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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Box-Cox back transformation with indicator in linear regression

I have a fitted linear regression of a Box-Cox transformed dependent variable, using an indicator variable as one of the two predictors : $$ g(Q, \lambda) = \hat{\beta_0} + \hat{\beta_1}P+ \hat{\...
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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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40 views

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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113 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 ...
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46 views

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 ...
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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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metrics of backtransform from logit-normal

Suppose I generate iid random data, logit-normal, where the mean (0.8472979) corresponds to mu=0.7 on the back-transformed probability scale (i.e., expit(0.8472979)=0.7). SD of the iid sample on the ...
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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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81 views

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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Transforming log-scaled splines regression outputs to an understandable scale

Please give me some advice. I am using brms package and mgcv package for two regression models: bernoulli lognormal The problem is that both of these models outputs are in lognormal scale. As much ...
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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 ...
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25 views

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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54 views

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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Do I need to backtransform the estimates of a model produced with the mhurdle package using box-cox normal distribution?

I am currently running a double hurdle model with the R command "mhurdle". My data is not normally distributed and I am using the box cox normal distribution on because that yields the ...
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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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Interpreting differences in log-transformed data when constant has been added first

I have performed an ANOVA on some log-transformed data. I had planned to transform the mean differences in the log-transformed data back to the original scale and interpret them as ratios of the ...
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257 views

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 ...
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What is the back-transformation of Log((Max Y + 1) - Y)?

I have performed a linear mixed model regression with the transformation on the outcome variable, Y, Log((Max Y + 1) - Y). This gives normally distributed residuals when simpler transformations did ...
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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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538 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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Transformation of Beta distribution prior parameters for group testing analysis

As described here Optimization of pool size and number of tests for prevalence estimation via group testing I'm trying to estimate the prevalence of a lab test in a population (PCR for COVID-19) ...
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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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72 views

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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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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274 views

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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928 views

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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88 views

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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180 views

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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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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163 views

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 ...
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347 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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201 views

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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43 views

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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197 views

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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705 views

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, ...
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158 views

slope in a log-transformation

Given y(x) = A*exp(x+c). I'm converting the y-axis into a log-scale. Then I calculate the slope at a certain point. Am I'm allowed to re-transform this value dy(x)/dx? Hence: exp(dy(x)/dx)?
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How to recalculate Confidence interval after logarithmic and square transformations?

I'm performing test on one variance and in order to asses normality of X, I've transformed data with first natural logarithm transformation,then square transformation and calculated confidence ...
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1answer
2k views

Reporting glmer.nb Results

I'm running a mixed negative binomial GLM that looks like this: Niche2 <- glmer.nb(log_density ~ height * factor(Year) + (1 | Grouping), data = NicheData2) ...
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224 views

Interpreting forecast predictions of log transformed data

Using the forecast function in R, I make a 1-step prediction for a log-transformed data set Y, ( Y = log(X) ). This prediction gives me a mean and a 95% prediction interval. How valid is this ...
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2answers
3k views

Linear mixed effect model interpretation with log transformed dependent variable

I have a dataset in which the response variable is non normal, but on log transforming, it follows the normal distribution. I constructed a mixed effect model using lme4::lmer() as below (multiple ...
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71 views

Back transforming in t test using sqrt [duplicate]

I have one sample with values of sugar intake pre and post intervention. I transformed the values for t test as the change from pre to post was negatively skewed but now I dont know how to report the ...
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1answer
9k views

How to back-transform a log transformed regression model in R with bias correction

I have created a model to predict the number of people with a certain characteristic (Y) based on predictor variables $X_1$, $X_2$, $X_3$, $X_4$. The model is a multiple linear regression and both the ...
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950 views

Smearing retransformation in r [duplicate]

I ran a regression model with the Y variable (length of stay of patients in days) log10 transformed. I would like to compare the fit of the log10 transformed model with a similar regression where the ...
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1answer
996 views

Backtransforming log(x+1) transformed SE

I am back-transforming y=log(x+1) data that represent individuals/m^2 of area. Data are in the form of X ± SE. I back-transformed the means, but I am wondering if it's possible to directly back-...
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698 views

Standard errors in R, package emmeans

I am fitting a multinomial logit model in R by using the multinom() function in the nnet package. I would like to retreive the proportions in each class for the two ...
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76 views

Interpret Quadratic Regression with Asinh transformation

I have a regression equation that uses covariates of the following form asinh(y) = b0 + b1 asinh(x) + b2 (asinh(x))^2 + error and am wondering how to intepret the ...