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Questions tagged [model]

A formalization of relationships between stochastically (randomly) related variables in the form of mathematical equations. DO NOT USE THIS TAG BY ITSELF: always include a more specific one.

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Definition and delimitation of regression model

An embarrassingly simple question -- but it seems it has not been asked on Cross Validated before: What is the definition of a regression model? Also a support question, What is not a regression ...
Richard Hardy's user avatar
45 votes
4 answers
61k views

Should covariates that are not statistically significant be 'kept in' when creating a model?

I have several covariates in my calculation for a model, and not all of them are statistically significant. Should I remove those that are not? This question discusses the phenomenon, but does not ...
A.M.'s user avatar
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27 votes
8 answers
98k views

When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]

I have a regression model to estimate the completion time of a process, based on various factors. I have 200 trials of these processes, where the 9 factors being measured vary widely. When I perform a ...
Zack Newsham's user avatar
49 votes
2 answers
77k views

Mixed Effects Model with Nesting

I have data collected from an experiment organized as follows: Two sites, each with 30 trees. 15 are treated, 15 are control at each site. From each tree, we sample three pieces of the stem, and ...
Erik's user avatar
  • 545
44 votes
2 answers
6k views

Why should we use t errors instead of normal errors?

In this blog post by Andrew Gelman, there is the following passage: The Bayesian models of 50 years ago seem hopelessly simple (except, of course, for simple problems), and I expect the Bayesian ...
Potato's user avatar
  • 1,105
17 votes
5 answers
14k views

Is R-squared truly an invalid metric for non-linear models?

I have read that R-squared is invalid for non-linear models, because the relationship that SSR + SSE = SSTotal no longer holds. Can somebody explain why this is true? SSR and SSE are just the ...
Greg's user avatar
  • 323
6 votes
2 answers
5k views

Which model should I use to fit my data ? ordinal and non-ordinal, not normal and not homoscedastic

Here is the kind of data I have: I have two predictor variables: discrete non-ordinal --> c('a', 'b', 'c') discrete ordinal --> ...
Sulawesi's user avatar
  • 349
32 votes
5 answers
5k views

How can you account for COVID-19 in your models?

How are you dealing with the coronavirus "event" in your machine learning models? Let's say you used to predict the number of sales each month. The virus affected your results last year and ...
dsbr__0's user avatar
  • 827
18 votes
1 answer
9k views

The difference between with or without intercept model in logistic regression

I like to understand the difference between with or without intercept model in logistic regression Is there any difference between them except that with the intercept the coefficients regard the log(...
user148087's user avatar
16 votes
3 answers
31k views

Should I remove non-significant variables from my regression model

I have run a multiple linear regression using stepwise regression to select the best model, however the best model returned has a non-significant variable. When I remove this the AIC value goes up ...
Poppy's user avatar
  • 161
15 votes
1 answer
16k views

Interpreting the regression output from a mixed model when interactions between categorical variables are included

I have a question about my use of a mixed model/lmer. The basic model is this: lmer(DV ~ group * condition + (1|pptid), data= df) Group and condition are both ...
vizzero's user avatar
  • 275
31 votes
6 answers
9k views

In layman's terms, what is the difference between a model and a distribution?

The answers (definitions) defined on Wikipedia are arguably a bit cryptic to those unfamiliar with higher mathematics/statistics. In mathematical terms, a statistical model is usually thought of as ...
AlanSTACK's user avatar
  • 640
8 votes
4 answers
5k views

What is a 'true' model?

A short question, but I am somehow unable to find any concrete answer. I suppose it means that the model is as good as it can be? Containing all relevant variables and hence not suffering from any ...
Anon's user avatar
  • 199
5 votes
2 answers
1k views

Coronavirus growth rate and its possibly spurious resemblance to vapor pressure model

I collected the latest data on the coronavirus from Johns Hopkins University as shown and fitted different curves to this data to model the relationship between the number of confirmed patients $P$ ...
Stats IT's user avatar
  • 548
35 votes
5 answers
10k views

Is an overfitted model necessarily useless?

Assume that a model has 100% accuracy on the training data, but 70% accuracy on the test data. Is the following argument true about this model? It is obvious that this is an overfitted model. The ...
Hossein's user avatar
  • 3,494
10 votes
2 answers
16k views

Fitting exponential decay with negative y values

I am trying to fit an exponential decay function to y-values that become negative at high x-values, but am unable to configure my nls function correctly. Aim I ...
Mikko's user avatar
  • 1,332
7 votes
1 answer
3k views

If ϵ is uniformly distributed, then a linear probability model is appropriate? Can I find any Literature?

A latent variable model involving a binomial observed variable $Y$ can be constructed such that $Y$ is related to the latent variable $Y^*$ via $ Y = \begin{cases} 0, & \mbox{if }Y^*...
user37115's user avatar
29 votes
4 answers
4k views

Is there any theory or field of study that concerns itself with modeling causation rather than correlation?

My understanding is that probability (at least from a frequentist viewpoint) is a mathematical tool for modeling correlations. So, for example, we can say that two events $X$ and $Y$ are defined to be ...
Maximal Ideal's user avatar
15 votes
3 answers
2k views

How can I fit a spline to data that contains values and 1st/2nd derivatives?

I have a dataset that contains, let's say, some measurements for position, speed and acceleration. All come from the same "run". I could construct a linear system and fit a polynomial to all of those ...
dani's user avatar
  • 203
11 votes
1 answer
11k views

Model selection for GAM in R

Apologies in advance I new to this forum and to GAM models. I am trying to model complex ecological data. I have programmed a lot of GAM models using the mgcv ...
Kilian Murphy's user avatar
5 votes
1 answer
1k views

Linear model with constraints on coefficients in terms of ratios

How to fit a linear model (such as lm() in R) of the form: $$y = a_1 x_1+ a_2 x_2+ a_3 x_3 + a_4 x_4 + a_5 x_5 + \epsilon$$ with the constraint that : $a_2a_5 = ...
Toby1729's user avatar
1 vote
1 answer
1k views

Cox Model and proportional hazards

I'm trying to fit a Cox model, but there is some problems. I have the following variables in the model. Group: 1, 2, ..., 9 Sex: 1 female and 0 male Weight Age The first thing that I did is split ...
user avatar
8 votes
2 answers
3k views

Why is a Normal Mixture Model not identifiable and why does it matter?

Suppose that we have a mixture model: $$ p_\theta(y) = \sum_{k = 1}^{K}w_k \phi(y;\mu_k, \sigma^2_k) $$ where $\phi(y;\mu_k, \sigma^2_k)$ is the normal density at $y$ with mean $\mu$ and variance $\...
user321627's user avatar
  • 4,428
40 votes
7 answers
6k views

Should parsimony really still be the gold standard?

Just a thought: Parsimonious models have always been the default go-to in model selection, but to what degree is this approach outdated? I'm curious about how much our tendency toward parsimony is a ...
theforestecologist's user avatar
28 votes
1 answer
37k views

what happens when a model is having more parameters than training samples

In a simple neural network, say, for example, the number of parameters is kept small compared to number of samples available for training and this perhaps forces the model to learn the patterns in the ...
Upendra01's user avatar
  • 1,956
24 votes
3 answers
45k views

What is a null model in regression and how does it relate to the null hypothesis?

What is the null model in regression and what's the relationship between the null model and the null hypothesis? From my understanding, does it mean Using "an average of the response variable&...
Haitao Du's user avatar
  • 37.1k
22 votes
2 answers
4k views

What would be an example of a really simple model with an intractable likelihood?

Approximate Bayesian computation is a really cool technique for fitting basically any stochastic model, intended for models where the likelihood is intractable (say, you can sample from the model if ...
Rasmus Bååth's user avatar
18 votes
2 answers
746 views

Statistical Inference Under Misspecification

The classical treatment of statistical inference relies on the assumption that that a correctly specified statistical is used exists. That is, the distribution $\mathbb{P}^*(Y)$ that generated the ...
Julian Karch's user avatar
  • 1,980
16 votes
1 answer
1k views

Is there any "standard" for statistical model notation?

In, for example, the BUGS manual or the upcoming book by Lee and Wagenmakers (pdf) and in many other places a type of notation is used that to me seems very flexible in that it can be used to ...
Rasmus Bååth's user avatar
15 votes
3 answers
2k views

What are the options in proportional hazard regression model when Schoenfeld residuals are not good?

I am doing a Cox proportional hazards regression in R using coxph, which includes many variables. The Martingale residuals look great, and the Schoenfeld residuals ...
jeffalstott's user avatar
14 votes
8 answers
35k views

Flexible and inflexible models in machine learning

I came across a simple question on comparing flexible models (i.e. splines) vs. inflexible models (e.g. linear regression) under different scenarios. The question is: In general, do we expect the ...
alittleboy's user avatar
  • 1,013
13 votes
2 answers
28k views

How to know if model is overfitting or underfitting?

I understand that using cross validation we can validate our model, but it is also possible that maybe our model is underfitting; hence, providing wrong results. One possibility that I can think of is ...
DKP's user avatar
  • 241
13 votes
4 answers
8k views

Can Tree-based regression perform worse than plain linear regression?

Hi I'm studying regression techniques. My data has 15 features and 60 million examples (regression task). When I tried many known regression techniques (gradient boosted tree, Decision tree ...
amityaffliction's user avatar
11 votes
1 answer
3k views

How can I tell if a statistical model is "identified"?

My econometrics professor used the term "identified" in class. We are considering data generating processes of the form $$Y = \beta_0 + \beta_1 X + U$$ where $X$ is a random variable and $U$ is a ...
Stan Shunpike's user avatar
8 votes
4 answers
24k views

Is MSE decreasing with increasing number of explanatory variables?

I am wondering, if there is a negative correlation between Mean Squared Error \begin{equation} MSE = \frac{1}{n} \sum (\hat{Y}_i - Y_i)^2 \end{equation} and the number of explanatory variables. ...
Joachim Schork's user avatar
8 votes
3 answers
16k views

Comparing Cox proportional hazards models - AIC?

I have some very empirical data derived from texture analysis of radiology images of lung cancer. As a result of post-processing, there are two nearly identical datasets of 53 cases each, differing ...
Maelstorm's user avatar
  • 286
7 votes
1 answer
563 views

Is there a counterexample to the claim that throwing away "insignificant" predictors doesn't generally harm a model?

I have learned from this site (see question here), and from Frank Harrell's Regression Modeling Strategies that generally speaking one should not remove variables because they are insignificant. I was ...
Lepidopterist's user avatar
7 votes
1 answer
929 views

Are these data underdispersed? If so, what mechanisms may explain this?

Say someone who is well practiced (appears to have reached a performance plateau) shoots 20 free throws on 15 different days and is successful the number of times shown in the upper histogram (...
Livid's user avatar
  • 1,168
6 votes
4 answers
573 views

Bayesian inference and testable implications

I have one question regarding testable implications of a model and Bayesian inference. My main doubt is how to exploit testable implications to reject a model. Here is a simple example. Suppose my ...
user avatar
6 votes
2 answers
839 views

Variance as a function of parameters

I am currently building a statistical model. According to data, the variance is non-constant, and it is likely based on a factor. Is there any statistical model with variance as a function of other ...
ucanuup's user avatar
  • 147
6 votes
1 answer
560 views

Determining if a function is additive

I have data collected on a grid of values $f(x,y)$. I have a hypothesis that the data is "additively separable", i.e. $$ f(x,y) = h_1(x) + h_2(y) + g(x,y) $$ where $g(x,y)$ is small and only ...
Hooked's user avatar
  • 441
5 votes
3 answers
2k views

Does AIC require the residuals of the model to be normally distributed?

Does AIC require the residuals of the models to be compared to be normally distributed?
Jacqueline's user avatar
5 votes
0 answers
5k views

AIC or ANOVA to compare models?

What are the relative merits of each approach, and which circumstances call for one rather than the other? To some extent I have a specific example in mind, which I've discussed here. In that example ...
user1205901 - Слава Україні's user avatar
5 votes
3 answers
10k views

Using AIC, for model selection when both models are equally weighted, and one model has fewer parameters

I am using AIC (Akaike information criterion) for model selection. There are 2 models. The first model has 2 parameters with log likelihood of -10182.0284 and the second model has 3 parameters with ...
Vass's user avatar
  • 1,695
5 votes
1 answer
2k views

How to check permutation testing exchangeability assumption when using a General Linear Model

I have a question on the assumption of exchangeability in permutation tests. Although I read a lot about this topic, I am still confused. For $N$ subjects, I have the value of a clinical measure $Y$ (...
Helm's user avatar
  • 91
3 votes
0 answers
6k views

How to fit exponential y=A(1-exp(B*X)) function to a given data set? Especially how to determine the initial start parameters? [duplicate]

I have a data set in which $y$ is roughly related to $\log(x)$. Now I wish to fit the curve $$y=A(1-\exp(BX))$$ When I use R and the nls2 function, then I ...
Aditya Vikram Singh's user avatar
2 votes
1 answer
331 views

Is best model selection by RSS equivalent to best model selection by R2 value?

I am trying to compare models using K-Fold-CV using the regsubsets function in R. By default, it states that the ideal model is determined by the $RSS$. I wished to ...
h3ab74's user avatar
  • 133
2 votes
2 answers
218 views

What is a "model" in machine learning?

In every machine learning discussion, the term "model" is used to describe how the prediction is made. Does this "model" refer to the learning algorithm used? What exactly is a model?
yathirigan's user avatar
1 vote
1 answer
6k views

linear probability model interpretation

I have a question regarding the interpretation of a log independent variable in a linear-probability model. For example: I have $\log(GDP)$ as my independent variable and the coefficient is 0.35. Can ...
Julian's user avatar
  • 11
1 vote
1 answer
1k views

Difference in Differences Model Specification with Year-Quarter Effects (treatment non-binary)

I am currently creating a difference-in-differences (DiD) model and have a few questions left: I am examining the effect of Airbnb-listings on the hospitality industry in major German cities. I have ...
Markus R's user avatar