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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29 views

Linear least-square fitting of two variables with uncertainty on both

I am trying to find an R function to calculate the linear least-square fitting of two variables when both have an error (expressed as standard deviation). I have found this problem referred to in half ...
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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 ...
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1answer
92 views

Big outlier in dependent variable

I have my data from the official statistics office of my country and I rechecked multiple times already. I have a big outlier skewing all my glm (poisson) modells to the extreme (like 5 times the ...
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22 views

Interview question (incomplete): extension of linear regression (errors in variable)

Here is a interview question I head from others, but I think the information may be not complete and correct. Could anyone help me to modify it? Question: Suppose $X\sim N(0,1), \epsilon\sim N(0,1)$ ...
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1answer
134 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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How do I use American Community Survey income estimates and standard errors in an error-in-variables model?

Income distributions tend to be highly skewed. Yet the American Community Survey (ACS) provides only two summary statistics for its median income estimates in small areas: the mean estimate and a ...
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1answer
240 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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2answers
106 views

If the $\varepsilon$ in $Y = \beta_0 + \beta_1 X + \varepsilon$ does not represent measurement error in $Y$, then what does it represent?

The classical simple linear regressoion model is $$ Y = \beta_0 + \beta_1 X + \varepsilon. \tag{1} $$ On page 3 of these slides, the author says if there are measurement errors in the outcome then we ...
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In reality, there is almost always measurement error in the independent variable(s), so why is this ignored in almost every linear regression model?

In the vast majority of cases, linear regression models are used in practice as opposed to the more complicated errors-in-variables models. For the sake of example, consider modelling height $Y$ vs ...
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33 views

Regression problem with “error in variables”

Suppose that there is a deterministic relation $y_t=ax_t$ where $x_t,y_t$ are real sequences or real functions and $a$ a constant. But only $X_t=x_t+e_t$ and $Y_t+u_t$ can be observed, with $e_t, u_t$ ...
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47 views

How to do Error in Variables regression with known standard errors

I need some help with EiV regression and comparison of two methods. I have used two different methods to estimate the size of the same population and would like to find out how good method 1 is ...
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Interpolating between poorly-defined stratification levels - modeling with very large errors-in-variables

I'm trying to estimate the mean response error associated with a measurement device (Device A) for concentration of a chemical in solution. The measurement device uses a disposable component whose ...
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81 views

What kind of statistical analysis is required to compare two methods for regression

I want to do comprehensive study of errors in variables and compare the results with regression for selected parameter estimation problems in my domain where it is expected to perform better in terms ...
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2answers
409 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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1answer
163 views

meaning of error term being correlated with regressor

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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17 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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1answer
58 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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46 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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14 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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85 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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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 ...
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1answer
783 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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61 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 ...
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158 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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128 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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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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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)...
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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 (...
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2answers
249 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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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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35 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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142 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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112 views

Confusion related to calculation of likelihood

I was reading this paper related to Learning from multiple annotator using Gaussian processes. The idea is if we don't have the actual ground truth of a certain data, but only the labels from some ...
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258 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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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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431 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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81 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
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 ...
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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
121 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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73 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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79 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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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}(...
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1answer
1k 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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1answer
899 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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960 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
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 ...
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199 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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0answers
36 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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592 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). ...