# Tag Info

15

That’s the logarithm of the odds ratio, not the odds ratio itself. An odds ratio less than zero is nonsense. Looking at the behavior of a logarithm function (the base could be 2, could be 10, could be $e$), the function achieves values less than zero when the argument is less than 1, so a negative log of the odds ratio means that the odds ratio is between 0 ...

12

Is it okay that the direction of the fixed effects is opposite to the intercept in my model? Yes. The interpretation of the intercept is that it is the log-odds of the event (DV = 1) for the those in the none group (so, being negative, it is a protective effect), while the estimates for the other 2 groups are the log-odds of the event in each of those ...

6

The problem with using the estimated coefficients for interpretation is that because of the link function used in Logistic regression their effect is nonlinear to $\bf{X}$. $$log(\frac{\pi_i}{1-\pi_i}) = \alpha + \beta X_i + \epsilon_i$$ Therefore, \frac{\pi_i}{1-\pi_i} = exp(\alpha + \beta X_i) = e^\alpha e^{\...

5

The odds ratio for LR2 is simply the exponentiated value of the estimate for it: > exp(0.4539) [1] 1.574441

4

The standard approach to calculating confidence intervals for odds ratios is to treat them as log-normally distributed. Your data are consistent with this, specifically, In the test group, log parameters $\hat{\mu}_T=3.08$ and $\hat{\sigma}_T=1$ are consistent with an estimated odds ratio of $\exp(\hat{\mu}_T)\approx 21.76$ and a confidence interval from $\... 3 The interpretation of coefficents from logistic regression is due to the formulation, specifically: $$ln(\frac{P}{1-P}) = \beta_0 + \beta_1x$$ The log odds is on the left and the linear predictor with your coefficients is on the right. If we exponentiate both sides, we now have exp(linear predictor) related to the odds ratio, or a unit change in exp(... 3 I have been able to explain the need for the use of the odds ratio (cross-product ratio) to estimate effect size in a case-control study to students with a simplified example of two hypothetical studies of the same (hypothetical) people—one a cohort study and the other a case-control study. The hypothetical people are 300,000 adults. 100,000 of these adults ... 3 Ideally, I would like to see reported the Odds-Ratio (OR) and the cell counts underlying the formation of the constituting probabilities. Also, displaying the natural log transform of the OR would be informative as to quote a source: The distribution of the log odds ratio is approximately normal... and the source further notes, that a standard error ... 2 Your results differ because you are actually fitting two different models, one where you adjust for all predictors except for$x_1$, and another where you adjust for all predictors except$x_2$. What's happening is that you are trying to treat the vector of predictors$\{x_1, \ldots, x_k\}$as dummy variables by assuming that one needs to be omitted from the ... 2 The table displayed in this question shows the choices of parameter values for a simulation study, not experimentally determined or calculated odds ratios. The simulation involved 12 binary covariates (the$\mathsf {x_i}$) each with a prevalence of 20% having the indicated associations with outcome without treatment ($\mathsf {OR_C}$). In one set of ... 2 While it cannot create the table in exactly how you specified, you can calculate risk ratios (and other measures) using the zEpid library. This library supports both calculating from summary counts (details here) and directly from pandas DataFrame objects (details here). The library does not directly calculate p-values, but you can easily do this by a ... 2 I assume that you have scaled your percentages to values in [0,1] (or in the open interval (0,1) after you've added/subtracted 0.001; you might want to consider adjusting by smaller values, as values very close to 0/1 will be extreme on the log-odds or logit scale; e.g. logit(0.001) = -6.9, logit(0.01) = -4.59). I'll call these numbers "pleasure indices". ... 2$\newcommand{\op}[1]{\operatorname{#1}}Let's use some abbreviations as follows: \begin{align*} \op{UTRS}&=\text{Upper Trunk Rotation Strength}\\ \op{I}&=\text{injuries}\\ \op{A}&=\text{Age}\\ \op{W}&=\text{Weight}\\ \op{PCS}&=\text{Posterior Chain Strength}\\ \op{GS}&=\text{General Strength}. \end{align*} Now the basic model under ... 2 It's saying that the odds of females graduating is 4.31 higher than the odds of males, holding constant disorder. That doesn't mean females are 4.31 times more likely to graduate, but it does mean females are more likely to graduate. You can think of it as that among females, the ratio of the number who graduate to the number who don't graduate is 4.31 times ... 2 Norm Breslow argued that we should prefer the odds ratio as an association measure precisely because it's possible to have an odds ratio of exactly\infty$. Some exposures in reality have deterministic relationship with the outcomes, but relative risks have theoretical upper bounds that depend on the "design" (margins of the contingency table). If the ... 2 Exponentiation of coefficients will generally be useful when the expected value involves an exponential function in some way. This non-exhaustive list includes Poisson negative binomial other related GLMs OLS regression with a logged outcome logit ordered logit some parametric regression survival-time/duration models Sometimes you will need to go beyond ... 2 The short answer is that you seem to be trying to interpret a linear term in the presence of higher degree polynomial terms (as evidenced by the .L, .Q, .C, ^4, ^5 suffixes on your coefficients). Don't trust your intuition about what should be reasonable versus not reasonable in this situation. Your odds ratio of 5.57 is interpreted as the relative increase ... 2 It's unfortunate that you don't know the subcohort sampling fraction, but you can still calculate odds ratios. Cases who were subcohort members will need to be treated the same way as cases who were not subcohort members (which is desirable anyway). The cases are sampled with probability 1. I'll use the word controls to refer to subcohort members who do not ... 2 One good thing to do is to scale the predictors first, if the primary aim is to visualize the effects via odds ratio. You just need to note that the coefficients will change in odds ratio per unit of standard deviation per predictor. Using an example dataset, in R, I make one predictor binary: library(MASS) library(sjPlot) dat = Pima.tr dat$npreg = as....

1

Yes. First metric is called risk ratio (RR), while the second is called odds ratio (OR). First one is considered to be more intuitive so it should probably be preferred. Second one is (very) often used when RR can't be estimated (case-control studies or logistic regression models).

1

Best-case Scenario The smallest possible value of $N$ where we could be $95\%$ confident that the student has "mastered" a concept (meaning that their probability of answering a question correctly is $1/2$) would correspond to picking $c = N$, because $P(M_1 | c)$ is an increasing function of $c$, and $c$ is constrained by $c \le N$. In this case, $... 1 In (mixed effect) logistic regression, which I expect you have conducted, the odds ratio is a way to express the effect of your predictor of interest conditional on the other predictors that is invariant to the levels of the other predictors. This why the OR is widely used in discussions of logistic regression, even though it is far less intuitive to ... 1 An odds ratio is an effect size. A lot of people use the term effect size to mean standardized mean difference (i.e., Cohen's d), but this is not correct terminology. Imagine the term effect size stands for car and things like odds ratio, risk ratio, standardized mean difference, and so on are brands/types of cars. Right now, you are asking how to transform ... 1 This link may be helpful for you: https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-how-do-i-interpret-odds-ratios-in-logistic-regression/ Typically, odds ratios are interpreted as scalars that represent the increased/decreased likelihood of association to the response variable. Your first interpretation is correct, with a slight modification: ... 1 Note that with the command shown here, the use of the cumulative logit model renders the (REFERENCE=FIRST) specification irrelevant, and the default setting of (ORDER=ASCENDING) is applied, so the model is set up to predict the probability of the lower category (I'm assuming that's non-use). Thus the threshold (intercept) term is opposite in sign of what you'... 1 You can just divide that variable by its IQR. The reason Z-scoring a variable allows you to interpret its coefficient as a change in the outcome corresponding to a one-standard-deviation change in the predictor is that you are dividing by the standard deviation. The same logic applies regardless of the measure you divide by. Note this will not change the fit ... 1 I think the reason that OR is far more common that PR comes down to the standard ways in which different types of quantity are typically transformed. When working with normal quantities, like temperature, height, weight, then the standard assumptions is that they are approximately Normal. When you take contrasts between these sorts of quantities, then a ... 1 All this is explained in details in the book Modern Epidemiology by Sander Greenland. But forgive me for not being able to remember the details, the answers to your questions are: Yes. It's one way to calculate the overall odds ratio. Besides the logistic regression method, there's also the Mantel-Haenszel method, widely used before the age of computers. ... 1 Let's write the risk ratio and the odds ratio in comparable forms with the numerators and denominators each representing a row in your table: $$RR = \dfrac{30/(30+70)}{20/(20+100)} =1.8\\ OR = \dfrac{30/70}{20/100}\approx 2.143$$ so they are not the same, as you say. If one of them had been$1$then the other would also be$1$, as for example in $$RR = \... 1 Yes, you could report it that way. The probability of the outcome when eat_hotdog17=0 is$$ p = \dfrac{1}{1+\exp(-0.814)} \approx 30\% $$When eat_hotdog=1$$ p = \dfrac{1}{1+\exp(-0.814 - 0.464)} \approx 21\%$\$

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