# Questions tagged [inverse-prediction]

Predicting an explanatory variable from an observation of the dependent variable, also called inverse regression or calibration.

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### How can I make predictions for new samples in the same subject, conditional on one observation?

I have fitted a Bayesian multilevel model. Example: $$Y \sim Normal(\mu, \sigma)\\ \mu = \alpha + \beta * time + z_{subject}\\ z_{subject} \sim Normal(\bar{z}, \sigma_z)$$ I have fitted this to some ...
13 views

### Statistical Inference on Covariates (Instead of the Response Variable)

In statistical modelling, it seems as though we are always more interested in predicting the expected value of the response variable conditional on some observed vector of covariates. However, are ...
22 views

### How to deal with treatment variable when using inverse probability weighting (IPW)?

I have a dataset which contains around 10,000 observations. I want to estimate the treatment effect (suppose the treatment variable is T, which is a dummy and outcome variable is Y, and X represents ...
193 views

### Inverse Predictive Posterior

Suppose I have a parametric nonlinear model, say $$y_i |\theta \sim N(f_{\theta}(x_i), \sigma^2)$$ with known form of $f_\theta$. We get data $d=(y_i,x_i)_{i=1,\ldots,n}$ and obtain posterior ...
9 views

### Is it inappropriate to predict an independent variable using a linear model? [duplicate]

In an A-Level maths textbook that I am reading about least-squares regression, it states that a regression line should only be used to predict the dependent variable and not the independent variable. ...
130 views

### R's lm(), get x when y is known [duplicate]

Here is some data and a logarithmic model: df <- data.frame( x = 1:8, y = c(7.5,6,5.2,4.3,3.9,3.4,3.1,2.9) ) model <- lm(y ~ log(x), data = df) I am ...
123 views

### Should I use the prediction interval or inverse prediction interval to calculate the uncertainty of $x$ when using reverse regression?

I'm calibrating a piece of lab instrumentation. I create solutions of known concentration ($x$) and measure my instrument response ($y$). On unknown samples, I measure the response and use the ...
44 views

### Model fit after inverse regression and forward stagewise on residuals

I work with prediction of height based on genetic information. The data is several hundred thousand data points from every organism, but a simplified version could be: ...
39 views

### Which is the error of a value corresponding to the maximum of a function?

This is my problem: I use data observed with MUSE (which is an astronomical instrument provides cubes, i.e. an image for each wavelength with a certain range, link ) to extract a measure of redshift. ...
948 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 ...
127 views

### Neural Network Inversion and its consequences

I am currently looking at Federated Learning. Here is a good example from google. The idea is that training happens on multiple devices. This means on one hand that training data never leaves a user (...
249 views

### Regression and calibration/inverse regression - the same?

In principle, I've a simple task: There are some physical quantities (temperature, pressure and molecule number) measured by a sensor and I want to use them to regress the concenctration of a gas. I ...
327 views

### inverse.predict chemcal package

I have noticed that the inverse.predict function (chemCal package) does not take into account all the degrees of freedom of the ...
13k views

### If X can predict Y in regression, why isn't Y guaranteed to predict X?

Intuitively, if X can predict Y in a multiple linear regression model, $y$ = $\beta_0$ + $\beta_1$$X + \beta_2$$Z$ + $e$ X and Y are associated. Since there's an association between them, why is ...
139 views

### Regression vs Calibration [duplicate]

When reading on the wikipedia page of Calibration they said : " A reverse process to regression, where instead of a future dependent variable being predicted from known explanatory variables, a ...
454 views

### Is a confidence interval symmetric when constructed on an inverse prediction of a logistic regression?

I have a dataset with a continuous variable paired with a binomial response. We want a one-sided confidence bound to determine at what value of the continuous variable would we get a desired ...
4k views

### How to calculate the confidence interval of the x-intercept in a linear regression?

Since standard error of a linear regression is usually given for the response variable, I'm wondering how to obtain confidence intervals in the other direction - e.g. for an x-intercept. I'm able to ...
21k views

### Error bars, linear regression and "standard deviation" for point

I have a set of experimental data points. I performed the measurements in triplicate, for each of the point of the data set. Therefore, I can draw each data point with the standard deviation of each ...
1 vote
1k views

### Inverse prediction of SVM because AUC is lower than 0.5

I am training SVM by a dataset with 8 features using 10-fold CV. The AUC for testing data is under 0.5. I remember that somewhere it had been written that in cases with ...
821 views

### Confidence interval for vertex of quadratic model, transforming parameters estimated by MLE

If I have a model $y=ax^2+bx+c+\epsilon$, and I use maximum likelihood estimation (in R, with nlm function) to estimate $(a,b,c)$ with a Hessian matrix $H$ as a ...
645 views

### Finding ideal hypothetical data according to a regression model

Analogy We have 10 athletes. Each athlete is represented as a binary feature vector. We make these athletes compete in a 100 metre race. We get real value numbers corresponding to the time they took ...
1 vote
642 views

### Regression involving multiple measurements on known values (calibration)

Suppose I have two continuous variables Y and X and I want to predict a Y value given a specific X value. However, the dataset I have is composed of 15 particular Y values (that are known values) ...
65 views

### Prediction of features given predictor

I am working on a problem where my objective is to predict y given some features x1,x2,x3,...x8,x9 I solved this problem using some statistical and machine learning techniques like regression, trees, ...
81 views

### Confidence interval from two methods

I have some data in the form of (x,y) tuples, 50 tuples. I am trying to fit a quadratic so y = ax^2+bx+c My goal is to find the max of the quadratic, so max = -...
4k views

### Why inverse of 'predict' function in R can not be used for dependent variable prediction in linear model?

When a regression is calculated with a simple linear model that returns intercept and slope for an equation like this $y=a + bx$ one can predict $y$, the response variable, based on that equation. ...
1 vote
256 views

### Inverse prediction of percentile

Suppose we consider a linear normal regression $y\sim$Normal($\mu,\sigma$) and $\mu=a+bx$. I have seen documentations for methods for obtaining a confidence interval for $x$ for a specific mean value ...
366 views

### linear model, given y, calculate the confidence interval for x

I fit the model y = a + b * x. And 95% CI for estimates of a and b are (a1, a2), (b1, b2), respectively. If we have a new observation ...
24k views

### How to do 4-parametric regression for ELISA data in R

I am a biology student. We do many Enzyme Linked Immunosorbent Assay (ELISA) experiments and Bradford detection. A 4-parametric logistic regression (reference) is often used for regression these data ...
531 views

### inverse logistic regression with binary covariates

I am currently using a hierarchical Bayesian framework to investigate a problem with both a single binary response variable and binary covariates, $P(Y=1 | X_i=1), i=1,\ldots,n$. Using R/JAGS I can ...
1 vote