Categorization may be ok when

• the distribution is clearly multimodal and the categorization captures the different modes, or
• there is a theoretically justified (more or less sharp) border line (example: I think of age post fertilization; categorizing "pre-natal" vs. "post-natal" is usually ok, since the birth is a major, obvious and relatively sharp border).

These are rare and special cases. In most cases where categorization is done, it is not ok. One should usually not categorize but instead model the variable as continuous. If the variable in question (e.g. age) is a relevant predictor in the model, one should come up with a meaningful functional relationship between this predictor and the dependent variable. If it is instead used as a covariable (to adjust for), one can use over-parametrized functions (e.g. splines) that allow for arbitrary flexible functional relationships with the dependent variable.

Categorizing a continuous independent variable has many consequences: loss of information and statistical power, underestimate the variance, residual confounding, obscure the non-linearity, etc. The best practice is not doing categorization. Sometimes it is recommended to categorize in multiple groups on the ordinal scale. Also, check whether the transformation of the variable is helpful. Check these two articles: https://www.bmj.com/content/332/7549/1080.1

Article On the Practice of Dichotomizing Quantitative Variables

The answer boils down to one question: Does the x have a uniform relationship with y or not, i.e. either a linear positive effect or a linear negative effect. If yes, there is no need to categorize. If no, you have to address then non-linearity between x and y in some way. If you have few observations, the typical way to proceed is by quadratic regression (x-squared and so on). If you have lots of observations, you MAY ALSO try out some categorization of x and use a set of dummy variables (and a reference value) to highlight the non-linearity in the most efficient way. In some instances, you might also have a theoretical reason for where to set the "thresholds" on the x-variable.

There is no simple answer.

Some continuous variables have accepted cutpoints – body mass index, for example, or birth weight. However, categorisation always loses information.

I always recommend starting by looking at a graphical display, and using a smoother to check that the relationship is adequately summarised by a linear model.

One can categorize the continuous predictors in regression models if it will give a better understanding of relationship among variables especially when dealing with age related issues.

As has been noted, categorization always loses information. However, it can be a useful simplification for some purposes. As a rule of thumb I think using continuous data for modeling and using categorization to explore or describe the behavior of a model (e.g., graphically) can be a good combination. It should always be done with care.

I've also done research where we've categorized continuous information for practical purposes (related to the computational and practical difficulties of that specific context). A good tip is to use a large number of categories. For a normal distribution reducing to two categories loses about 1/3 of the information (in terms of statistical power). Using 3, 5 or 7+ categories would be better (e.g., we used 9 categories and when we did some checking there was negligible practical loss of information in our case).

You can include the continous and the categorized. For example, in US driving age is 16, so predicting parent stress by kid's age:

stress = b0 + b1 age + b2 (age >= 16) + e

The answer to the question depends on the objectives of the study. If a researcher is interested in the effects of each level of a categorised predictor on the dependent variable, He/she has no alternative than to categorise the predictor variable even though information will be lost. Otherwise, the predictor variable will remain continuous.

Generally, it is advisable to leave the predictor variable (e.g. age) as continuous when carrying out regression model to avoid loss of information unless the research interest lies on the effects of the levels of the categorised predictor variable.

Actually, Thom Baguley 's answer made me recall one very useful application of categorising a continuous variable.

If you have a predictor variable that is on an arbitrary scale (for example, a score on a health anxiety questionnaire) and you want to calculate a measure of effect size, then using a standard score will probably be inaccurate because these scales are often highly skewed, and may have floor or ceiling problems.

An alternative is the use quantiles. In the case of health anxiety, we were able to report that compared with a person in the lowest quintile of health anxiety, a person in the highest quintile would make roughly one extra visit to their family doctor each year. Multiply this up by the one fifth of the population in the highest quintile and it's a lot of visits!

Dealing with ordinal scales as predictors is an area that is rather neglected, come to think of it.

Ronán Michael Conroy - that is a good example of using continuous info in the modeling and using categories to explore, explain and communicate findings.

If the underlying data are categorical it is is more complex and there are trade-offs. With modern computing power however it is increasingly possible to model ordinal and discrete data.

Peter Koleoso - I think the key point is that there is rarely a need to categorise the predictor in the model. You can derive predictions for different categories from the underlying model.

When error term does not have the properties you want, you can use binning of the age variable:

https://docs.tibco.com/pub/spotfire/7.0.1/doc/html/bin/bin_what_is_binning.htm

It is, however, more desirable to keep it as it is or apply transformations depending on the distribution. You can use this guide to choose the right transformation:

https://xdplot.blogspot.com/p/data-transformations-guidelines.html

Thank you all for your great answers. They were very helpful to me. To this point, I can conclude from the comments that generally we should try to keep the predictor continues unless:

a) When there is a well-known qualitative scale for the variable that leads to a meaningful inference (as mentioned by Ronán Michael Conroy Awoyomi O. J. Peter Koleoso )

b) When there are few values of the continues variable or a non-linear relationship (as mentioned by Christer Thrane Thom Baguley ).

I would be appreciated if anyone can add any other point to this.

One time I used categorization to overcome the collinearity.

Sometimes, it is the easiest but less elegant way of estimating non-linear effects. For instance, the options for Non-parametric models are fewer in longitudinal models, so the simple categorization makes it easier.

Seyyed Amir Yasin Ahmadi – I don't see how categorisation would overcome collinearity, except that by losing almost all of the variance in the variable it reduces the correlation to near zero. Which means that you are essentially suppressing the variable by a sort of gagging effect.

Can you describe the situation in more detail? It sounds curious…

Ronán Michael Conroy

Yes, you are right! collinearity is not overcome by mere categorization. It can just decrease inter-correlation coefficient (of course sometimes it may decrease some matrix cells to lower than 0.7). In general, in models with more of binary and factorial variables occurring collinearity is lower (I think because the algorithm of software packages for collinearity detection is based on Pearson correlation).

However, as you know, in nowadays of statistics we are facing with complex datasets. We don't know what are our specific aims until we face with the results of our analyses unlike routine research proposals. Therefore, we should perform many trial and errors to achieve a suitable result.

An example of trial and error to find the best model is categorization.

About to overcome collinearity, I checked again my previous work that I mentioned it in my above post. It was a set of changes including reducing the number covariates, integration of some variables as well as categorization. Yes, this overcoming was not attributed to my categorization.

Best!

Daniel Wright wrote: "You can include the contin[u]ous and the categorized."

Apologies if someone else already noted this, but yes, that is exactly what one does when fitting a piecewise (or spline) model. See this page for some simple examples (using Stata):

• https://stats.idre.ucla.edu/stata/faq/how-can-i-run-a-piecewise-regression-in-stata/

Bruce Weaver , good adding this! I didn't mention splines because the norm using these the user does not choose where to have the knots but the algorithm calculates the median or tertiles or whatever. I interpreted the "we catgorize" part of the question as this, and of course in splines you can choose them, that people usually try to make the spline smooth at the not (e.g., if the spline is cubic, being quadrative at the knot). I also was think where the break point is meaningful so a discontinuity. So like zero inflated models. So piecewise regression of which splines is an example. So depends what the questioner is thinking. Splines are nice in terms of saving degrees of freedom.

For logistic regression, categorization can be used to deal with a violation of the assumption of linearity at the log odds. Read Hosmer and Lemershow on this issue. Otherwise what agree with Jochen Wilhelmùs idea (distribution clearly multi-modal + theoretical justification)

One situation in which we need categorizing continuous data is handling inapplicable features.

Suppose for a certain model, feature-2 depends on the answer of feature-1 … and featue-1 is missing in many instances.

So, we can categorize feature-2 into some categories, one of them should be Inapplicable for example.

For more info, you can read this paper:

"Missing or Inapplicable: Treatment of Incomplete Continuous-valued Features in Supervised Learning"

http://cse.msu.edu/~ptan/papers/sdm2013b.pdf