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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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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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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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Interpret model estimates after log transformation [duplicate]

I asked this question before, but maybe on the wrong audience at math.stackexchange.com. So, sorry for the redundancy. I sat up a mixed-effects linear model with the dependent variable log-...
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Transforming back after a log transformation with subtraction

I needed help with back transforming my data. My initial data was positively skewed so I had to log transform it, after which I did my statistical test. One of my regression test required for my ...
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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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How to back-transform glmer() cbind() proportion data

I have fit a binomial GLMM (glmer) to a response variable that is a proportion. How my data looks: ...
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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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Negative Binomial Regression Coefficients and Std. Errors in R

I've done my due diligence in looking throughout crossvalidated to look for a solution but instead have found very different approaches. I'm running a negative binomial random-intercept model using ...
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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, ...
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29 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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Get forecast after modelling on differenced series

I'm trying to apply exponential smoothing methods for a forecasting exercise in R. Since the data has seasonality component, I differenced and got a time series that is stationary. I tried to perform ...
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287 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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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
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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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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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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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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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Back transform the integral of a log-log model?

One of my colleagues has an issue with back transforming the integral of model back to its original units. His model has a log transformed Y as a function of a log transformed X predictor. He can ...
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1answer
359 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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1answer
251 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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57 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 ...
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How to convert estimated precision to variance?

I have a simple model in INLA (the regressor is a single model=iid term), which reports the precision of the hyperparameter. How ...
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Box-Cox Transformation on Single Variable and Interpretation of the Transformed Variable's Mean and Standard Deviation

I'm revisiting the Box-Cox transformation in one of my stats books, and I started playing around with the SAS macro %BCTRANS2 (Source: http://support.sas.com/resources/papers/proceedings12/430-2012....
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95% CI interpretation on transformed data using (abs(x-mean(x)))

I have a problem for which no search has provided an answer. I am using lm() to build a model which I tested to ensure it met all assumptions using the following <...
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1answer
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back transformation of log means and log standard deviations

I have a set of values reported as the 'log mean'. I know from elsewhere in the text that it is the natural log that is being referred to. I'm trying to ascertain if there is a way I can derive the ...
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How to calculate the standard deviation of a sample and its 95% CI if I know the variance and its 95% CI?

I apologize if my question is extremely simple, but you know my name. I have only the variance of a sample and its 95% confidence intervals, nothing more, nothing less. Please correct me if I am ...
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1answer
2k views

Regression RMSE when dependent variable is log transformed

I want to predict the duration a trip would take. For this I transformed my dependent variable (trip time in sec) to log transformed. When I do regression on this variable with some other features, ...
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1answer
111 views

Multiple linear regression back-transformations

My Multiple Linear Regression equation is (I had log-transformed swim beach E. coli and canal E. coli for the MLR since the data were not normal): (LN)Swim Beach E. coli = 2.4 + 0.43 * Reservoir ...
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How to compute confidence intervals for a scaled reciprocal normal statistic

I have the following statistic of which I want to compute confidence intervals: \begin{equation} Z = \frac{(X-Y)^{-1}}{\mathbb{PVE}[(X-Y)^{-1}]}, \end{equation} where \begin{align} X &\sim\mathcal{...
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1answer
1k views

Back transform mixed-effects model's regression coefficients for fixed-effects from log to original scale

I am running a mixed-effects model with the lme4 package. The model specifications are: ...
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152 views

How to untransform/interpret results after a Lambert W transformation?

Suppose I have some heavy-tailed data that I want to transform so it's roughly normal in order to perform a t-test. ...
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Deal with negative predicted values in a linear model [duplicate]

I have a mixed effect model to model crop yield as a function of rainfall and temperature: ...
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225 views

Interpreting log transformed linear regression

I have created a linear regression model using log transformed data but I'm having issues interpreting the results. The r^2 of the model is .67 but I'm not sure what else I can report. I guess ...
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466 views

How do I estimate the prediction interval of back transformed log-normal data from Gaussian process?

I have some data that are clearly positively skewed and follow a log-normal distribution, lets assume the initial data is $Z = exp(Y)$, where $Y \sim N(\mu,\sigma^2)$. A Gaussian process assumes ...
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1answer
187 views

Re-transformation problem with different base in log

I have a Data that Distribute as Log-Normal. I do a log transformation in base e. And build a linear model. And after that I backward to original data with $e$$^Y$$e$$^{Var(Y)/2}$. Back ...
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1answer
108 views

A question about the trimfill function in the “meta” package in R

I was doing a meta-analysis of single proportion using the meta package in R. I performed a double arcsine transformation to my data. I also wanted to do a trim ...
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1answer
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Log model too good to be true, maybe I'm interpreting results incorrectly?

I am unaware of how to generate a sample data set for reproduction that has the same characteristics as my actual data that would deliver similar results when running a log(response_variable) model vs....
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1answer
2k views

Evaluation of log Vs. non log models

There are several posts on here about this question. The gist of them, as far as I understand, is that you cannot compare RMSE or MAE of two models where one is log transformed on the dependent ...
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1answer
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Interpretation of linear regression results where dependent variable is transformed using ln(y+1)

Similar questions have been asked before, e.g. Back-transformation and interpretation of log⁡(X+1) estimates in multiple linear regression However, this question is a little different because (a) I'...
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1answer
2k views

Transforming regression coefficients back to original values from square-root -transformed data

I've ran linear regression with square-root transformed dependent variable. Due to negative skew of the dependent variable, the formula for data transformation prior analysis was as follows: NewVar = ...
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1answer
112 views

GLM backtransform in proc [closed]

I want to visualize and plot a ROC using pROC in R. I found this code. However, I can't track the source to find the explanation....
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2answers
115 views

Basic math: x-y versus sqrt(x)-sqrt(y)

First, sorry if this has been asked before. I searched and found lots of info on transformations and back-transformations, but none that offers insight into how you get into the forest and back out ...
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440 views

Bayesian parameter estimation: Transforming parameters to use uninformed priors

First of all: Please excuse my ignorance. There are some parts of the concept of bayesian inference I may have not yet understand! What I have so far: I have count data with a negativ binomial ...
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How to explain results from a graph of a variable transformed with exponential function?

I had to transform my response variable before my analysis, but the only transformation that worked well was the exponential. So, I could not back-transform my values to the original scale. How do I ...
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1answer
997 views

Back-transforming contrast lstrends results in r

I calculated a linear mixed model using the packages lme4 and lsmeans with the lmer-function, where i have one dependent variable rv and the interacting factors treatment, time, age and race. I'm ...
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1answer
307 views

is valid to log transform a variable and then re-transform to z score

I have to model 5 variables (in the same model to test for the most important factor) which include measures of distance (m) and percentages. At the beginning, I transformed the variable distance to ...
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1answer
558 views

log transformation logistic regression

I have a logistic regression in which i transformed geographical distance measured in km using a natural log. I've have run the regression, and now i am having trouble how to interpret the findings. ...
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162 views

How do I back transform predicted values when multiple transformations are present in multiple regression?

Suppose two predictors are desired for a multiple linear regression. Upon reviewing scatter plots, the first requires a power transformation, log(y)= b0 + b1log(x), and thus the back transformation of ...