I have enjoyed two trips with Manfred. The first was to Rennes. We developed statistical software (in R) and we were to present it at a conference. It was a great adventure for me, as I was still a student who had attended few conferences before. I remember the midnight sessions, frantically working to program new features, and to improve performance. Making it the best we could. But I also remember the open conversations we had, about family, about mental illness. About unconventional paths into university.

The second trip it was only Manfred travelling, as he came to visit me in Stockholm. Again, we were to work on a statistical software project and this time we thought it would be easy. How wrong we were. We worked days on end without getting any closer. Long days trying all kinds of angles, but everything we tried failed. At the end of another long weekend-day of relentlessly failing to solve our puzzle, and just in time before our frustration reached a boiling point, we decided to take a break and go for dinner. And just like that, over a steak, we had our breakthrough. Manfred matched my vague intuition with the expertise to come to a formal solution. It’s the moment captured in this photo. The excitement! We raced home to do more testing, and early in the next morning Manfred confirmed: We nailed it!

This is how I will remember Manfred. I enjoyed working with him so much, and he was a fantastic teacher. Driven to be the best, energetic to get everything right. A very friendly guy, into good music. He loved his job and continued teaching even when he got sick. He had the unique ability to talk about statistics to very different audiences: complex scientific debates on statistical methods, motivating reluctant students to learn statistics, and entertaining a crowd at a music festival with a lesson on probability theory (‘This can’t be a coincidence!’). He could be stubborn and short-tempered when things didn’t work out. And Manfred was very involved when it came to personal matters. At my graduation, he spoke about what my family was going through, how death comes ‘unexpectedly and deviously’.

His e-mail, this summer, came as a shock. Braintumor. I’m grateful that we still had the chance to exchange a few emails, and share some memories. Manfred approached his death without remorse, and lived his final days in the moment. He enjoyed these days, undertaking adventures with a group of friends, and even gave a hashtag to the whole process, in Dutch and untranslatable: #derannn.

The attractive property of applying weighted effect coding to categorical (‘factor’) variables is that each category represents the deviation of that category from the sample mean. This is unlike the more commonly used treatment coding where each a specific category has to be selected as a reference. Weighted effect coding is a generalized form of effect coding that applies to both balanced and unbalanced data.

A form of weighted effect coding was already formulated in 1972 by Sweeney and Ulveling, but it seems to never have found its place in statistical repertoires. Weighted effect coding was not implemented in mainstream statistical software. In an ongoing project, we have now further developed weighted effect coding to also apply to interactions (with both categorical and continuous variables), and provide procedures for mainstream statistical software. For R, we developed the ‘wec’ package, and procedures for STATA and SPSS are available as well.

A key innovation in our article in the R Journal is the formulation of interactions between a categorical variable with a continuous variable. This is visualised in the Figure above. The benefit of estimating such an interaction with weighted effect coding is that upon entering the interaction terms the estimate for the continous variable (as well as the ‘main effects’ for the categorical variable) does not change. The ‘main’ continous term reflects the average effect in the sample, and the interaction terms represent the deviation of the effect size for each category.

References

Grotenhuis, Te, M, Pelzer, B., Eisinga, R., Nieuwenhuis, R., Schmidt-Catran, A., & Konig, R. (2017b). A novel method for modelling interaction between categorical variables. International Journal of Public Health, 62(3), 427–431. (open access!)

Grotenhuis, Manfred, Ben Pelzer, Eisinga, R., Nieuwenhuis, R., Schmidt-Catran, A., & Konig, R. (2017a). When size matters: advantages of weighted effect coding in observational studies. International Journal of Public Health, (62), 163–167. (open access!)

Nieuwenhuis, R., Grotenhuis, Te, M., & Pelzer, B. (2017). Weighted Effect Coding for Observational Data with wec. R Journal, 9(1), 477–485. (open access!)

Sweeney, R. E., & Ulveling, E. F. (1972). A transformation for simplifying the interpretation of coefficients of binary variables in regression analysis. The American Statistician.

To avoid choosing a reference category, weighted effect coding provides estimates representing deviations from the sample mean. This is particularly useful when the data are unbalanced (i.e., categories holding different numbers of observation). The basics of this technique, with applications in R, were detailed here.

In a new publication, available open access,, we show that weighted effect coding can also be applied to regression models with interaction effects (also commonly referred to as moderation). The weighted effect coded interactions represent the additional effects over and above the main effects obtained from the model without these interactions.

To apply the procedures introduced in these papers, called weighted effect coding, procedures are made available for R, SPSS, and Stata. For R, we created the ‘wec’ package which can be installed by typing:

install.packages(“wec”)

References (Open Access!)

Grotenhuis, M., Ben Pelzer, Eisinga, R., Nieuwenhuis, R., Schmidt-Catran, A., & Konig, R. (2017). A novel method for modelling interaction between categorical variables. International Journal of Public Health, 62(3), 427–431. http://link.springer.com/article/10.1007/s00038-016-0902-0

Grotenhuis, M., Ben Pelzer, Eisinga, R., Nieuwenhuis, R., Schmidt-Catran, A., & Konig, R. (2017). When size matters: advantages of weighted effect coding in observational studies. International Journal of Public Health, 62(1), 163–167. http://doi.org/10.1007/s00038-016-0901-1

If all categories have (roughly) the same number of observations, you can also test all categories against the grand mean using effect (ANOVA) coding. In observational studies, however, the number of observations per category typically varies. Our new paper shows how categories of a factor variable can be tested against the sample mean. Although the paper has been online for some time now (and this post is an update to an earlier post some time age), we are happy to announce that our paper has now officially been published a the International Journal of Public Health.

To apply the procedures introduced in these papers, called weighted effect coding, procedures are made available for R, SPSS, and Stata. For R, we created the ‘wec’ package which can be installed by typing:

install.packages(“wec”)

References

Grotenhuis, M., Ben Pelzer, Eisinga, R., Nieuwenhuis, R., Schmidt-Catran, A., & Konig, R. (2017). When size matters: advantages of weighted effect coding in observational studies. International Journal of Public Health, (62), 163–167. http://doi.org/10.1007/s00038-016-0901-1

Sweeney R, Ulveling EF (1972) A transformation for simplifying the interpretation of coefficients of binary variables in regression analysis. Am Stat 26:30–32

Exact p-values for pairwise comparison of Friedman rank sums, with application to comparing classifiers, Eisinga, Heskes, Pelzer & Te Grotenhuis, BMC Bioinformatics, 2017, 18:68. http://dx.doi.org/10.1186/s12859-017-1486-2

Grotenhuis, M., Ben Pelzer, Eisinga, R., Nieuwenhuis, R., Schmidt-Catran, A., & Konig, R. (2016b). When size matters: advantages of weighted effect coding in observational studies. International Journal of Public Health, 1–5. http://doi.org/10.1007/s00038-016-0901-1

Grotenhuis, M., Ben Pelzer, Eisinga, R., Nieuwenhuis, R., Schmidt-Catran, A., & Konig, R. (2016a). A novel method for modelling interaction between categorical variables. International Journal of Public Health, 1–5. http://doi.org/10.1007/s00038-016-0902-0

As some of the real advantages of weighted effect coding come into play when using interactions, that was what we focused in the current update to our ‘wec’ package (version 0.4). The package now supports interactions between a weighted effect coded factor variable and an interval variable, and the calculation of interactions between two weighted effect coded factor variables was much improved. An example is given below (with more to follow, hopefully soon).


library(wec)
data(PUMS)
PUMS$race.wec <- factor(PUMS$race)
contrasts(PUMS$race.wec) <- contr.wec(PUMS$race.wec, "White")
PUMS$race.educint <- wec.interact(PUMS$race.wec, PUMS$education.int)
m.wec.educ <- lm(wage ~ race.wec + education.int + race.educint, data=PUMS)
summary(m.wec.educ)$coefficients


The code above results in a regression model (shown below) in which the main effect for education (9048) remains the same, whether the interaction terms are included or not (you can try this yourself). Thus, the interaction terms represent how much the average education effect varies by race.

                            Estimate Std. Error t value Pr(>|t|)
(Intercept)                     52320        559    93.5  0.0e+00
race.wecHispanic                -4955       1736    -2.9  4.3e-03
race.wecBlack                  -11276       1817    -6.2  5.7e-10
race.wecAsian                    5151       2381     2.2  3.1e-02
education.int                    9048        287    31.6 2.3e-208
race.educintinteractHispanic    -3266        977    -3.3  8.3e-04
race.educintinteractBlack       -3293        990    -3.3  8.8e-04
race.educintinteractAsian        3575       1217     2.9  3.3e-03

Manfred te Grotenhuis is currently visiting the Swedish Institute of Social Research (SOFI), where he presented our joint work on Weighted Effect Coding. The recoding of his presentation is available on Manfred’s YouTube channel, and embedded below:

The relevant papers are available here (open access):

• When size matters: advantages of weighted effect coding in observational studies
• A novel method for modelling interaction between categorical variables

More information, as well as software for SPSS and STATA are available from the project website.

ps. Stay updated for an exciting update to the ‘wec’ R package!

In a second paper in the same journal, the procedure is expanded to regression models that test interaction effects. Within this framework, the weighted effect coded interaction displays the extra effect on top of the main effect found in a model without the interaction effect. This offers a promising new route to estimate interaction effects in observational data, where different category sizes often prevail.

To apply the procedures introduced in these papers, called weighted effect coding, procedures are made available for R, SPSS, and Stata. For R, we created the ‘wec’ package which can be installed by typing:

install.packages(“wec”)

This is why I love the open source community so much. Not only can users extend the use of influence.ME, and all other R packages, to do things that the package authors/maintainers did not implement. Or to check procedures. Or fix mistakes. Moreover, in line with the positive attitude towards sharing in the open access community, the improved code was shared back so that other users can benefit.

So, thanks to the help of the community, I am happy to announce an update to influence.ME, with two improvements:

• influence.ME now better handles binomial models
• influence.ME now supports functions inside the model call;for instance:
  model.a <- lmer(math ~ structure + scale(SES) + (1 | school.ID), data=school23)

influence.ME is an extension package for the R statistical software. It provides tools for detecting influential data in multilevel regression models (also known as mixed effects models). It was introduced in the R Journal (Nieuwenhuis, Te Grotenhuis & Pelzer, 2012). influence.ME can be downloaded from with the R software.

Nieuwenhuis, R., Grotenhuis, te, H. F., & Pelzer, B. J. (2012). Influence. ME: tools for detecting influential data in mixed effects models. R Journal, 4(2), 38–47.

influence.ME depends on lme4. As the authors of lme4 have completely revised the inner workings of lme4 and are currently releasing version 1.0, influence.ME required an update to maintain forward compatibility with lme4. I just uploaded version 0.9.3 of influence.ME to CRAN, which will be available soon. This version should work with the new lme4, but if you happen to run into any problems please contact me.