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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Why doesn't standard error for ratios have log in it?
The formula for SE of risk ratios: $\sqrt{\frac1a - \frac1{a+c} + \frac1b - \frac1{b+d}}$ Where a+c is group1 and b+d is group2. ...
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Interpreting a logarithmic difference as an error
This is a fairly simple question but I can't figure out which one is the correct approach.
In astronomy it is usual to report age values via their base 10 logarithms instead of the actual value. So a ...
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Looking for a layman's explanation of how to manually calculate log odds?
I will start that I am not as math oriented as I would like to and could use a layman's / non-staticians explanation walk through of how to calculate the log odds.
I am reading Hosmer, Lemeshow, and ...
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PSM, Diff-in-Diff and Neg-logged income variable? How to interpret estimates?
I am estimating a difference-in-difference based on propensity score matching. The "treatment"-variable defines whether a household registered for a public insurance which was only active for two ...
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Log probability vs product of probabilities
According to this wikipedia article, one can represent the product of probabilities x⋅y as -log(x) - log(y) making the ...
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multiplicative model in r [duplicate]
I have to estimate a model forecasting the sales (as stock units) for AXE deoderants.I want to apply the multiplier specification on this model. The model should look like this:
log(Sales) = b0 + ...
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What are the advantages of using log GDP per capita versus simple GDP per capita when analyzing economic growth? [duplicate]
I have quite a lot to learn regarding analysis and economics, one thing I have noticed is that when analyzing growth, log is used quite often, why is this so?
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Maximum Likelihood estimator of population variance and its derivation process
I have 2 questions about maximum likelihood and using it to calculate variance:
Question #1:
The question is about finding the derivative of the score function with respect to the parameter $ \sigma^...
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Multi-class logarithmic loss function per class
In a multi-classification problem, we define the logarithmic loss function $F$ in terms of the logarithmic loss function per label $F_i$ as:
$$ F = -\frac{1}{N}\sum_{i}^{N}\sum_{j}^{M}y_{ij} \cdot Ln(...
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Interpreting Log-Transformed Percentages in OLS
In a log-log model, such as $\log(y) = b_0 + b_1 \log(x)$, I know that with OLS the standard interpretation is a "1% increase in x is associated with a $b_1$% increase in y."
I have three related ...
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How to compute the marginal probability form conditional probabilities in logspace?
Normally the marginal probablity is computed as
$p(x) = \sum_y p(x | y) \cdot p(y) $
Now, suppose I have all these probabilities at the right-hand side in logspace (so as logprobabilities).
How do ...
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Approximation of logarithm of standard normal CDF for x<0
Does anyone know of an approximation for the logarithm of the standard normal CDF for x<0?
I need to implement an algorithm that very quickly calculates it. The straightforward way, of course, is ...
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Why can certain variables in a multiple regression not be included in logarithmic form? [closed]
I have a multiple regression equation where log(salary) = b0 + b1(ceotenure). What is the purpose of putting the dependent variable in logarithmic form? How would you interpret the change in y for a 1 ...
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What to do with coefficients of log-transformed predictors in meta regression of effect sizes?
I am preparing data for a meta-analysis regression of effect sizes, in which I will study the determinants of effect size for a specific variable across several studies. I have some studies in my ...
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Creating a composite variable from 2 log transformed variables?
I have a data set of 1,100 observations, I have two continuous variables (counts of different things) that were positively skewed, so I first log transformed each of them.
Now I need to make a ...
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How to interpret log-log regression coefficients for other than 1 or 10 percent change?
I have read many threads here on how to interpret coefficients in a regression where the predictor and the dependent variable are log-transformed. Most give an answer for a one or ten percent change. ...
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Log and natural log
I have few seemingly simple questions.
I am working on time series data and applying vector error correction model. I find different results when I transform the data into LOG and LN. Which one is ...
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Metropolis Hastings when acceptance rate is not a probability
I need to implement a Metropolis Hastings where the acceptance probability $\alpha$ is not a probability but a logarithm of a score. The logarithm of a score is a negative float.
In original ...
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dealing with exponentials in python - infinities and overflows [duplicate]
In a machine learning algorithm that I'm using, I need to get the exponential values of something in one of the steps.
This is the step that I'm dealing with right now:
I've already got all the 1+...
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Regression and link function
Suppose we have $E (\log (Y)) = a+bx $ vs $\log (E (Y)) = a+bx $. Can $\exp (b) $ in both cases be interpreted as a geometric mean?
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Log-scaled chart for visualizing extreme range
I need a simple bar chart or the like. I am not a statistician by any means, but this chart is supposed to accurately represent FileIO in MB/s compared to the theoretical peak of a specific drive.
...
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Understanding stationarity with Inflation
I am looking at the link between inflation and insolvencies for an econometrics project. I have the raw quarterly insolvency data and raw quarterly CPI data for the UK (roughly 100 samples) from 1988-...
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Reporting regression statistics after logarithmic transformation
I'm a bit troubled about how to report linear regression statistics after log transformation of the dependent variable.
I suppose I should report the transformed coefficient, but would they be easily ...
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Use of log of an independent variable and its implications
I am currently analyzing the relationship between Google Search frequency and the CDS market. I used a monthly backward rolling regression to determine the 30 search queries which have the biggest ...
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Interaction term in a linear log model
I am using a linear-log model to test whether overseas development assistance and remittances positively affect FDI in cases of good governance and financial market development. Let's say I want to ...
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Expectation operator and logarithmic function
$$\frac{1}{C_t}=E_t\left[\beta \frac{1}{C_{t+1}} \right]R_{t+1}$$
How to log linearise the function? $C_{t+1}$ is the stochastic term; $\beta$ is known.
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Avoiding large variances when taking the logs of small values
I have two random variables $(X$ and $Y)$ that are always positive. The assumption I'm making is that their logs follow normal distributions (i.e., $N(\overline{\log(X)},s^2_{\log(X)})$ and $N(\...
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interpreting the coefficient on a logged independent variable from a probit model
I am using a double model with log transformed independent variables and have calculated average partial effects. Now I am now not sure how to interpret the coefficients; particularly those from the ...
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Best way to estimate a regression with reaction times
I have reactions times in a no-normal distribution, so I am using logarithms.
Which can be the best way to estimate a regression?
Later, I would like to plot the results according to the age of my ...
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Linear-logarithmic Regression in MATLAB with two input arguments - which model to assume?
Look at the following plot and ignore the solid lines please (just look at the dotted/dashed ones).
ONE curve is described by the following parameters and ONE fixed value for the second input ...
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Is it correct to use 'Ln' instead of 'ln' for natural logarithm?
In some research papers, authors use 'Ln' for natural logarithm instead of 'ln'. Is it correct?
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Use logarithmic or linear values when performing correlation and ANOVA?
The data was collected using a logarithmic scale: scores (explanatory variable) are collected with values from 0-5. A score of 3 is 10x the value of a score of 2.
I wasn't sure if using either the ...
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Log Transformation in Growth Mixture Model (Mplus user)
I am using parallel process growth mixture modeling to estimate bidirectional longitudinal dynamics between pain (0-100 theoretical range of values) and sleep measures (0-20 theoretical range of ...
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Interpret interactions and logarithms in linear regression
I'm currently playing around with linear regression in R, and I've come up with a regression that fits data quite well. I'm just having some problems with interpreting the coefficients of my model. I ...
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Doubt in derivative of logarithm
This seem to silly but I wanted to confirm if the derivative of the log-likelihood $\hskip 2 pt l(x_i)$. The derivative of $$\frac{d (\sum_{i=1}^{M} log(x_i))}{dx} = \frac{1}{x_i} \sum_{i=1}^{M} \...
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Taking the log of variables
Just before I start the question I would like you all to know that I have checked the other threads on taking the log of variables but I still think I have a question that hasn't been touched on yet. ...
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Estimating the effects of cumulative odds ratios - additive or exponential?
I have run some regression models that examine the effect of variable X (a 15 point continuous scale) on Y (a binary variable - not perform/perform a particular behaviour) using logistic regression.
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Plotting variables in transformed space
Suppose $A = X_1/X_2$ and $B = X_3/X_4$. Why would one plot the data in $(\log A, \log B)$ space as opposed to $(A,B)$ space?
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Clarification of log interpretation
Let us say we have this regression
$$\ln(y) = a + B_1(age) + B_2\ln(savings) + B_3\ln(income+1)$$
When carrying out the regression we obtain:
$$\ln(y) = 0.3445 + 0.5(age) + 0.4556 x_1 + 0.55566 ...
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Performing calculation of a product of a sequence,
I have performed a calculation that a sample of records will contain at least 1 defective record assuming replacement. There are 20,000,000 records in the population, 7,000 are defective, and I will ...
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Questions on equation of log linear regression
I have been asked to check over a paper. The paper is using log linear regression. In the following log linear equation, $x$ is the dependent variable, $y$ is a continuous covariate, $z$ is a ...
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Bias correction of logarithmic transformations
I read that there is a bias when we transform a series with a logarithm and then applying the inverse function, but only in forecasts of the mean values.
I don't understand what it means exactly.
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Is it valid to log-transform percentages?
My thesis is to examine the validity of the relationship between tourism represented by tourist exports (real growth) and economic growth using a dummy variable and force workers. I tested the ...
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Binary Models (Probit and Logit) with a Logarithmic Offset
Does anyone have a derivation of how an offset works in binary models like probit and logit?
In my problem, the follow-up window can vary in length. Suppose patients get a prophylactic shot as ...
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Why are time-related covariates log transformed in modelling? [duplicate]
I have seen a lot of examples of transforming time-related variables (e.g., age, year, days, etc.), but I don't understand the reasoning behind doing this. I don't think it's for stabilizing the ...
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When analyzing a difference for log-transformed data, when to take the log?
I am working with laboratory data that needs to be transformed due to skewness. It has been gathered at 2 time points and I am interested in the change from time #1 to Time #2. My question is, do I ...
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First difference or log first difference?
I am evaluating the effect of covariances between series on returns. That is I run the following regression: $$ r_t = \beta_0 + \beta_1\text{Cov}(Y_t,r_t) + ...$$
I have conducted my analysis with ...
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OLS standard error log log regression
I am estimating the following Power Law relationship:
$$\ln(\text{Rank}) = \text{constant} + \alpha \ln(\text{Size})$$
where $\text{Rank}$ is $1,~2,~3,~...,~n$, and $\text{Size}$ is the raw value.
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Plotting 0 in a log scaled axis
I have a very large and sparse dataset of spam twitter accounts and it requires me to scale the x axis in order to be able to visualise the distribution (histogram, kde etc) and cdf of the various ...
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Expected value and variance of log(a)
I have a random variable $X(a) = \log(a)$ where a is normal distributed $\mathcal N(\mu,\sigma^2)$. What can I say about $E(X)$ and $Var(X)$? An approximation would be helpful too.
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