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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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
2k 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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366 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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86 views

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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299 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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882 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
277 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
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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
664 views

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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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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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
4k 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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934 views

Back transforming GLM standard errors

This is a very simple question. When I back transform log transformed coefficients it usually looks like this: exp(interceptvalue) + exp(paramter1 coefficicent) ...
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158 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
123 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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Back-transforming Log data from a paired t.test (R)

I am working with this data set: ...
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1answer
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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
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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
591 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
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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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267 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 ...
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873 views

Log transformed outcome in quantile regression

I know in OLS, back transformation is not recommended so smearing estimators are often employed. As I understand it, this is not an issue in quantile regression -- you can simply exponentiate to back-...
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Question regarding back transformation of data

I have a data set that boils down to accuracy levels in a response task. In order to run an ANOVA on the accuracy data I've been advised to perform a arcsine square root transform on the data first. ...
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Interpreting Standard Deviation of Natural Log Transformed Data

I am interested in interpreting (back transforming) the effect of a one standard deviation (sd) increase in a log transformed on the non-transformed variable. So let's say I have a variable Y: ...
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Mean and Standard Error of True Percentages (Not Binomial Proportions)

In my line of work I occasionally deal with data on the percent lipid of fish fillet (environmental sampling). The question came up today about how to calculate the mean and standard error and ...
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Detect grid in 2D plane

Given is a set of points (x,y) in a two dimensional Cartesian coordinate system. Many points are near the crossing points of an affine transformed grid. The points have been measured and may have: ...
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540 views

AIC in R: Back-transformation of model averaged coefficient estimates

I am running an analysis using a mixed model with lmer in R. I am using AIC as my model selection process. I have a global model and am including within the selection process all subset models ...
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812 views

Back transforming reciprocal transformation for difference between means

Say I have the following datasets which concern normalised masses like this: Set 1: 3.08, 2.79, 3.62, 2.62, 2.85, 2.45, 2.80, 2.62 Set 2: 3.25, 3.14, 3.30, 3.13, 3.19, 3.17, 3.35, 3.35, 3.82, 3.13 ...
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1answer
3k views

Back transformation of log10 transformed data in SPSS

I have transformed my quantitative variable by using the log10 function in order to run some parametric tests (ANOVA) but when I want to make pairwise comparisons ...
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1answer
795 views

back transforming confidence intervals

Purpose: Construct a 95% confidence interval for $\theta$. A common strategy is to construct a confidence interval for $\log(\theta)$ and then exponentiate. Why is it valid? My concern is that $E(...
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152 views

Rewriting linear equation

So I have a linear equation produced in R: logBodyWt = -1.08968 + 1.22496 x logBrainWt And that's all groovy but there is a question in a module which asks me to "Rewrite your model as a non-linear ...
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317 views

Smearing estimate for cubic root transform in linear regression

I am building a cost model with cubic root transformation of the cost. Hence dependent variable is (cost)^(1/3). Now, am at a stage where i need to re-transform the predicted value to the actual cost. ...
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1answer
487 views

Arcsin CI for proportion

I'm trying to replicate a study. I have 165 observations of a proportion variable (the distribution is skewed to the right as many proportions are low). I need to report the CI. I've applied arcsin(...
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1answer
482 views

Antilog of a semilog regression model with dummy variables

I have a semi-log regression model, with two continuous predictors, two categorical predictors (0 or 1 dummy variables) and a non-zero intercept. The response variable is log10 transformed, none of ...
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2answers
1k views

Which residuals to analyse when dependent variable is transformed?

I am running a multiple linear regression where the dependent variable is sqrt-transformed. As far as I understand, the residuals from the regression are different from the residuals calculated as ...
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2answers
2k views

re-reflecting variable after transformation

I have a question about the process of re-reflecting transformed data. I see many questions and answers around this but I am not sure any answer my specific question. Many of my variables were ...
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1answer
260 views

Back-transformation

I have a simple linear regression model, and I have done transformations on the response and the explanatory variable (see call in code below), and I obtained an r-squared of 0.415. When I back-...
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1answer
99 views

Back-transforming elasticities to level coefficients, with standard errors

I would like to use some literature estimates of supply and demand price elasticities in an illustrative model that is in levels, not logs. The elasticities come from models of the kind $$ \ln Y=\...
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222 views

Back transforming a constant for geometric mean

I have a series of non-normal variables that include negative values. I have transformed the data by adding a constant of +10 to each variable (the lowest value was close to -9) and then log ...
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1answer
326 views

Back transformation with power function

I have the following distribution, where each observation represents a metric. $Metric = \frac{NExplored Nodes \times NGenerated Nodes}{NRepeated Nodes}$ This metric is highly correlated (0.99637) ...
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1answer
7k views

back transformation of arcsine square root transformation

I have a LSD that has been produced from the transformation of percentage data. I want, if possible, to transform this number back in a % that can be plotted onto the graph with the percentages on it. ...
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1answer
15k views

Back transforming regression results when modeling log(y)

I'm fitting a regression on the $\log(y)$. Is it valid to back transform point estimates (and confidence/prediction intervals) by exponentiation? I don't believe so, since $E[f(X)] \ne f(E[X])$ but ...
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98 views

Plotting data and polynomial equation when x-values have been transformed

I hope I can make my question clear, if not I will be happy to clarify. I want to present a simple regression plot with the polynomial equation line linked to it. Those data have been tested in a ...
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593 views

Proper back-transformation of lognormal standard deviation to find confidence intervals around a mean [duplicate]

I want to determine the 95% confidence interval of a mean. I logged-transformed my data in order to achieve a normal distribution. Several observations contained 0, so I changed these to 1 so that ...
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1answer
1k views

Interpreting transformed dependent and independent variables [duplicate]

How would I interpret a transformed dependent variable (4th root) with some of its predictor variables transformed as well? In our study, we transformed our dependent variable to 4th root, $Y^\frac{1}{...
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4answers
2k views

Beta confidence intervals in transformed linear regression

Let's say I have a model: $$Y_i = \beta_0 \beta_1^{X_i} \epsilon_i$$ (note: This is slightly different than the more common example case of $Y_i = \alpha e^{\beta x_i}\epsilon_i$.) I can take the ...
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Can I normalize a data proportion?

Is there any way to normalize this variable (attached)? In fact, this is a proportional data (a percentage). But I need transform it in order to do some contrasts. I try with arcsine transformation: 2 ...
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1answer
3k views

Back Transformation

If I had a response variable that was square-root transformed, and an explanatory variable that is log transformed, and I wished to back transform the model using the summary statistics below, such ...