The logarithm of a number is the power to which the base must be raised to get the number.

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setting log-uniform priors in Stan

I have been using Stan for a couple months now and I want to adopt a log-uniform prior on some parameter array real theta[N]. I want to do something like a ...
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17 views

Interpretation of LOGIT transformed predictor when outcome variable is LOG transform

I have a linear mixed effect model in which the dependent variable is a log-transformed frequency of livestock predation predation, and there are three predictor ...
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1answer
46 views

power regression when the power is a variable

I have this function : $y = x^\alpha$ using log: $\ln(y) = \alpha\,\ln(x)$ Now, $\alpha$ itself can be decomposed and considered as a function of two variables $w_1, w_2$. We have: $\alpha = \...
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1answer
32 views

What mean should be used for the variables that are involved in a linear regression model in a log-transformed space?

This has been bothering me for a while. Both $X$ and $Y$ are material properties. They can be described using a linear regression model built in the log-transformed space, i.e., $\log Y=a \log X+b$. ...
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1answer
43 views

Why should I choose features or plot them manually when there are built-in functions to do that?

Why should I select variables due to my intuition if there are builtin functions in sklearn python like SelectKBest() and PCA() If I plot graphs of features of the data to see if they can detect the ...
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1answer
23 views

How to interpret a log transformed (x+c)? [duplicate]

I need to use log-log regression and because I have lots of zero values I tried to add a very small constant c=8E-12 to x and it works pretty good. Xs are very small probabilities. lnY= a + b ln (x+c)...
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29 views

Estimating elasticity of $y$ with respect to $x$ in a log-log specification

My rudimentary workings so far is that; $\log(y_i/x_i) = \log(y_i)-\log(x_i)$ Factorise, so, $\log(y_i/x_i) = \log(y_i) + \upsilon_i - \log(\gamma_i + 1)$ Thus, elasticity of $y$ to $x$ is always $...
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2answers
114 views

Alternatives to multilevel model with log transformed outcome

I'm working with linear mixed-effects model in Stata. Dataset has three levels of 100k observations, nested in 500 regions, nested in 70 regions. Currently my modelling strategy is to use three-...
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3answers
1k views

In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?

I'm studying statistics and often come across formulae containing the log and I'm always confused if I should interpret that as the standard meaning of ...
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0answers
9 views

Amplitude and confidence intervals using log transformed dependent variable

I have two questions: - I am fitting a cosinor model to estimate the seasonality of vitamin D levels, which is natural-log transformed. Now, I will estimate the amplitude = sqrt((beta1^2)+(beta2^2)), ...
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11 views

Logarithmic transformation and regression for Product sequence

So, I have an equation like below: $k_{A}*A*k_{B}*B*k_{C}*C=f$ (eq1) The only value I have is A,B, C, and f. I want to estimate $k_{x}$ and I have several equation so that I think it is possible ...
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1answer
40 views

Modeling a Y~Log(X+constant) equation

I have this data set of Xs and Ys. I am trying to fit an equation to it using R, of the form: y ~ log(x+constant) Any ideas how to do it?
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2answers
66 views

Conflicting interpretations for coefficient of log transformed predictor

If you think this is a duplicate, please have a look at the last paragraph. In a regression model where both dependent ($Y$) and independent ($X$) variable are in natural logs, what is the exact ...
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1answer
24 views

Inverting logarithmic output from VAR model

I'm working on a VAR model and am doing a log transformation of the raw data. x = log(x) After differencing, running various tests and running a VAR(2) model, I ...
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1answer
48 views

Why do the predictions of a linear (log-log) model not approximate those of a nonlinear (power) model?

I am having trouble using a linear (log-log) model to approximate the predictions of a nonlinear (power) model. I wish to plot the predictions of the linear model on untransformed axes, and I believe ...
5
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1answer
77 views

Find the distribution of $ N = \min \left\{k: \prod_{i = 1}^{k}U_i \lt .6\right\}. $

I'm cross-posting this from math.SE because it's not getting any love over there. However, if that's considered heresy, I can delete the posting over there. The Statement of the Problem: Let $ \{ ...
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0answers
31 views

Can we take natural log of a variable in ratio form e.g. age dependency ratio? [closed]

I have been through many posts arguing about whether we should use the natural log of a ratio or not. Yet I am still unable to understand the concept completely for I feel even ratios differ from each ...
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4answers
147 views

How to interpret regression equations with logarithms, based on log difference being approximate to percentage change?

$y = 4 + 2.5\,x + u$ For an increase of 1 unit of $X$ (that is, $X$ to $X+1$), we expect an increase $2.5$ units of $Y$ (that is, $Y$ to $Y+2.5$). Is that right? What if there's a/an $\ln$? $\...
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14 views

Trendline for data with two phases

I'd like to know how to fit a curve to a set of data that has two phases. For the below data I've tried using a third order polynomial, but I think that's overfitting the data and I've tried using ...
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1answer
64 views

Log transform produce sign change on coefficients

I want to regress $x_1, x_2, x_3$ and $x_4$ on $y$. Question: When fitting a regression model in the regular fashion without any transformations the coefficient for $x_4$ is positive. However when I ...
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36 views

How should I deal with a nonlinear objective function in linear programming? [closed]

What I tried: Let $x_i$ be the number of units in compartment $i$. We want to minimise the probability $$z = 0.3^{x_1} 0.4 ^{x_2} 0.2^{x_3}$$ s.t. Space: $$30x_1 + 40x_2 + 20x_3 \le 400$$ ...
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1answer
17 views

How to get real value from log adjustement value

I am looking for some data for my research, and found reliable graph which showed the correlation of fetal weight and gestational age which is what I want. However, the weight in that scatter plot ...
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0answers
68 views

Is there a model with additive effects for always positive dependant variable?

When modeling a dependant variable always positive and continuous, models as log-transformed linear model or GLM with log link are generally used. The log-transformed linear model is : $\mathbb{E}[...
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If you transform response time data, e.g. to generate a CI, do you transform the values back for interpretation? [duplicate]

I would like to create a CI or highest density interval for response time data. The distribution of the response times is quite skewed and I think about transforming them by LN(y). However, my ...
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1answer
25 views

Normality test on logarithmic data

I had to take the log of my data, and now I want to test for normality of my data. Can I use the standard normality tests or do I have to use some special test? I used the ...
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0answers
131 views

Back-transform coefficient from linear mixed model with log-transformed response

I ran a linear mixed model (lme4::lmer in R) with a log-transformed (base 2) response, and predictors were not transformed. I want to back-transform my coefficients to make a statement about effect ...
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350 views

Curve Fit with logarithmic Regression in Python

I need to find a model which best fits my data. It's look like this: So I thought about logarithmic regression. But when I try to make a simple fit in python I get the following result: My code ...
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0answers
10 views

Multiplicative Measurement Error in Response Variable

I understand that taking log of the multiplicative error model transforms it into the additive error model. Let $y'$ be the observed response variable, with $y$ being the true response variable and $\...
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1answer
91 views

Log-transforming time series data before cointegration testing

I am testing the cointegration between these variables: Gold Price (Ringgit), Exchange Rate - MYR to USD (Ringgit), Real Effective FX Rate Based on CPI, T-Bill 10 Years Rate, Consumer Price Index. ...
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1answer
74 views

log-log transformation

I am making a linear regression model for house prices. My data set includes price per square foot of a property and floorspace so I have multiplied them to get the total price of each property. My ...
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1answer
30 views

Exponential Regression with x outside of exponential

I am trying to do exponential regression by matrix notation, and I am trying to figure out to create my $\mathbf{X}$ matrix to fit my model. I know that I need to use a model function of the form $c_1 ...
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1answer
37 views

Running Same Regression Across Multiple Individuals

I am trying to run a log log regression of the form LNX ~ LNP, where X = Units Sold and P = Price (in reality, I would have a number of other variables included in the model). The data is retail data;...
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27 views

Alternative scaling methods to log

I have data (as below). When I plot, the details of 0-10 are lost. So I scale it using a log function and then it seems that detail is lost throughout. Is there another scaling method that would work ...
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0answers
57 views

Normalizing logarithmic data in a range from 0 to 1

i am replicating a multilevel-analysis for my bachelor thesis (with newer data + corrections). The author i am citing used the unstandardized coefficients of every independent variable as beta ...
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1answer
30 views

data transformation in regression

I am going through a research paper on HbA1C (hemoglobin) management of diabetic patients. The author has used multilevel model as it has repeated measures. The DV has been log transformed. To ...
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0answers
23 views

Transforming Log Values in Predicted Values (Low Predicted Scores)

I have a problem with the logging of a price variable. The logging of the variable helps the model performance considerably. The value is positively skewed so this makes sense mathematically. I run ...
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2answers
46 views

How do I correctly compare bacterial counts from mice with different genotypes?

As far as I know, CFU counts from bacterial suspensions should approximately follow a Poisson distribution. So in order to perform a One-way Anova, a mathematical transformation to achieve normality ...
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1answer
58 views
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37 views

Nonparametric estimation of the logarithm of a density

I was wondering whether there is an equivalent to Kernel Density Estimation to estimate nonparametrically the logarithm of a density. Or if there is any nonparametric method for that. (Taking the ...
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227 views

Do we need to log-transform a variable that already is in percentage form?

I came across this website while searching for knowledge and help in statistics. As far as I know, we log-transform variable in order to avoid the heteroskedasticity problem. However, if any of the IV ...
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95 views

Minimizing RMSE while using a log-transformation

I am trying to fit a linear model to some data, but the dependent variable y is clearly not normally distributed. It has a heavy tail on the right. A log-transformation helps to make the ...
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1answer
36 views

Store logarithm of a variable in data set

I have seen many data sets where some of the variables are listed both with their original value and the logarithm of the variable. For instance, a data set could have the variables ...
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151 views

How to perform logarithmic binning

I'm trying to program (in C++ if relevant) some functionality to plot a histogram that does logarithmic binning. The range of values run from 0 to M (there is a possibility for negatives but we're not ...
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0answers
10 views

Re-arranging log-linear equation to get slope on standard (not logarithmic) scale [duplicate]

The equation for log-linear regression is: logY = mx+c [eq 1] therefore: (logY-c)/x = m [eq 2] And to get slope on standard scale we can do: exp((logY-c)/x) = exp(m) [eq 3] but Im ...
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68 views

Coefficient in differences-in-differences regression significant for log-level specification but not for level level

I am estimating a differences in differences model: $Y_{it} = \alpha_i + \beta_t + \tau T_iP_t + \epsilon_{it}$ where $\alpha_i$ and $\beta_t$ are fixed effects, $T_i$ is a dummy variable indicating ...
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40 views

Correction for logarithmic bias

I fitted the variable that has been log transformed (log(y + 1)) by means of mixed model. I used lme function from ...
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1answer
39 views

multiplying an outcome and predictor values by ten flips the sign of an effect size when log transformed. WHY?

I have a model, y~ x1 + x2 + x1*x2, where y and x1 are strongly correlated and ...
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0answers
20 views

How to use ln-transformation with loads of zeroes?

I came across a method of ln-transforming exogenous variables in non-negative data sets with loads of zeroes in a lecture. With the method proposed, one simply ln-transforms the variable in question ...
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1answer
106 views

Is there something clever I can do with a log of a sum?

In something I'm working on, the expression $$\lim_{n\rightarrow\infty}\exp\left(-\frac{1}{n}\log\left(\prod_{i=1}^{n}X_{i}+\prod_{i=1}^{n}Y_{i}\right)\right)$$ came up, in which all $X_{i}$ $iid$ and ...
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2answers
98 views

How do I change logarithmic scaled data to linear scaled data?

I am using decibels for my research, and I was told by someone that I cannot perform any statistical analyses on these measurements other than basic descriptive statistics because the data are ...