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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15 views

Errors-in-variables with correlated latent variable

Suppose I have data generated as follows: $\tilde{X} = k \cdot X + u$, where X is an unobserved latent variable (say the temperature of the room) and X_tilda is the observed variable (say temperature ...
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47 views

meaning of error term being correlated with regressor [duplicate]

I have encountered the statement that "the error term and one of the regressors are correlated" a few times and I am having trouble understanding what is meant exactly. Let's say we have a DGP $$y=\...
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103 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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Mismatched sampling rates between predictors & response plus measurement errors on categories

Background I'm unsure how to best model data from a widget manufacturing process with measurement "uncertainties" on categorical variables (relative to an ordered indexing variable) and an overall ...
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1answer
49 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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Estimating coefficients of a linear model with collinear dependent variables that have errors with known variances

I want to estimate the coefficients $\beta$ of the linear model $Y=\beta X$ from observations of $(Y_i,X_i), i=1\ldots n$, where $X$ is multidimensional. Two problems: All variables have been ...
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1answer
60 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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15 views

Least squares regression when all variables have errors with known variances

I have a large number (n>1000) of independent measurements $x_i,y_i,z_i,\; i=1\ldots n$. Each of these measurements has an error with a known variance $\sigma^2_{x_i}, \sigma^2_{y_i}, \sigma^2_{z_i}$...
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Is the maximum likelihood estimator unbiased for the error-in-variables model?

The following linear model for one scalar parameter $\theta$ is under consideration: $$ \begin{cases}\pmb{\hat{x}} \theta = \pmb{\hat{y}} + \pmb{\epsilon}_y \ , \\ \pmb{x} = \pmb{\hat{x}} + \pmb{\...
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38 views

Correct error estimation for linear fit

This may be a simple problem, but I want to be thorough in setting up my problem as I'd like to know why I should proceed in one of two ways (or another if someone thinks it is suitable), so please ...
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11 views

Exponential errors in variables model with known uncertainties

I have $N$ data points that I am trying to fit using a function of the form $y_i = \prod_j {X_{i,j}}^{b_j}, \quad j=1..N$ where $\mathbf X$ and $\mathbf y$ are measured values. The form of this ...
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668 views

Non-negative least squares with errors-in-variables, no repeated measurements

In an experiment, I measured an enzymatic activity $y$ of many solutions containing mixes of different bacterial species. In each of these solutions, I also measured the number of individual cells of ...
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109 views

Prediction intervals with experimental errors

Engineer here, so apologies for my simplistic stats language. I am missing some experimental data that I would like to "fill in" based on a linear regression to other data. I need to do this because ...
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17 views

How would you attempt to distinguish measurement error from a true distribution but no “true” singular value?

I am self-taught amateur in statistics and I have confusion is based calculations with error-in variables with the added object being measured having a no "true" value but a "true" range. For me, ...
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1answer
242 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 (...
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2answers
200 views

Find error interval of linear relationship

I have two sensors of different quality capturing the same process, where one of them is much more accurate than the other. Hence, I want to find out how much better. Let us for example say that the ...
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32 views

Fitting a logarithmic growth curve with error (an interval) of the explanatory variable?

I have a series of human growth data that I wish to fit to a 3 parameter logarithmic growth curve: s(i) = Beta0 + B1*T + B2*ln(t), where s is a length and t is an age. The only problem is that this ...
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68 views

Rotation changes correlation - correction from OLS

Let $X,Y$ be real random variables with finite variances, and with no loss of generality assume $\mathbf{E}[X] = \mathbf{E}[Y]=0$. For simplicity, I will focus on the case $\mathrm{Var}X \neq \mathrm{...
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1answer
2k views

Control Function Approach and Bootstrap

Let's start assuming that I have cross-sectional data on $y$, $x_1$, $x_2$ (see below for $y$, $x_1$, $x_2$). I want to estimate the effect of variables $x_1$ and $x_2$ and their interaction ($x_3= ...
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383 views

What to do when expectation maximization results are invalid (they don't match the likert scale)

I have missing values (MCAR) for which I used EM to fill in those values. Some of the imputed values are negative integers or zero. I am using a likert scale to measure responses, and thus i need the ...
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75 views

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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1answer
30 views

correlation when x and y are uncertain

Suppose that for $1\le i \le N$ $$\begin{align} Y_i^j &= f(X_i) + \epsilon_y \qquad &1 \le j \le R_y^i \\ Z_i^j &= af(X_i)+b + \epsilon_z \qquad &1 \le j \le R_z^i \end{align}$$ where $...
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1answer
876 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 ...
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20 views

Dealing with independent variables where each point is an coefficient

I want to test if a behavior is influenced by population size. The former is measured as a continuous normal variable. The latter is estimated using Schnabel's method, and thus each sample has a ...
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1answer
100 views

OLS Assumptions - Errors are normally distributed

I am currently working on a research project based on the data of a big survey. I derived a variable set, which I would like to investigate. Before starting with it, I would like to check the ...
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60 views

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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65 views

Intuition: Why do I have to worry about errors-in-variables?

I've read that (ordinary) linear regression assumes that there are measurement errors in the dependent variable, but no measurement error in the independent variables -- and if I have measurement ...
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136 views

Standard error of mean - under measurement error

I have two observations of a normally distributed random variable: $$ X_1 = 0.02 \\ X_2 = 0.10 $$ Obviously the sample mean equals 0.06, and the standard error of the mean (SEM) is equal to 0.04. ...
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1answer
999 views

Bayesian errors-in-variables model definition in JAGS and symbolically

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 ...
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717 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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1answer
159 views

Fit error-in-variables polynomial regression using mle2 (R)

I need to fit a polynomial regression that accounts for measurement errors. I found out how to do it with a mcmc model (using RJags) and I would like to do it with a Maximum Likelihood Estimator (...
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1answer
901 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 ...
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188 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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35 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 = x-Z'^{inc}\...
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1k 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)...
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139 views

Total least square intuition

I have yet to find a good intuitive explanation of TLS. Online resources tend to focus on the vertical vs. perpendicular square error pictures (I don't need to see perpendicular lines to understand ...
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0answers
550 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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1answer
861 views

Biased estimator for regression achieving better results than unbiased one in Error In Variables Model

I am working on some syntatic data for Error In Variable model for some research. Currently I have a single independent variable, and I am assuming I know the variance for the true value of the ...
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222 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} X_{i,j}&=\mu_{X,i}+\...
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163 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 $(X_1,Y_1), ..., (X_n,Y_n)$. ...
4
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416 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 ...
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1answer
764 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 ...
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0answers
60 views

Linear regression with estimates of error in predictor

I have data with two different kinds of measurements at the same set of $S$ sites. One of these (call it $X$) returns m estimates at each site, which are not necessarily independent of one another. So ...
2
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1answer
724 views

How to estimate mean and standard deviation of a normal distribution from noisy data?

I have $n$ observations, $x_i$ following a normal distribution. I would like to estimate $\mu$ and $\sigma$ from my samples. Normally I would simply estimate $\mu=(\sum x_i)/n$ and $\sigma^2=\sum (...
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1answer
102 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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25 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
795 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}(...
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1answer
1k 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
353 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 ...
3
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1answer
492 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 ...