The question says it all - I'm just wondering whether Cox regression models are used to model non-linear relationships.
628
If polynomial regression models nonlinear relationships, how can it be considered a special case of multiple linear regression?  Wikipedia notes that "Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function $\mathbb{E}(y | x)$ is linear in the unknown parameters that are estimated from the data."  How is polynomial regression linear in the unknown parameters if the parameters are coefficients for terms with order $\ge$ 2?
34862
1) What is meant by linear dependence?  2) How can I convince myself that covariance measures linear dependence?   3) How I can convince myself that non-linear dependence is not measured by covariance?
103364
In  titled "CHOOSING AMONG GENERALIZED LINEAR MODELS APPLIED TO MEDICAL DATA" the authors write:     In a generalized linear model, the mean is transformed, by the link   function, instead of transforming the response itself. The two methods   of transformation can lead to quite different results; for example,   the mean of log-transformed responses is not the same as the logarithm   of the mean response. In general, the former cannot easily be   transformed to a mean response. Thus, transforming the mean often   allows the results to be more easily interpreted, especially in that   mean parameters remain on the same scale as the measured responses.   It appears they advise the fitting of a generalized linear model (GLM) with log link instead of a linear model (LM) with log-transformed response. I do not grasp the advantages of this approach, and it seems quite unusual to me.  My response variable looks log-normally distributed. I get similar results in terms of the coefficients and their standard errors with either approach.  Still I wonder: If a variable has a log-normal distribution, isn't the mean of the log-transformed variable preferable over the log of the mean untransformed variable, as the mean is the natural summary of a normal distribution, and the log-transformed variable is normally distributed, whereas the variable itself is not?
76747
I'm trying to fit a linear model on some data with just one predictor (say (x,y)). The data is such that for small values of x, the y values give a tight fit to a straight line, however as x values increase, the y values become more volatile. Here is an example of such data (R code)  y = c(3.2,3.4,3.5,3.8,4.2,5.5,4.5,6.8,7.4,5.9) x = seq(1,10,1)   I'm curious to know if there exists any power transform (Box cox perhaps?) that lets me get a better fit for the data than simply doing a linear fit as shown below.  fit = lm(y ~ x)
28105
Is it possible for more than one "linear regression" line to fit a given set of points? (i.e.... "least squares" is minimised equally in both cases)  I'm assuming a simple one-variable regression in which we have a single "dependent" variable for a given x-value. It may be that regression is forced "through the origin" for the purpose of the Q (if that matters), so, I know it wouldn't be a great fit.  Or is there something intrinsic about a regression line that means it is unique? I am interested in a 'proof' (could be just an intuitive proof) if it exists, that a regression line must be unique.
76990
For plot 1, I can test the association between x and y by doing a simple correlation.   For plot 2, where the relationship is nonlinear yet there is a clear relation between x and y, how can I test the association and label its nature?
6137
I am thinking of building a model predicting a ratio $a/b$, where $a \le b$ and $a &gt; 0$ and $b &gt; 0$. So, the ratio would be between $0$ and $1$.  I could use linear regression, although it doesn't naturally limit to 0..1.  I have no reason to believe the relationship is linear, but of course it is often used anyway, as a simple first model.  I could use a logistic regression, although it is normally used to predict the probability of a two-state outcome, not to predict a continuous value from the range 0..1.  Knowing nothing more, would you use linear regression, logistic regression, or hidden option c?
28221
I am trying to fit a model to predict a quantitative response variable, using several binary variables. In particular, I am interested in measuring the relationship between one of the binary variables and the outcome variable, holding the other binary variables constant.  My inclination is that ANOVA is the appropriate method to use. The advantage of ANOVA over a series of t-tests should be avoiding Type 1 errors. But I seem to recall from stats that ANOVA is primarily designed for predictor variables with more than 2 levels, aka not binary.   Which is preferable?  Final question: is there any reason not to use multiple regression in this case? Thanks.
112518
I am using a scale which consists of discrete values 0 (normal), 1 (mild), 2 (moderate), 3 (severe). I have used this scale for 200 patients.   I am going to find the correlation of this scale with some continuous variables, these variables also measured for 200 patients.   I don't think I can use multivariate or multiple regression because the dependent variable is discrete and the independent variables continuous. Can you please suggest a method to find this correlation?
114294
I've been studying the Cox Proportional Hazards model, and  this question is glossed over in most texts.    Cox proposed fitting the coefficients of the Hazard function using a partial likelihood method, but why not just fit the coefficients of a parametric Survival function using the maximum likelihood method and a linear model?    In any cases where you have censored data, you could just find the area under the curve.  For example, if your estimate is 380 with standard deviation of 80, and a sample is censored >300, then there is an 84% probability for that sample in the likelihood calculation assuming normal error.
110823
I am trying to predict what are the determinants for foreign direct investments in Lithuanian regions from 2011 to 2017.   My dependent variable is foreign direct investments per capita in Lithuanian regions. And I have a variety of explanatory variables such as unemployment rate, labor cost, infrastructure quality and so on.   However, the data is really not normally distributed. Data does not show any linearity.     That is why I cannot use the multiple linear regression.     I found out that for the data which has a Poisson distribution, two regressions are suitable: Poisson and Negative binomial regression.   According to my calculations the dispersion is higher that the mean, so I should use the negative binomial regression.   Please correct me if I am wrong.   Also, how do you account for changing variables in time? (From 2011 to 2017)
44946
I'm building a predictive model for a medical condition that happens in both men and women. Physicians have reported that in some cases for women, their menstrual history seems to be a risk factor, though epidemiologists haven't been able to verify this claim. My data includes information about female subjects' menstrual history. My goal is to build a logistic regression model that determines the probability of the existence of this condition.  Here's my problem: I'd like to build a model that includes gender and includes menstrual history questions for female subjects, but how do I assign values for male subjects for things like "number of months since last pregnancy"?  Is there a general method to deal with this kind of problem?
123696
I know correlation does not imply causation but instead the strength and direction of the relationship. Does simple linear regression imply causation? Or is an inferential (t-test, etc.) statistical test required for that?
79854
If I am correct, the linear regression model is said to be a model where the response is linear in the parameters. That allows the response to be nonlinear in the predictor variables.  I was wondering if there is a name for the model where the response is linear in both the parameters and in the predictor variables, so that people will easily understand its difference from the linear regression model?
50402
I've got a study which is kinda messed up by the design...Turns out I ended up with about 50 patients of which 80% have the outcome and 20% don't (binary outcome).  I've been turning in my bed for the last month trying to figure out what to do with this. The only real answer is "don't" but I have to deliver something in the next days as it's part of a master's thesis.  I have about 10 predictors of interest for the outcome (various variable types) and the research question is whether any of these predictors can predict the outcome. Some already have an established correlation in the literature while some are original hypothesis. Several are significant with a univariate logistic regression, but it doesn't look good in any other way than the actual p-value.  Now obviously I'm not going to be able to answer this research question sufficiently but if you were in my shoes, what sort of statistical analysis would you perform to relay to your supervisors?  EDIT: Link to my (anonymized) data (CSV):
1463
Let's say I am building a logistic regression model where the dependent variable is binary and can take the values $0$ or $1$. Let the independent variables be $x_1, x_2, ..., x_m$ - there are $m$ independent variables. Let's say for the $k$th independent variable, the bivariate analysis shows a U-shaped trend - i.e., if I group $x_k$ into $20$ bins each containing roughly equal number of observations and calculate the 'bad rate' for each bin - # observations where y = 0 / total observations in each bin - then I get a U shaped curve.  My questions are:   Can I directly use $x_k$ as input while estimating the beta parameters? Are any statistical assumptions violated which might cause significant error in estimating the parameters? Is it necessary to 'linearize' this variable through a transformation (log, square, product with itself, etc.)?
24468
I am trying to understand the benefit of propensity matching over non-parametric regression for causal inference from non-experimental data. As background: the way I understand it, parametric regressions are generally a poor choice for causal inference when selection bias exists. One can try to create a model that takes into account the different baselines between treatment and control groups, but she/he will be be extremely vulnerable to model misspecification.* Matching solves this issue by making the two datasets look &quot;alike.&quot; The exact meaning of alike depends on the matching algorithm used, but all the algorithms strive to eradicate model dependence, with the most common types being stratified and weighted propensity matching. The mathematics for these algorithms are well-developed, and in particular, we know how to extract error bars and statistical significance. What I'm struggling with is why this is superior to just using a non-parametric regression like a decision tree or random forest, which are also designed to prevent model misspecification. After creating the forest, one could run individuals through it assuming treatment or no treatment, and call the difference the estimated treatment effect for that individual. My first guess is that extracting significance, which is critical to causal inference, from trees is difficult, but it seems that statisticians have made strides in that regard over the last decade or so. To be clear, I am not asking about using a tree to develop the propensity scores, but to use one instead of propensity matching. To help kick off the conversation, I've developed five hypotheses for why matching is preferred to non-parametric regression, but haven't been able to find anything proving or disproving any:  Empirical research demonstrates that stratified or weighted propensity matching (the most common types) yield results closer to causal experiments than non-parametric regressions like trees.  Though it is possible to extract significance from non-parametric regressions like random forests, the math isn't settled, or the notion of &quot;significance&quot; for a decision tree variable doesn't map precisely to the notion of &quot;one minus the odds of a type I error.&quot;  Though it is possible to extract significance from non-parametric regressions, the code is difficult to write.  Model misspecification actually is an issue for decision trees due to the tuning required to run them. Empirical observation has demonstrated this is more of an issue for decision trees than it is for matching algorithms.  We don't actually know a lot about whether we can use non-parametric regressions for causal inference, but we do know that matching works, so it there's no reason to reinvent the wheel.   *As detailed in the first ten minutes of this wonderfully intuitive Youtube: