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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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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29 views

Errors-in-variables model with multiple measurements

Suppose I have a simple linear regression $$Y = \beta_0+\beta_1X+\varepsilon_X $$ $$Z_1 = X + \delta_1$$ $$Z_2 = X+\delta_2$$ where vectors $Y,Z_1$ and $Z_2$ are observed and $\delta_1,\delta_2$ are ...
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43 views

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 ...
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19 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 = ...
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27 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 ...
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134 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). ...
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86 views

Making Predictions in an Error in Variables Model

Say I have estimated some parameters $\hat{\beta}$ between input $x$ and output $y$, according to a generalised linear model $y=x^T \beta$, by using the Least Squares method. I can then easily make ...
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22 views

Interaction model with measurement error without replicate measurements

I am currently working on a simple OLS model with two independent variables and one dependent variable: \begin{equation} \ Y_i = \beta_0 + \beta_1 X_i + \beta_2 S_i + \beta_3 X_iZ_i \end{equation} ...
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65 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} ...
2
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52 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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42 views

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 ...
3
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1answer
55 views

Selecting variables using SAS and R - all effects are significant even when shuffling the data

Dear all: I need to test which effects I should include in my model for genetic evaluation of cows. I was using the following code in R: ...
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24 views

Using aggregated data from a database with data from another

Let's say I have two databases, in the first (DB1) there is individual data on how much people trust in the government ($X_{j,r}$), and on the second (DB2) there is individual data on how much people ...
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1answer
207 views

Probability limit calculation

My class notes list the following steps for calculating a plim under classic errors in variables: $$ {\rm plim}\ \beta_1 = \frac{{\rm cov}(\beta_0 + \beta_1 x_1 + \epsilon - \beta_1 e, x_1)}{{\rm ...
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1answer
314 views

Probability limit formula for coefficient in errors in variables regression

I found an online resource which lists the plim formula for a simple regression under the classic errors-in-variables assumption as: $$ \text{plim }\beta_1=\frac{{\rm Cov}(y, x_1)}{{\rm Var}(x_1)} $$ ...
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1answer
222 views

Comparing power law fits with large uncertainties

I want to test how well my data fit the particular power law: $y=ax^b$ where $b$ , for physical reasons, should equal exactly $-0.5$. I would like to find the probability that the data do not obey ...
5
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1answer
180 views

When should I use errors-in-variables?

I have been reading about errors-in-variables (also called regression dilution and attenuation) but I've found it hard to decide whether it is appropriate for my setting. I want to calculate ...
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1answer
474 views

Uncertainty from linear fit on additional data

Let's say I have 5 known data points with coordinates $X$ : Area under curve $Y$ : Activity The 5 points have individual error ($\Delta X_{i}$,$\Delta Y_{i}$) on both $X$ and $Y$ and I know that ...
5
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1answer
91 views

Is the following an error-in-variance problem, and is there a recommended R (or SAS) package for it?

I have data from several different measurements of physical performance, each done on the same individual, and I'm looking for ones that correlate with each other. A typical question might be, "does ...
12
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1answer
747 views

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 ...
13
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2answers
296 views

What can you do when you have predictor variables that are based on group averages with different sample sizes?

Consider a classical data analysis problem where you have an outcome $Y_{i}$ and how it is related to a number of predictors $X_{i1}, ..., X_{ip}$. The basic type of application in mind here is that ...
5
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1answer
332 views

Linear regression with shot noise

I'm looking for the right statistical terminology to describe the following problem. I want to characterize an electronics device that has a linear response $Y = \beta_0 + \beta_1 X + \epsilon$ ...
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2answers
311 views

Formula for single linear regression for dataset that has uncertainties on both x and y

I'm going to teach classes on Physics Laboratory on First year of Bachelor studies. In most of the excercises during data analysis students will have to fit a line to measurements they have taken. I ...
4
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2answers
359 views

Building linear model from exact variable measurements for use with noisy variable measurements

I want to build a linear model to predict a scalar output from a vector of noisy scalar variable measurements. I have two separate training data sets. One has output data and corresponding exact ...
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1answer
467 views

Methods for fitting a “simple” measurement error model

I am looking for methods which can be used to estimate the "OLS" measurement error model. $$y_{i}=Y_{i}+e_{y,i}$$ $$x_{i}=X_{i}+e_{x,i}$$ $$Y_{i}=\alpha + \beta X_{i}$$ Where the errors are ...