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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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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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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90 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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Adjusting regression for correlated errors-in-variables

I have a set of data points $\{x_i\}$. These data points are grouped so that (say) $i\in\{1,2,3\}$ is group $A$, $i\in\{4,5,6,7\}$ is group $B$, etc. I would like to test the null hypothesis of no ...
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126 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 ...
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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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311 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 ...
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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 ...
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464 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 ...
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264 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 ...
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217 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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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 ...
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203 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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340 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 ...