# Questions tagged [errors-in-variables]

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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I'm fairly new to probability theory and am attempting to understand and implement an errors-in-variables simple linear regression model. I am assuming a model of the form $$Y=\theta X_a+\epsilon_Y ... 1answer 1k views ### Errors-in-variables regression: is it valid to pool data from three sites? I recently had a client come to me to do a bootstrap analysis because an FDA reviewer said that their errors-in-variables regression was invalid because when pooling data from sites the analysis ... 1answer 787 views ### Methods for fitting a “simple” measurement error model I am looking for methods which can be used to estimate the "OLS" measurement error model.$$y_{i}=Y_{i}+e_{y,i}x_{i}=X_{i}+e_{x,i}Y_{i}=\alpha + \beta X_{i}$$Where the errors are ... 4answers 2k 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 apparatus)... 1answer 1k views ### How do errors in variables affect the R2? I've got a question about errors in variables. So, if I run a standard linear regression to estimate b in y = a + bx, but my ... 1answer 1k views ### Total least squares with weights [duplicate] 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 ... 1answer 908 views ### Intuitive meaning of error-in-variables I understand the explanation of the example of error-in-variables used wikipedia. What I do not understand is how could we explain intuitively the error-in-variables problem? One way would be to say ... 0answers 549 views ### Statistical Tests with Data Having Measurement Errors For example, can the results of the t test on y1 and y2 be interpreted in the usual way (i.e., like the results of the t test on x1 and x2)? If not, how should I go about testing whether or not y1 and ... 1answer 254 views ### If in this problem I regress x on y instead than y on x, do I need to use an error-in-variables model? I was trying to write an answer for this question: Selection of data range changes coefficients too much in lmer (inverse regression) Basically the OP has lots of data of Amplification vs Voltage (... 0answers 504 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 ... 2answers 212 views ### Inverse Regression vs Reverse Regression I'm aware there's a great number of questions which deal with the mathematical difference between the two, but I'm still confused as to best practice. Basically I'm looking at a situation where we ... 1answer 747 views ### How to do regression with error in variables and known correlations among the errors? After the very satisfying answer to: How to do regression with known correlations among the errors? I take the question to my next point of interest: What can you do when you have a regression with ... 1answer 949 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 var}(...
I found an online resource which lists the plim formula for a simple regression under the classic errors-in-variables assumption as: $$\text{plim }\beta_1=\frac{{\rm Cov}(y, x_1)}{{\rm Var}(x_1)}$$ ...