# Questions tagged [back-transformation]

Back transformation refers to efforts to reverse the effects of a transformation of one or more variables. Usually, the transformation has been done to meet assumptions of a model, but interest is in the original variable(s).

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### Interpreting Predictions from the Log-Linear Model (or Log-Log Model...)

I understand that when we fit an OLS regression to the log(y) (as either a log-linear or log-log model), the predicted value from that model [log(y).hat] cannot be simply exponentiated to solve for y....
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### Back-transformation of confidence intervals

I have read that I can simply back-transform my confidence intervals from my (mixed) linear models, which seems very handy for model interpretation. What I don't understand is why log-transforming the ...
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### R: emmeans back-transformation when using a constant value in the response formula

I am fitting a linear mixed model ...
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### Converting scaled parameters to unscaled parameters in exponential regression

I would like to calculate two types of bivariate exponential models on scaled data (therefore both variables are expressed as z-scores): Model 1: $$y=b_{0}*e^{b_{1}x} + \epsilon$$ Model 2 (is ...
89 views

### Back transform predict.gam() from nb link log model run?

I have model with 1 covariate. I would like to run y values from gam in another model. I used nb(log=link) in gam model. Because I used nb and link log in gam, do I need to back transform to use ...
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### How to deal with output transformation at inference/prediction time?

Suppose A machine learning model (e.g. RandomForest) which uses $x$ as input and produces $y$. Now as part of preprocessing and feature engineering, I applied some ...
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### Back-transforming meta-analysis results in metafor

The R package metafor offers various ways of back-transforming the results of a meta-analysis with a transformed effect size/...
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### Interpreting log multiple linear regression, backtransformations?

I'm investigating adherence to a special diet (that is scored from 0-18) in relation to C-reactive protein level and am in the process of building multiple linear regression models: To achieve a ...
1 vote
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### Bias correction for regression with t-distributed error

I have a GAM /regression model which is originally defined as: log10(Y)~s(log10(X1))+s(log10(X2))+s(log10(X3)) #using R mgcv The response needs to be back ...
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### Interpreting multiple regression with transformed response variable

I have build regression model focused on association between physical activity and fat mass. The model is as follows: ...
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### Bayesian lognormal model: how to correctly back-transform the estimates?

I have a Bayesian model of the form: \begin{align} y & \sim logNormal(\mu, \sigma)\\ \mu_n & = \alpha + \beta_0 c_n + \beta_1 d_n + \beta_2 c_n d_n \end{align} Where: $y$ is a ...
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### First difference in logs transformation produces biased results on back-transformation [duplicate]

I have a strongly trended series where the trend appears to be exponential and I believe the errors tend to be proportional to the current value. In order to convert it to a stationary series for ...
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### Reversing Log-transformed target after training : r2 score interpretation

I have been running a log-transform on my target values because the distribution appears to be highly right skewed as you can see in the picture. After having called ...
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### Multiple linear regression - assumption of normaly distributed estimates

In linear regression, there is said that normal distribution of residuals is required. Other than that I have found that it can be violated if the dataset is large enough. But what is large enough? Is ...
1 vote
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### How to interpret a transformed linear regression model

I'm playing with the trafo R-package and this small data. After using the assumptions function, I found the log shift opt transformation is the best for normalizing ...
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### Back-transformation in pairs function (lmer analysis)

I'm running lme4 and Im working with a dataset where the variables a,d,e are logtransformed. I wonder how to handle back-transformation concerning the "pairs" function. How do I get the ...
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### Back transformed Median of log normal data, not equal to median of original data

l was working with these data: 160,320,160,160,320,320,160,320,160,320,160,320. I needed to calculate the median so decided to calculate while the data was log transformed and I would just back ...
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1 vote
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### Backtransform a log-odds transformation of the dependent variable in a Fixed Effects panel regression

I'm modeling a fixed effects (within) panel regression for a fractional dependent variable (DV) bounded between 0 and 1. My aim is to model the relationship so that I can predict the frational DV on ...
1 vote
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### Back-transformations

I have been having trouble grasping the idea of back-transforming data in R. Lets assume that I would like to perform an ANOVA on transformed data. I transform the response variable and all the ...
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### Standardize-back the Standard deviation

I run an lmer model using standardized data like scale(y) ~ 1 + (1|categorical) Now, I have a standard deviation for the random effect in normalized world but I ...
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### Can we transform back calendar adjusted forecast?

I've monthly data, I adjusted it for monthdays and conducted a forecast. After that can I adjust it back and compare it with untransformed time serie?
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### Back-transformation of coefficients in a log-log model, and a model with a boxcox transformed y

There's a number of posts out there on back-transformations but none that I've been able to use to answer this problem, internet searches are returning surprisingly little on the issue of back-...
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1 vote
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### Pairwise contrasts for logistic regression in emmeans, back-transform or not?

I ran a mixed effects logistic regression in R (glmer). The model identified a significant three-way interaction that I am interested in decomposing using post-hoc multiple comparison in emmeans. In ...
1 vote
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### predicting waste per capita: is a Gaussian model correct?

I am trying to predict the daily amount of waste per person produced in the fishery sector. We surveyed fishing boats at the end of their fishing trip and the variables I have are duration of trip (...
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### XGboost Regression Log Transform Target

I'm training a XGBoost Regressor to predict price which has a highly right skewed distribution. (all prices are positive) I took log transformation on the target thinking it would help to 1) stable ...
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### Back-transforming coefficients of glmer model fit using rescaled independent variables for prediction & plotting

I've fit a model using the glmer function from the lme4 package. Because my predictor variables are on very different scales, I ...
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1 vote
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### Back-transforming forecast points and error bounds from a VAR model applied to alr-transformed compositional time series

The data I have a k=3 compositional time series from which I am trying to forecast future values. The series is compositional in that at each time ...
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1 vote
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### How do I back-transfrom my estimates (and confidence intervals) from log10 variables (both independent and dependent) in linear model

I ran linear models for a bunch of variables in R. Both variables are log10 transformed (dependent and independent). I already took a look in some online documents and videos about this but i guess I'...
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### How to get the actual mean absolute error in cross validation after transforming the target variable y?

For a target variable y, it is transformed using np.log1p. Then a random forest regression model is trained using the ...
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### Predicting y from log y as the dependent variable

In the book Introductory Econometrics by Wooldridge the chapter, which deals with predicting values of $\hat{y}$ (chapter 6.4 in the 5th edition) states the following: If the estimated model is: ...
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### Which one is correct presentation for descriptive statistic of a transformed variable between retransformed mean (estimated SD), and median (qurtiles)

If a collected variable has a skewed distribution toward one side and transformed for statistical analysis, which one is better for descriptive statistics presentation between re-transformed mean and ...
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### When is performing back-transformation of inferences on transformed variables Ok, and when is it not Ok?

Caveat: This question may be a tad rambly, and I welcome comments with specific directions for me to improve it. During a too brief exchange with the worthy @NickCox I got to thinking about ...
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1 vote
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### How to plot estimate + raw data of a Bayesian zero inflated poisson?

GENERAL QUESTION: How to back-transform estimates from a zero-inflated poisson to obtain the original scale in R? (I tried exponential like for poisson but the results are wrong) DETAILED ...
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### Why are the confidence intervals so large for the difference of differences?

I have run a generalized linear mixed effects model with the glmmTMB package to determine if there is an interaction between two categorical predictors, treatment and location, in predicting the ...
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### Back transforming the intercept of double log normal distribution

I apologise if this is a duplicate, i couldn't find a thread that seem to be talking about the same thing. I have a dataset with a bunch of duration of varying lengths in seconds, i log-transformed ...
633 views

### Back-Transformation for Ln(X+1) of zero rich data

I have seen and read several similar questions, but mine pertains specifically to zero rich data. I will be back transforming my data based on a first order Taylor series approximation. As outlined ...
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### How to back transform a folded root?

I have some data where the response variable is a proportion, and I am experimenting with transformation using Tukey's family of folded powers, $f(p) = p^\lambda - (1 - p)^\lambda$, with values of \$\...
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### Log transformed data

When you log transform data what is being tested on the original scale of the data? And why can we use our log transformed data to answer our scientific question? We are looking at data comparing ...
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### Transforming non-normal to normal distribution and back-transform

I would like to transform non-normal distribution to normal distribution, and back-transform to its original state (or at least close to the original state). From this article, I've read that you can ...
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### How to back-transform negative Beta coefficients of linear regression after log transformation?

For a linear regression model, I have had to perform a natural log transformation of a response variable due to non-normal distribution in R. I am in the process of back-transforming the coefficients, ...