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Questions tagged [logarithm]

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

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When to choose difference versus log ratio for expressing variables relatively?

Oftentimes I wish to express one time series (say) relative to a second one. The two obvious candidate approaches are to take their difference or their ratio. Whereas the difference is symmetric with ...
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77 views

Is $\ln\{E[f(x)]\}$ equal to $E\{\ln[f(x)]\}$? [duplicate]

Is the logarithm of an expectation the same as the expectation of the logarithm?
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9 views

Convert ratios into a standardized effect like Cohen's d

This is my first time working with log data. I have performed a contrast of the difference between two log means and have back-transformed this to give me a ratio of geometric means. I'd like to ...
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1answer
22 views

The interpretation of the economic significance in level-log and log-level models

I have the following two models. The first is a level-log model, and the second is a log-level model. These models are two separate regressions and are estimated independently. Assume that α=0.036 ...
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28 views

Interpretation of a log-level regression in its associated 'level' form

Is it conventional to interpret a least-squares regression with a log-transformed dependent variable (log-linear model) in its "level" form? In other words, running a model with the outcome in 'log ...
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21 views

Solving an equation with logarithms of negative numbers

I'm modelling a bunch of non-homogeneous poisson processes. I'm impossing on them a linear-log functional form. you end up with two parameters, theta1 and theta0 for each estimated process. The ...
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1answer
20 views

Why do we use natural logarithm in categorical outcome variables

I'm reading a chapter on categorical outcome variables (chi-square & log linear analysis) and the author, in an effort of fitting a linear model, said that because the outcome variable is a ...
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41 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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11 views

Interpretation of log(1+x) variable with y in percentage

In std regression analysis, I'm wondering what the correct interpretation of a log (1+x) variable is when my y is in percentages. My x variable takes on values from 0-4, with the the majority of the ...
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1answer
33 views

Log-Log Regression - Dummy Variable

I have following regression: logCPI = 1,2922 - 0,3525*logGDP + 0,4239*logImport + 0,2115*logNEER + 0,6291*logWAGE + 0,0121*dummy How should I interpret last variable (dummy variable)? The regression ...
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1answer
113 views

Interpret a multiple linear regression when Y is log transformed [duplicate]

I have the following multiple linear regression model: Log(y) = B0 + B1X1 + B2X2 + B3x3 + e. X1 is a dummy that can take 0 = male and 1 = female and X2 and X3 are continuous variables. I am not ...
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40 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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1answer
29 views

Fitting a logarithmic trendline on already logged values

This is the situation. I am running trials with a population simulator, which produces various outputs (y), with the variance of these outputs being dependent on the number of clones (x) (recursions) ...
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19 views

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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1answer
31 views

Am I Log Normalizing correctly?

I am sorry if this is a stupid question, but I have searched the other questions about log normalization found other sources on it all of which assume a level of understanding that I don't have. I ...
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49 views

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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Comparing log normal and propensity multiple imputation models using confidence intervals

I am imputing income data with information about individuals characteristics and I am comparing the following multiple imputation models: Regression method using logarithm of income. Propensity score ...
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1answer
146 views

Need help understanding what a natural log transformation is actually doing and why specific transformations are required for linear regression [duplicate]

I’m taking an online “Intro to AI” course for which I’m doing some azure machine learning labs. This course is largely about how to apply azure ML solutions and, while there is an “essential math for ...
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76 views

Converting log transformed and differenced time series back into original in R

I have built a Garch model in R based on taking a log transformation and a one order difference on the original time series. I would like to know how develop a forecast based on the Garch model for ...
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1answer
59 views

Interpreting GLM with logged variable

For my logistic regression model I have: glm(reconv ~ -1 + log(precon) + log(age), data = crime, family=binomial) With the following co-efficients outputted from ...
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31 views

Can I log-transform realized volatility in a co-integration setting

I'm writing my master's thesis and looking to see if there exists fractional co-integration between the volatility of some large stock-indices. My estimates of realized volatility are based on the ...
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1answer
48 views

How to calculate growth rate from a semi-log plot?

In the following plot, if we model the population growth as a linear function of time, what would be a good estimate of the linear growth rate? I don't know if it's the slope or the intercept!
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Using log odds ratio to compare bigram frequency between 2 profiles

I was reading an article where the author proposed using the log odds ratio calculation to compare the relative frequency of bigrams between 2 websites. From my understanding the odds ratios are used ...
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19 views

Bound for type of correlation measure

Assume you have a finite, discrete probability distribution for a joint random variable and such that $P(X=i,Y=j) = p_{i,j}$ for $i \in \{1, \dots, |X|\},j \in \{1, \dots, |Y|\}$. The marginal ...
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Why don't my GWAS QQPlots look the same?

I am trying to create a QQPlot of 100 log-transformed p values from a GWAS study. The idea is that taking the -log(p) will magnify the smallest p values to make them easier to see. (reference) I was ...
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35 views

Prediction intervals of a log return time series when converting back to levels

I am having a problem when calculating prediction intervals of an ARIMA model of a log return transformed time series. Assume I have the following point estimates for $h \in \{1, 2, 3\}$ where $y_{t+...
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1answer
93 views

A different proof for KL divergence non-negativity

KL divergence's non-negativity can be proved in many ways. One could use the inequality $\log x \leq x - 1$ as a main step in the proof, another one could leverage the property of concave of the ...
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19 views

Poisson bias adjustment

So I was hoping someone could help me make sense of this problem. I came across this paper that discusses how the FSL probabilistic DTT may yield bias tractography relating to the physical distances ...
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0answers
30 views

Scatterplot bounded by parabola

I have frequency data for several variables. Each type can take on one of two variants: ...
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1answer
68 views

Removing Variance in Time Series After Applying Log Transformation

I'm trying to look at natural gas prices from 2003-2018. The issue is after applying log transformation and then diffrencing data by 1, I still seem to get an increase in variance from mid 2014-2018. ...
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1answer
55 views

How can I interpret natural logarithm transformed value in the binary regression result

I have the binominal regression output result using R programming and x3 below is the natural logarithm of the data which is large. The x3 before imposing the natural logarithm has the following ...
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1answer
236 views

Impulse response: Interpreting shock and response for log-variables

I have a question related to the interpretation of Impulse Response Function (IRF) functions. Assume we do have two time-series that have been both log-transformed and are stationary. When applying a ...
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54 views

The average change interpretation when the dependent variable is in logarithm

Suppose the regression model is $\text{wage} = \beta_1x_1 + u$. The conditional expectation function is $\operatorname{E}[\text{wage} \mid x_1] = \beta_1x_1$. Then, we interpet $\beta_1$ as the change ...
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1answer
43 views

Is there a name for the distribution whose PDF is -ln(x) on its support [0, 1)?

If so, what is its name? If not, how/where can information about it be found?
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How could the size of the beta coefficients change order after log-transforming outcome variable?

I had a mixed effects model where the residuals were not normally distributed, so I log-transformed the DV to meet the assumption. There is one fixed effect with 3 categorical levels (L1, L2, L3). ...
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2answers
111 views

Regression with log transformation of dependent variable that has negative values

I am working with a dataset that contains: a dependent variable (DV) taking both positive and negative values a binary independent variable (IV). And I'm interested in the following specification: ...
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150 views

Logarithmic Transform of proportions (Weber's law)

Given we have a function as follows (context is the Weber-Fechner law): $$\frac{\Delta x}{x} = C \tag 1$$ Plotting here $\Delta x$ as a function of $x,$ this is clearly a linear function with a ...
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1answer
34 views

Is it ever convenient to maximize different functions of the likelihood than the logarithm?

We all know that it's often much more convenient to maximize the log-likelihood rather than the likelihood to get a parameter estimate, since it amounts to the same thing by the fact that the ...
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1answer
53 views

Log-Log in panel data for multiple regression

I'm using a model, for an article, with 6 independent variables. I used the logarithmic transformation of the dependent variable (Y) and 2 of the 6 independent variables. One of my professors said ...
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1answer
70 views

Backpropagation in a logarithmic layer of a regression NN

A "logarithmic neuron" is defined as follows [1]: Which for inputs $\left\{ {{x_1},...,{x_n}} \right\}$ yields an output of $z=\prod\limits_{i = 1..n} {x_i^{{w_i}}}$ (in MATLAB, the activation ...
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1answer
35 views

Control for over-dispersion. Why do this: take natural log of metric, exponentiate, rank, remove top and bottom 10%

I'm looking at some NHS healthcare data on the number of deaths in England The measure i'm looking at is called the SHMI - it's simply: The number of observed deaths at a hospital / The expected ...
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0answers
55 views

Discussing R-squared of log-log model with a non-technical audience

I have been asked to report on the relationship between two right-skew financial variables using R-squared e.g. "market cap explain ?% of the variance in CEO compensation". The purpose of the ...
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1answer
515 views

Interpreting RMSE of log-values

I am modelling a regression with a GBM and evaluate by RMSE. My model input & target is log-transformed which results in an RMSE that is also on log-scale. How can i interpret this in an ...
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192 views

calculate binomial deviance (binomial log-likelihood) in the test dataset

I'm predicting probabilities $P(Y=1)$ using a probability forest (ranger in R). I want to evaluate my predictions $\hat p_i$ in a test dataset by calculating average binomial deviance (log likelihood)....
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1answer
489 views

Predicting probabilities after log-linear regression

I would like to estimate a log-linear regression and examine the results with Stata's marginsplot command. I have transformed my dependent variable into natural logarithm (to make a highly skewed ...
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1answer
78 views

How do I interpret the coefficients of a log-linear regression with quadratic terms?

I have a regression equation of this kind: $$\log {y} = a + bx + cx^2 + \epsilon$$ where $a$ is the intercept, $b$ and $c$ are the coefficients of $x$ and $x^2,$ and $\epsilon$ is the error. How do ...
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1answer
77 views

Maximum likelihood estimation and $\log(0)$

I am thinking I can't be the only one encountering this. I am trying to do maximum likelihood estimation on a probit model, i.e. trying to find the most optimal fit for three parameters in my case ...
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1answer
15 views

multiple regression log transformed how do i see initial values

I log transformed my dependent variable and all 5 independent variables to get a better fit. The dependent variable is sale price in dollars. Before I logged it, the intercept and all coefficients ...
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2answers
453 views

How can I interpret intercept when my dependent variable is in log form?

My model consists of both log independent and dependent variables, and percentage share, as well as number of people and etc. My dependent variable is log(GPD per capita in USD), my statistic package ...
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1answer
35 views

Log-transformations and concave functions

Consider a linear equation $O = SW$ with $O \in \mathbb{R}^{g \times n}, S \in \mathbb{R}^{g \times k}, W \in \mathbb{R}^{k \times n}$, with $g \gg n, g \gg k, k < n$. $W$ is a frequency matrix and ...