer said that their errors-in-variables regression was invalid because when pooling data from sites the analysis include pooling data from three sites where two sites…
Michael R. Chernick
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15
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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 it? EDIT: each $x_i$ has a different…
rhombidodecahedron
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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: y x stdy stdx 1 1.2 0.23 0.67 2 1.8 0.05 0.89 4 7.5 1.13 0.44 ... ... ... …
Nico Coallier
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1 answer

Tolerance interval for Deming regression

I am trying to derive (one-sided) tolerance intervals related to the Deming regression model: $$ x_i=x^*_i + \epsilon_i$$ $$ y_i = (\alpha+\beta x^*_i) + \epsilon'_i$$ where the $x^*_i$'s are nonrandom fixed numbers, $\epsilon_i \sim {\cal…
Stéphane Laurent
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1 answer

Nonlinear total least squares / Deming regression in R

I've been using nls() to fit a custom model to my data, but I don't like how the model is fitting and I would like to use an approach that minimizes residuals in both x and y axes. I've done a lot of searching, and have found solutions for fitting…
Thomas
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1 answer

What is the prediction error while using deming regression (weighted total least squares)

Deming Regression is a regression technique taking into account uncertainty in both the explanatory and dependent variable. Although I have found some interesting references on the calculation of this property in matlab and in R I'm stuck when I try…
johanvdw
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5
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Bayesian estimates for Deming regression coinciding with least-squares estimates

Consider the following Deming model with independent replicates : $$x_{i,j} \mid \theta_{i} \sim {\cal N}(\theta_{i}, \gamma_X^2), \quad y_{i,j} \mid \theta_{i} \sim {\cal N}(\alpha+\beta\theta_{i}, \gamma_Y^2), \\ i \in 1:I, \quad j \in 1:J,$$ all…
Stéphane Laurent
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4
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1 answer

Estimated critical value for hypothesis testing

For the classical simple linear regression model I have derived an hypothesis test for $H_0\colon \left\{\frac{y^*(x^*)-x^*}{\sigma}>1 \right\}$ where $x^*$ is a given value of the covariate $x$ and $y^*(x^*)=a + b x^*$ is the theoretical mean of…
Stéphane Laurent
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What are good references for Deming's regression?

Do you know some good references (papers or books) for the theoretical inference in Deming's regression model ? EDIT: I was a little disconcerted about a point in Ripley and Thompson's paper Regression techniques for the detection of analytical…
Stéphane Laurent
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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-variables or measurement error). In my problem,…
rhz
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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 predictand. I use orthogonal distance regression (ODR,…
gerrit
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Total least squares with weights

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 squares) via PCA? However, I need a weighted version…
user19758
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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 $(X_1,Y_1), ..., (X_n,Y_n)$. I know that $Y = a X + b$ and that my $X_i$ and…
John
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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 want to know if the relationship between X and Y…
user137473
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