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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Confidence Intervals around Backtransformed Log-linear Regression

Suppose we are interested in the percentage effect of a binary $D \in \{0,1\}$ on an outcome $Y \in \mathbb{R}$, which might motivate a simple regression of the form: $$ \log Y = \beta_0 + \beta_1 D + ...
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Interpreation - Log tranformed dependant variable and model with square term of predictor (inverted U)

I am estimating a model of the following form: log(y) = b1 x + b2 x^2 + b3 log(z1) + b4 z2 This is an econometric model with a focus on the impact of ...
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Should I back-transform estimate and 95%CI after a survival analysis with log-normal distribution?

I need to run a survival analysis on my data. Based on the AIC, the lognormal distribution is the most suited one. Can I report the estimates and 95% CI as they are, or do they need back-...
MWE_Manet's user avatar
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Backtransform variables in ggeffects (logistic regression)

I am running a logistic regression. Two variables are transformed for linearity with the logit of the outcome. ...
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Interpreting linear mixed effect model results with log transformed dependent variable and log transformed predictor w/ normal predictors as well

I have a linear mixed effect model that I built using longitudinal country level data to help me predict TB incidence based on country level diabetes prevalence, HIV incidence, prevalence of ...
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Prediction Interval for back-calculation when observation has variance

Given an existing regression curve, how do I properly account for the known variance of the dependent variable when back-calculating for the (nominally) independent variable? If I had an observation $...
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regression question: backtransforming MAPE for log(y)

I'm fitting a linear regression between two variables and to reduce the problem of heteroskedasticity I have log-transformed the outcome variable y. However, this makes it difficult for me, a non ...
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Back transformation of dependent variable after square-root transformation in a two-part model in MPlus

I want to find out if one behavioral intervention had also an effect on another behavior (let´s say smoking). Currently, I am testing the moderation with a two-part model in MPlus, where smoking is ...
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backtransform confidence intervals from a log-transformed linear regression model

I have a linear regression model with violated assumptions (linearity and Constant variance), thus I decided to take the log of the dependent variable and this step solved the problem. Afterwards, the ...
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Why do I get this error when trying to obtain back-transformed estimated marginal means using emmeans?

I am trying to examine the interaction between temperature (factor: 6 levels) and species (factor: 2 levels) in determining the duration of the first larval stage in insects using the following model ...
Insect_biologist's user avatar
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Why use the bootstrap for a skewed distribution when you can use a transform?

Let's say you are working with a statistic (say, the mean of the population) of a skewed distribution with a long, long tail such that confidence intervals must be very skewed to achieve reasonable ...
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Can you back-transform standard errors from log-transformed data? [duplicate]

I fit a model with transformed data with log10 transformation. I would like to report the results using the original scale and not the transformed means. I know you can back transform the log means by ...
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What is the inverse normal transformation (INT) and what are the reasons behind using it?

I noticed a statistical method called inverse normal transformation in the following research article FTO genotype is associated with phenotypic variability of body mass index. I attached the ...
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How do you reverse log, square root, and Ln data transformations?

If you have transformed your data, is it true that when reporting results, such as descriptive statistics (e.g. mean, median, range, variance, standard deviation etc.), you need to revert the data ...
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GLMM with scaled variable: do I need to back-transform?

I am fitting a GLMM to powerline collision data for a bird species- using distance to seasonal water, habitat and the presence/absence of line markers as predictors. Incident is a binary response (50 ...
Christie Craig's user avatar
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Back Transformed Truncated Negative Binomial Model Results Less Than One

I'm using a truncated negative binomial model to describe my count data where all values are >=1. I have attempted to back-transform my model results using emmeans. However, all of my back ...
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How to transform prediction std of gaussian process back to origin

I am looking for a way of rescaling the predictions of my Gaussian Process Model back to the original scale. The data is scaled for training using a ...
sensation96's user avatar
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Interpreting regression output estimates with normal and square root transformed predictors and some log transformed response variables

I understand this topic is well covered here, but having read several threads, I can't find an explicit or clear answer to my question. I looked at the following threads and can't glean an answer from ...
user197410's user avatar
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GLMM Outputs from LMER: Random Effect Variance does not reside within 95% CIs in log-transformed response variables

I have produced a mixed-effects model (lmer) that is analysing the difference in area between three protocols of growing mini-brains. I have takes into account various fixed effects including the type ...
Sharna Lunn's user avatar
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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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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 ...
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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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How to correctly invert a confidence interval after a power transformation?

I have the following situation: I have some dataset in the form of samples $y_i, x_{i,j}$. I'm doing a GAM regression after a power transform (Yeo–Johnson - similar to Box-Cox). So I first learn the $\...
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Transformed Data with Boxcox and negative Lambda

unfortunately I'm a statistics beginner. I am trying to transform my data. Here, according to Boxcox, a transformation with negative lambda has resulted ( L =-0.25). But If I now run a T-tests with ...
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Given marginal tables back solve for contingency table

How to programmatically solve problems similar to the below: Most basic example: Given two marginal tables, solve for 2x2 distribution. A Sum 0 3 1 7 B Sum 0 4 1 6 Solve for A B Sum 0 0 0 1 ...
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Is this the correct way to compute confidence intervals on the original scale for GLM(M)s?

Suppose I have fitted a GLM and want to produce a confidence interval (or a prediction interval) on the original scale of the outcome. What I would do is estimate it on the link scale and then inverse ...
Frans Rodenburg's user avatar
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1 answer
180 views

Pearson's Correlation after power transformation of dependent variable

I have a simple model. y ~ x y is continuous (habitat gained per million $) x is continuous ...
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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 ...
Murphy's user avatar
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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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1 answer
842 views

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 ...
James Arten's user avatar
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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 ...
David Janda's user avatar
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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 ...
user11916948's user avatar
2 votes
1 answer
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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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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 ...
Beethoven_90's user avatar
1 vote
1 answer
872 views

How to back-transform ANOVA data?

I have been having trouble grasping the idea of back-transforming data in R. Let's assume that I would like to perform an ANOVA on transformed data. I transform the response variable and all the ...
John's user avatar
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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-...
Orla's user avatar
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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 ...
Nick Pardikes's user avatar
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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 (...
Alessandra Bielli's user avatar
4 votes
1 answer
5k views

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 ...
C.H.'s user avatar
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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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