logistic regression on small dataset

Thank you for this posting it has been very helpful. It looks like pooled cross sections.

background-color:#3f3f3f; if(sub_menu.hasClass('responsive-menu-submenu-open')) { } event.preventDefault(); [The event rate to variable ratio is set flexibly at 5]. background-color:#3f3f3f; A more conservative approach would be to do exact logistic regression. Categorical Outcomes I am fitting a discrete hazard model, so it feels strange not to specify clustered standard errors. I don’t see what this buys you beyond what you get from just doing the single logistic regression on the sample of 1000 using the Firth method. Firth could definitely be helpful.

Amanda Montoya, Instructor width: 100%; And ML estimates of fixed and random effects automatically adjust for selection on observables, as long as those observables are among the variables in the model. case 13: link.click(); Hi Paul! 2) Applying exact logistic regression will provide only the p values but how can check the fitness and r square value or should i only concentrate on checking the p values. McFadden’s R2 is probably more useful in such situations than the Cox-Snell R2. I am a recently joined Phd student. } Please let me know how did you perform the postestimation analysis? I am wondering which logistic regression method is suitable for my data(exact, firth, rare-event,..???) $(subarrow).addClass('responsive-menu-subarrow-active'); /* Fix for when close menu on parent clicks is on */ This can be achieved by specifying a class weighting configuration that is used to influence the amount that logistic regression coefficients are updated during training.

Would you please suggest me? The prevalence of smoking and alcohol drinking in the study sample (cross sectional study) are 15% and 2%, respectively. this.isOpen = true; top:-8px; I have an experiment that has 1 indepdendent variable with 3 levels, sample size of 30 in each condition. Also, do we have to stick to the 5 events per predictor if we use Firth, or can we violate the rule completely, and if it is OK to violate it, do I have to mention a limitation about that?

$(this.trigger).removeClass(this.activeClass); I have a serious conflict at work. } width:25px; dummy variables for age and province, so that in total I am including about 40 independent variables) Thank you very much for this helpful post. 0000069803 00000 n If not, would the sample size be sufficient if I removed the interaction terms? : Exact logistic regression gave p = 0.012 in the packages in which it didn’t give memory problems (R logistiX and SAS PROC LOGISTIC). A Bayesian approach could possibly be beneficial, but I have no experience doing that with logistic regression. Logistic regression is one of the most utilised statistical analyses in multivariable models especially in medical research. While running the tests for this model, I plan to do percentage split. 1. In this tutorial, we will be using the Titanic data set combined with a Python logistic regression model to predict whether or not a passenger survived the Titanic crash. I work in fundraising and have developed a logistic regression model to predict the likelihood of a constituent making a gift above a certain level. I would like to use a logistic regression for the analysis. I am in political science and wanted to use rare events logit in Stata, but it does not allow me to use fixed or random effects.
$(self.trigger).blur(); Your task is to: Use Logistic Regression and come with predictions. The "logistic" distribution is an S-shaped distribution function which is similar to the standard-normal distribution (which results in a probit regression model) but easier to work with in most applications (the probabilities are easier to calculate). #home-banner { Let's say we place the sigmoid curve in our logistic regression model through these data points that we want to best fit a line to. Hi Paul, #responsive-menu-container .responsive-menu-search-box { So you may simply not have enough events to get reliable estimates of the odds ratios. Good question. Haider Mannan. You have 6760 incidents, but you say your dependent variable is not binary. position: absolute; No oversampling is necessary. I am thinking the 100 events could be to little. Therefore, this result has no meaning. Now, I need to predict when machine will be down based on the historical data, I have 5 columns, 1) Error logs – which were generated by the machine (non-numeric) Dear Prof. Allison: I have 1629 observations and a binary outcome variable.

my sample size is 2153 out of which only 67 are of one kind the rest are of the other kind. }; 'https://connect.facebook.net/en_US/fbevents.js';);

$('#responsive-menu-button, a.responsive-menu-item-link,#responsive-menu-wrapper input').focusout( function() { I have a general question. I wanted to add an analysis of the Model Fit Statistics and the Goodness-of-Fit Statistics like AIC, Hosmer-Lemeshow-Test or Mc Fadden’s R. After reading your book about the logistic regression using SAS (second edition) in my understanding all these calculations only make sense respectively are possible if the conventional logistic regression is used. Now, even programmers who know close to nothing about this technology can use simple, efficient tools to implement programs capable of learning from data. This practical book shows you how. According to Stata Manual on the complementary log-log, “Typically, this model is used when the positive (or negative) outcome is rare” but there isn’t much explanation provided. A small p-value indicates the . doesn’t have options to estimate either Firth’s or Gary kings

In my project ‘yes’responses of my dependent variable are 80-85% while ‘no’ responses are 14-18%.

In particular, does the low number of “positive” outcomes affect the number of predictors that can be included in a logistic model? That is, there are omitted predictors (independent of the included predictors) or variability in the coefficients. (My colleague recommended the count data model like ZINB model because conventional logistic regression generates a problem of underestimated OR due to zero excess.

The number of variables is about 50 most of which are categorical variables which on an average about 4 classes each. I think that standard goodness-of-fit tests would be problematic. But, very simply, to get more sensitivity, you can lower your cutoff for predicting events. thanks for your response. One of the two classes (class 1) has only 108 samples. You may need to do exact logistic regression (and probably should try it in any case).

Thanks in advance. Dear Dr. Allison, You might want to try to collapse it in meaningful ways. Modeling Binary Correlated Responses using SAS, SPSS and R How reliable is the P- value of firthlogit? I am thinking to use Poisson regression in case where event is rare, since p (probability of success) is very small and n (sample size is large). And I see know advantage in reducing the number of non-events by taking a random sample.

Also, what should be the best strategy here. So my advice is, if you can tolerate the computational burden, use the whole sample with the Firth method to reduce bias. I have a dataset of 10000 observations. gtag('js', new Date()); al. color:#ffffff; border-left:1px solid #212121; This is a legitimate concern. Besides, if I have 700 responders out of 60,000 samples and the variables in final model is 15, but the number of variables is 500 in the original varible selction process, do you think the 700 events are enough ? Thank you in advance for this fascinating discussion and for your assistance (if you reply, but if not I understand). Birth weight categories are my main predictor variables of interest, but I would also want to account for their time varying effects, by interacting BW categories with age-period. I have a data set of 949 observations sampled from 19 locations with 48 disease postive samples. button#responsive-menu-button img { The sample sice is 1 900 000. I would primarily want to know the percentage of INDIVIDUALS who have events. Found inside – Page 115k k 5.4 Logistic Regression 115 M1 and 0 elsewhere, Electrolytes a 1 in M2 and 0 elsewhere, and Steroids assigned 0 in both variables M1 and M2. This dataset is unrealistically small and only used to demonstrate how to obtain S from ... Would you be able to clarify this? And you may want to use the Firth method or exact logistic regression. } color:#ffffff; line-height:40px; I have a small data set (100 patients), with only 25 events. Four of the independent variables are statistically significant and 4 not. Reference: I am using xtnbreg in STATA to analyze about 40 separate groups over 11 years (so roughly 440 group-year observations). #home-banner-text { Now, set the independent variables (represented as X) and the dependent variable (represented as y): X = df [ ['gmat', 'gpa','work_experience']] y = df ['admitted'] Then, apply train_test_split. As I said in my post, what matters for bias is not the rarity of events (in terms of a small proportion) but the number of events that are actually observed.

In fact, a case could be made for always using penalized likelihood rather than conventional maximum likelihood for logistic regression, regardless of the sample size. Thank you very much for the advice.

} I believe SPSS does not offer exact logistic regression or the Firth method. Logistic Regression for Rare Events | Statistical Horizons It may not be too small. As I point on in the post, what matters is not the proportion of events but the actual number of events. This data set contains 2 continuous variables where one is an example of normally distributed data and the other one is an example of skewed data. Ideally this would be a survival analysis using something like Cox regression. Are you estimating your model only for the incidents? if(self.isOpen){

display: none; I got 20 events for my dependent variable (dummy 1 and 0). Of course, I understand that this still does not address selection on unobservables [and hence your comment about I cannot say that data is missing at random]. By the standard rule of thumb, you should be able to estimate a model with about 29 coefficients. @article{Steyerberg2000PrognosticMW, title={Prognostic modelling with logistic regression analysis: a comparison of selection and estimation methods in small data sets.

The standard (but very rough) rule of thumb is that you should have at least 10 events for each coefficient that you want to estimate.

Can we put “minimum number of events” data must have for modeling. I think you can reasonably go with standard logistic with robust standard errors. – dropping the continuous variable representing the distance to that particular substrate (as it only would be 0) top:25px;right:5%; } And there would be a cost: larger standard errors. )#ܙZ���늯��u*�5�p��_���E�����BƏ�zel�Ԁ*e&:���9Y�k�I�'�^��,@w*����j !��� ���@�Nv width: 100%; I can see now that if this size category only occurs in one particular substrate, perhaps I should focus the analysis only on that substrate type. #responsive-menu-container.slide-left { Logistic regression uses the sigmoid function to predict the output. } Remote Seminar Thank you for your answer, I have one last question. I am interested to determine what are the significant factors associated an “outcome”, which is a binary variable in my sample.My sample size from a cross-sectional survey is 20,000 and the number of respondents with presence of “outcome” is 70. transition-property: transform; chi²:0.000 For some reason, both logit and probit models give me null effects to variables that are significant under a linear probability model. } } -moz-transform: translateX(0); I have a small dataset (90 with 23 events) and have performed an exact logistic regression which leads to significant results. I have been always suggested that we should have 80-20 or 70-30 split for logistic regression. I’m working with a bariatric surgeon and we want to predict the likelihood of leaks post surgery (0 = no leak, 1 = leak) on a sample of 1,070 patients. triggerTypes: 'click', old_href = $(this).attr('href');

However, perhaps using a variable that perfectly separates the data for a particular size category might not be useful. If that’s the case, maximum likelihood methods (like random effects models) have the advantage over simply using robust standard errors. }, The firthlogit command is user written and thus may not support the post estimation use of the margins command. I am analyzing a rare event (about 60 in 15,000 cases) in a complex survey using Stata.

I think Firth could be helpful in this situation. Continue exploring. color:#ffffff; I am also unaware of any software that does Firth logit for multi-level models. Is it possible to included 12 independent variables in the model. #responsive-menu-container #responsive-menu ul.responsive-menu-submenu li.responsive-menu-item a:hover .responsive-menu-subarrow.responsive-menu-subarrow-active { Would a low R2 still represent a poor model ? I am in this situation right now and I badly need your help. Do the warnings of bias stated in the article above still apply with this estimation technique, and if so, would it be smart to change the estimation method to penalized quasi-likelihood? By lowering the cutoff, you can increase sensitivity but that may greatly reduce specificity. border-color:#3f3f3f; For the model build for my base, should I just use random sampling of my entire population and just make sure that I have a readable base of my events? Thank you for the insights. } But then you can’t use svyset to handle strata and psue. So the regression analysis with Firth or Exact method will not be appropriate for this situation either, right? case 'right': logistic-regression-and-xgboost-on-diabetes-dataset, https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwiv0cDEgK70AhWA4zgGHVmzBFoQFnoECAYQAQ&url=https%3A%2F%2Fwww.kaggle.com%2Fuciml%2Fpima-indians-diabetes-database&usg=AOvVaw2ilekeng_yP6oPctS-8i6s.

If so, can this be done in stata or another software? PDF To tune or not to tune, a case study of ridge logistic ... } pageWrapper: '', Best wishes 1.

border-color:#3f3f3f; .responsive-menu-open button#responsive-menu-button .responsive-menu-box { padding-bottom: 5px; Logistic Regression, Model Selection, and Cross Validation GAO Zheng March 25, 2017. . I’m not aware of any good reason to prefer complementary log-log over logit in rare event situations. Plz clarify me on this.

In the classification table With the full dataset I predict only about 10% of my abandoned and with the 50/50 I can predict about 90%.

So, yes, with 10 predictors, I’d switch to Firth or exact logistic. We are studying an event with a low incidence (0.8:1000 up to 10:1000) in a large dataset (n=1,570,635). Any recommendations???? #responsive-menu-container #responsive-menu-title, return; These can be unreliable when there is separation or near-separation, in which case likelihood ratio tests are preferable. Is the Firth method implemented for SAR or SMA models? – is there a way to obtain marginal effects after the firthlogit command in Stata? Which is preferred?

I don’t have any other recommendations. Notebook. In that case, I’d probably go with exact logistic regression. if ( dropdown.length > 0 ) { If I understand you correctly, I don’t think this should be a problem. I am running Logistic Regression on a categorical data set , hence the accuracy is a mere 16% but its worth checking out. } The sample size is small (less than 200), the number of successes is very small and all of them are in one of the categories of an explanatory variable (9 or 2 successes depending on how stringent the threshold to consider a success is). I am studying the prognostic value of a diagnostic parameter (DP) (numerical) for outcome (survival/death). If you’re using .5 as your cutoff for predicting an event vs. a non-event, you’re always going to get a much higher percentage correct for the non-events (“specificity”) than for the events (“sensitivity”). A different modeling technique is not necessarily going to do any better. But when we ran the logistic model, we did not apply any weight to bring the results to be representative of the population. 1. Yes, 96 events is sufficient. 3600.6 second run - successful. #responsive-menu-container #responsive-menu li.responsive-menu-current-item > .responsive-menu-item-link:hover { where denotes the (maximized) likelihood value from the current fitted model, and denotes the . data set by cross-validation, as its sampling variability contributes to the uncertainty in the regression coefficients. Linear regression datasets for machine learning.

But some literature suggests that you could go as low as 5 per variable, yielding 10 predictors. I have a data set with approximately 26000 cases where there are only 110 events. this.isOpen ? Shall we go for multivariable logistic regression for a sample size of 25 with three predictor variables? of hours the machine ran till failure thanks for your helpful post. They are 98 cases reported fistula from a sample of 16148 women. transform: translateY(0); .responsive-menu-open .responsive-menu-inner::after { case 'top': For example, you can set the test size to 0.25, and therefore the model testing will be based on 25% . My “rule” would imply that you could only estimate one coefficient. If you have a sample of 50 events and 10,000 non-events, the only benefit in sampling down to 50 non-events would be a tiny reduction in computation time. Nicolas. �\���& – STATA FIRTHLOGIT by default gives Wald-based p-values and CI's based. Many thanks. .logo { But with only 39 events and 12 predictors, you certainly don’t meet standard recommendations. Found inside – Page 26Exact logistic regression [12] is a method for fitting logistic regression models that produces valid estimates, test statistics and confidence intervals even for small datasets or sparse data. For example, exact logistic regression was ...

if($(e.target).closest('.responsive-menu-subarrow').length) { Anything you could offer here is appreciated. My question is whether I can trust the p-value for the interaction term (this is the only thing I need from this model). would be of great benefit to me. 0000048436 00000 n

} self.setWrapperTranslate(); Sometimes, when the number of bads is too small. It’s purpose is to ensure that the asymptotic approximations (consistency, efficiency, normality) aren’t too bad. What would you suggest? This allows me to include 3 (minimum) to 7 (maximum) independent variables in the estimations. In any case, the fact that you have zeroes in some cells of the contingency table means that you’ve got quasi-complete separation, and that’s a big problem for conventional logistic regression. $('.responsive-menu-button-text-open').hide(); background-size: cover; padding-left:15%; I am looking at comparing trends in prescription rates over time from a population health database. Run the model unweighted using both firthlogit and logistic. Feature Engineering for Machine Learning and Data Analytics If you have other predictors, do exact logistic regression. I wonder whether your EPV rule of thumb also applies to a multilevel setting because up to now, following your rule, I apply a simple multilevel logistic regression. Many thanks for your quick reply. I’m sorry but I really don’t have any knowledge or experience with postestimation after firthlogit. ����"�aR � !��s��b_�!��L!L?���7�wY�(ǚ�Y�� �(��}�c��E����� �X4x.�F�}0t0r�`8)u�� ����;C�A�&K�Zl� ��)�ft� ��L������p�ћ��N��� � 2�9�'XV00�$�2�6\2`\������ For examples see Sullivan & Greenland (2013, Bayesian regression in SAS software. Logistic regression needs a big dataset and enough training samples to identify all of the categories. If they give similar results, that’s reassuring. Am really not that happy with the accuracy rate of the model only 50% among predicted to result to the outcome had the actual outcome. Chapter 10 Binary Logistic Regression | Companion to BER ... Select some reasonably representative ML classifiers: linear SVM, Logistic Regression, Random Forest, LightGBM (ensemble of gradient boosted decision trees), AugoGluon (fancy automl mega-ensemble). I want to cluster the standard error at company level. self.closeMenu(); Proceedings of International Conference on Artificial ... - Page 13

I have included the location as a random effect in a glmer(R package lme4)logistic regression in R with approxiamtely 4 predictor variables in the final multivariate. Exact logistic regression is a useful method, but there can be a substantial loss of power along with a substantial increase in computing time. color:#ffffff; In one dichotomization, you’ve got 10/500 and in the other it’s 260/250. }

} if (jQuery('#responsive-menu-button').css('display') != 'none') { But if it’s because of drop out, then you have to worry about the data not being missing completely at random. Dear Dr. Allison 0000071021 00000 n Yes, logistic regression should be fine in this situation. this.isOpen = false; Mobile Computing and Sustainable Informatics: Proceedings of ... 174 0 obj<>stream Hi Dr. Allison, BTW, if you do dummy variables, there is no need to normalize them to a zero mean. 0000061221 00000 n @'u���̘��73fo���Y׼fm(AX����N�#�'K�] � \���2�@s1P�� ԰Y � ���ʸyx�(@�|\[��Uv�Z�O�������u�g�� Л*]�'k�(l��,�}!`ISPPII�ظ5Y An Introduction to Logistic Regression That suggests that you could reasonably estimate a model with about 10 predictors. If you need more information about the MNIST data set, take a look at this post. Any suggestions what kind of analysis to be used? So if you’re really interested in those coefficients, you may want to consider the Firth method to reduce the bias. 0000002675 00000 n #responsive-menu-container #responsive-menu ul.responsive-menu-submenu.responsive-menu-submenu-open { background-color:#ffffff; If you want a higher c-stat, try getting better predictor variables. background-color:transparent !important; As I understand a random effect cannot be used with Firth’s but I could be mistaken as I am not hugely familiar with this method? You can do this with PROC NLIN in SAS or the nl command in Stata. .responsive-menu-boring.is-active .responsive-menu-inner::after { Time-Series, Domain-Theory . (Your words ‘quite safe’ in your reply imply that he is wrong, I guess) After reading your work, I am not even sure my events are rare. For a dataset with similar prevalence of the two outcome levels and sufficient sample size, the maximum likelihood estimation of the regression coefficients facilitates inference, i.e. I want to increase the number of events by bootstrapping and thus the events are enough to make parameter estimation. Logistic Regression: Large dataset, small coefficients? If you definitely want to sample, I would take all 4500 cases with events. I plan to begin with 20 predictors and use the Penalized Method due to some of my predictor variables also being ‘rare’ (< 20 in some categories). I am trying to assess the association between the outcome variable(binary) and independent variable (categorical). You have mentioned that 2000 events out of 100,000 is a good sample for logistic regression, which is 98% – 2% split. input[type=submit].um-button, Let us first import all the required libraries, data and explore the dataset. breakpoint:768, In the panel data setting,the binary dependent variable is skewed towards positive outcomes such that there are 1330 events (ones) and 25 non events (zeros) in my sample. Mehta, Cyrus R., Nitin R. Patel, and Pralay Senchaudhuri. If results are pretty close, then just use logistic with svyset. } If the response rate (i.e. What method do you recommend me to use when I have 3600 observations and 80 events? 0000005781 00000 n background-image: url(https://statisticalhorizons.com/wp-content/themes/statisticalhorizons/images/banner-bg.jpg); To make the logistic regression model work as a classification model we have to apply a small trick (don't worry it won't be difficult). Do you know if/how either one of these options can be implemented as a regularized model (ideally in python or R)? Does Firth logit automatically account for clustered observations? (i = {1,n} ) Evidence-Based Statistics: An Introduction to the Evidential ... I know that the judgment of rare events pertains to the overall data set and not to individual variables, but I can’t help thinking that variables like Pred 5 are potentially very unstable. Similar to using “Dummy Variables” for category based predictors. You could try the ZINB model, but see my blog post on this topic. Someone in the The dependent variable has 600 events.

My question is, do you really need to sample? #responsive-menu-container #responsive-menu li.responsive-menu-item a .responsive-menu-subarrow{ For p-values, I’d recommend exact logistic regression.

when the sample size is small.
} e.stopPropagation(); $('#responsive-menu li').css({"opacity": "1", "margin-left": "0"}); first of all, thank you for the work you are doing with this blog.

So often, results are described as the latter.

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