Know Your Methods: Regression (Linear, Multiple and Logistic)

This is a follow-up to Know Your Methods: EFA vs. PCA, and just like that summary, this one is also based on Field’s Discovering Statistics Using R (2012), because I’m studying for an exam at the moment and it’s a bloody awesome book to be studying with.


What’s regression?

Regression is a type of analysis used to predict an outcome from a predictor – which is, in essence, what we’re trying to do in psychology most of the time.
Linear Regression is what we use when we have one predictor variable and one continuous outcome variable. Let’s say I had the hypothesis that GPA in highschool predicts future income – linear regression would be the method of choice. Linear regression is, together with a simple scatter-plot, generally the first step to analysing bivariate data (i.e. data for two variables).
Multiple Regression is to be used when we have several predictor variables for one continuous outcome variable. To give an example for that, I could extend my previous hypothesis by including number of semesters spent at university, height or age. The predictors can be any level of measurement we like and we assume the outcome to be a random variable.
Logistic Regression is a special type of multiple regression in which there are several continuous or categorical predictor variables and one categorical outcome variable with two categories. For example, say I knew that certain personality traits are significantly different in men and women, and say I had done a personality test with lots of people, but had forgotten to ask for their sex; I could then use the personality test scales which I know to differentiate between men and women (each a continuous predictor) to predict whether the person who filled in the questionnaire was a man or woman (categorical outcome). Sadly, I can’t use it to find a more realistic example right now.
There’s also multinominal (or polychotomous) logistic regression, in case our outcome has more than two categories.

How does it do that?

The general equation for any type of regression is outcome = model + error, in which the model can be further broken down into b0 + b1*X (b0 being the intercept, i.e. the point where the regression line crosses the Y-axis, the location of the model in geometric space, and b1 being the regression coefficient of predictor X which tells us the gradient, i.e. the shape of the model). This model can be extended for multiple regression by adding further regression coefficients and predictors, but basically, that’s it: our outcome is predicted by our model, i.e. its intercept and slope, and an error term that’s always there.

Regression analysis does not only give us an equation describing our model, which we can then apply to other data, it also tells us how much of our total variance our model explains.

Assumptions

We generally – with one exception – make the same assumptions for all types of regression.
First of all, we assume that there will always be a portion of variance that our model won’t be able to explain. Other assumptions include:

  • homoscedasticity (basically means that at any point along the levels of any predictor variable, we expect the spread of residuals to be fairly constant)

  • normal distribution
  • consistent error variance

The latter two can be tested using the residual plots.

About the error term in that equation in particular, we assume that:

  • the error term is a statistically independent random variable
  • the error variance is the same for every value of the predictor
  • it’s normally distributed
  • its average = 0

Finally, there is the assumption of linearity: we assume the outcome variable to be a random variable with a mean that is a linear function of the predictors. This assumption, by definition, is not made in logistic regression.

Problems

Not so much an assumption as a problem for all types of regression is multicollinearity. This is the case when correlations between the predictors are too high, and this is problematic because these predictors will then explain the same fraction of variance – so the sum of explainable variance is restricted and interpretation of the predictors is complicated by this. Another effect of this problem is that the model’s predictions become less reliable.
So how do we find out whether there’s multicollinearity in our data? For starters, we simply take a look at the correlation matrix. There’s also the factor of variance-inflation which can be computed to figure this out. As a rule of thumb, if the largest VIF > 10, we have cause for concern – as we have when the average VIF is substantially > 1 (this may indicate that the regression is biased). If we do find individual variables which are particularly highly correlated with each other (as indicated by the VIF), we should try and see whether we can drop one of them, or maybe summarize them; with all of this, we have to bear in mind that our actions also need to make sense from a theoretical point of view. We should run a PCA before the MR in this case.
Additionally, we could take a look at the tolerance statistic, which is computed by dividing 1/VIF. A tolerance < 0.1 points to a serious problem; a value < 0.2 just means there might be a problem.

Another problem with regression (and really, with any data) are outliers and unduly influential cases. Outliers can be identified by looking at the standardized residuals: anything with standardized residuals < -2 or > 2 is a potential outlier and should be investigated further. Specifically, we should get Cook’s distances, leverages and covariance ratios for each of these outlier-cases to determine whether they exert undue influence on the regression model. The most important of these indices is Cook’s distance: if Cook’s distance is < 1, it means the case does not unduly influence the model; so, even if the case is an outlier, it’s not a problem for our regression analysis. The boundary for problematic leverage values is either twice or three times the average leverage, depending on the statistician one relies on. The CVR (covariance ratio) statistic works the same way: two boundaries can be computed (using a somewhat complicated formula), and as long as values are within those boundaries, everything’s fine.

Testing these assumptions

The assumption of independent errors is assessed using the Durbin-Watson test, the results of which should be between 1 and 3; anything above or below these boundaries might indicate that the errors are related in some way. The test also produces a p-value which should not be significant.
The data should also be inspected visually, as this is a good way to check assumptions related to the residuals (homoscedasticity, normality, linearity). A histogram of studentized residuals is a good way to check the assumption of normal distribution (though it’s worth noting that a visual check isn’t the be-all and end-all of normal distribution, because in small samples, distributions can look very non-normal even if they aren’t).

If assumptions have been violated, the model can still be good for the data at hand; however, the findings can then not be generalized beyond the sample. There are some solutions for this, depending on which assumption it is that has been violated.

  • heteroscedasticity or non-normally distributed residuals: transforming the raw data may (or may not) help
  • linearity: try a logistic regression instead
  • generally: robust regression (bootstrapping)

Model parsimony

As a ground rule, we are looking for the simplest model that fits our data well, meaning a model that uses as many predictors as necessary, yet as few predictors as possible. There are three different types of methods to try and figure out which predictors should be included in a multiple regression:

  • Backward Selection: starts by including all predictor variables in the model and then removing them one by one until the removal of a variable does no longer significantly improve the model.
  • Forward Elimination: does the exact opposite (i.e. starts with zero predictors and keeps including new ones until the model no longer explains significantly more variance).
  • Stepwise Regression: combines the former two iteratively.

I just said that these methods do what they do until R^2 no longer significantly increases; this is only half-true, in that this is the most popular criterion, but you can also apply other criteria here, e.g. RSS-reduction (residual sums of squares).
A general problem for all of these methods is yet again caused by multicollinearity, in that it leads to instable models; so be careful when using automatised model-selection methods!

For logistic regression, there are two types of methods:

  • Forced Entry Method: this is the default method; it adds all the predictors to the model in one block and estimates the parameters.
  • Stepwise Methods: just like with multiple regression, there are forward, backward, and a combined method. Again, the combined methods (forward/backward or backward/forward) are to be preferred.

The selection of methods should ultimately depend on whether you are trying to carry out exploratory or confirmatory work.

Indices for model parsimony you want to look at are the AIC (Akaike’s Information Criterion; the smaller the value, the better the model fit) and the BIC (the Bayesian Information Criterion, which is a slightly stricter version of the AIC and to which the same rule applies).

Diagnosis of the regression model

Closely tied in with the subject of model parsimony is the general question: does our model fit the data well? If not, we may find ourselves needing a more complex model. To find this out, we should take a look at some fit indices as well as the residuals. The residuals may suggest a more complex model, a transformation, or even a different trend (quadratic, cubic, … rather than linear).

The standardised residuals before and after deletion of a variable should be looked at, as well as Cook’s Distances, which indicate the deviation between model and observation, i.e. the model fit.

Locally weighted regression

There’s also a specific way to do regression in an explorative manner. We use this when we believe there to be a complex relationship between variables, but are not sure how that relationship might look, and so we want a model that is shaped by the data. This type of regression analysis simply summarizes the data into a function. There are different types of locally weighted regression: Lowess Fit or piecewise defined functions. However, I won’t go into further detail about these right now (maybe one day, when I understand them better); for now, suffice to say they are also a thing.

Specifics for logistic regression

Logistic regression is essentially a multiple regression except the outcome variable is a categorial variable with two categories; consequently, the assumption of linearity is not made here, or not in the same sense as in multiple regression. Instead, here we assume a linear relationship between any continuous predictors and the logit of the outcome variable. The test for this assumption lies in the interaction term between the predictor and its log transformation. Independence of errors is assumed just like in standard regression (i.e. if we want to measure people multiple times and thus cause the data to be related, we need to use a multilevel model instead). Also, multicollinearity is as much a problem here as it is in any other type of regression.

When assessing the logistic regression model, there are some specific statistics that need to be looked at:

  • log-likelihood statistic: analogous to the residual sum of squares in multiple regression, i.e. indicates the amount of unexplained variance after the model has been fitted; the higher, the worse
  • deviance statistic: = -2LL (because it’s calculated as -2*log-likelihood); subtract baseline model deviance from new model deviance = likelihood-ratio; chi-square distributed and therefore more convenient than log-likelihood statistic
  • R and R^2: R can’t simply be squared and interpreted here as it could with linear regression; use Hosmer and Lemeshow’s R2L instead (between 0 and 1, with 0 being bad); or Cox and Snell’s R2CS or Nagelkerke’s R2N – they’re conceptually similar
  • information criteria: AIC and BIC => use to judge model fit; they take into account explained variance, but penalize for more predictor variables
  • z-statistic: analogous to t-statistic in linear regression; significant test means tested b-coefficient contributes significantly to the prediction; the z-statistic is underestimated when b is large; likelihood ratio is more accurate than z-statistic, and therefore preferable
  • odds ratio: odds of an event occurring = probability(event occurs) / probability(event doesn’t occur) => odds ratio = odds after unit change in predictor / original odds; OR > 1 stands for a positive linear relationship between predictor and odds; OR < 1 stands for a negative relationship

Finally, there are two specific problems that one needs to be aware of when doing logistic regression:

  • incomplete information from the predictors:
    There need to be data for all possible combinations of variables – if this is not the case, R will have problems computing the coefficients, which is signalled by the coefficients’ standard errors being unusually large.
  • complete separation:
    This is the case when the outcome can be perfectly predicted from one variable or a combination of variables and often arises when too may variables are fitted to too few cases. This is problematic because, when the two outcome categories are perfectly predicted but there are no cases in between, R is unsure about how steep it should make the curve connecting the two extremes. Again, large standard errors hint at this problem.

 

Let me conclude this rather complicated topic with another relatable stats comic:

Bildergebnis für comic regression

Know Your Methods: Explorative Factor Analysis vs. Principal Components Analysis

As mentioned in my first blog post (and that little “about me” thingy on the bottom of the page), I’m a Master’s student in Psychology. As such, I have to deal with unpleasant things like exams every so often. Currently, I’m studying for a massive statistics exam and figured I might as well try to sort out all that newly acquired knowledge via blogging because somewhere, somebody might benefit from reading this.

A prefacing note: aside from my lecturer’s slides, I’m mainly using Andy Field’s Discovering Statistics Using R (2012); get. this. book. As someone who was always scared and confused while studying statistics, I can tell you this book has been worth every cent, and every minute spent working through it (of which there were quite a few because it is quite long, but my God, does this guy know how to explain shit); I am now far less scared, and still confused, but that’s not because of the statistics-part so much as because this whole book is on drugs – you’ll quickly discover what I mean by that once you take a look inside and get to know Field’s ludicrous sense of humour. So, yeah, end of the random free advertisement.

 


 

Explorative Factor Analysis vs. Principal Components Analysis

What are their goals?

Broadly speaking, both methods strive to reduce dimensions and make the data at hand more manageable; we should think about using one or the other when we have a large amount of correlating variables.

PCA does not differentiate between the different types of variance; it simply produces components that explain the largest portion of the total variance by combining variables in a linear manner. As such, it should be used when the goal is simply to reduce the volume of data.

EFA, in contrast, should be used when we expect an underlying structure of relationships between latent variables (factors) and our observed variables (indicators). An example, and simultaneously one of the most common applications of EFA, is questionnaire construction: let’s say we’re trying to measure a broad concept like intelligence. To do this, we compose a very large questionnaire with lots of different items in it: we may expect, based on theoretical assumptions, that this broad concept consists of several non-observable but more concrete concepts, such as verbal skills, logical skills, spatial skills, etc.; the items of the questionnaire act as indicators for these latent factors, and EFA can tell us which items belong to which factor, and which may belong to none of them and should therefore be excluded from the questionnaire.
The difference is what EFA tries to explain, which is not just the total variance, as is the case with PCA, but rather the correlations between the measured variables.
It’s also worth noting that, while the PCA simply summarizes the present data, the EFA yields a proper mathematical model which can be tested with another set of data.

When the specific variance is small, PCA and EFA deliver similar results (a variable’s total variance consists of its communality, which is the part of the variance being explained by the factors, i.e. the sum of its factor loadings, and its uniqueness, which is the inverse, i.e. 1 – communality; the uniqueness, in turn, consists of the error variance and specific variance, i.e. the portion of variance that is specific to the variable and can neither be explained by the factors nor by errors of measurement). That is because when the specific variance is small, the common (or shared) variance is consequently large. PCA uses the total variance and EFA uses the common variance, so the larger the common variance, the more similar the results of the two methods will be. However, when the specific variance is large, their results differ considerably, so we should find a good reason to use one or the other method. When variables are un- or just barely correlated, we shouldn’t use either.

How do they (and I) do it?

In PCA, we start by creating one component which explains as much of the total variance as is possible by way of a linear combination of the original variables. We then extract a second component which explains as much of the remaining variance as is possible without correlating with the first component. If our goal is to compress the existing set of data without a loss of explained variance, which should usually be the case with PCA, this goes on until all of the variance is explained.
The components can be extracted from either the matrix of covariances or the matrix of correlations. Solutions from these will differ; the matrix of correlations should be used when the original variables are of different scales.

EFA makes some noteworthy additional assumptions. It recognizes that the total variance consists of shared factors and specific variance. It is assumed that residuals are neither correlated with each other nor with the factors. The common factors explain the correlations between variables. Factors are allowed to correlate, though interpretation is easier when they don’t (whether that is theoretically realistic is another question; in psychology, the answer will often be no). A problem that poses itself with EFA is that it is originally unknown how large the shared variance is (i.e. the shared variance is both necessary for computing the FA and a desired result of the FA); this is solved by an iterative approach:
First, the shared variance needs to be estimated. This can either be done by using the squared multiple correlation of one of the original variables with the others, or by picking one of the original variables and using the largest correlation it has with any of the others. Using either of these as an initial estimate of the shared variance, a FA is conducted which estimates the factor loadings through the first k components’ eigenvalues. Through this, an improved estimate of the shared variance can be obtained. This process is iteratively repeated until a convergence-criterion has been reached.
An example for such a convergence criterion would be the Maximum-Likelihood FA: this method starts out by defining a distance D between the observed matrix of covariances and the one resulting from the FA. Factor loadings and specific variances are then estimated (in R, this is done by PCA) and these estimates are changed until the distance is minimized.

 

Specific to EFA

Selection of factors

Now that the factors have been extracted, how do we know which ones to include in our model? Usually, we’ll get one huge factor which explains the largest portion of variance, then two or three other ones that also explain quite a lot, and then a bunch of small ones that explain very little. If that is not the case, e.g. if we get a lot of factors that all explain about the same, small amount of variance, then chances are there’s just no factor structure behind our data and we might want to approach it another way.

But assuming the results seem fine – how do we choose the factors we’ll include in our model? There are several criteria, the most well-known and popular being the scree-plot.

The rule of thumb if we’re going by scree-plot is simple: include all factors before the “elbow”, i.e. before the point in the curve where it changes slope. In this case, that would mean the first 3 factors. Several other criteria have been suggested, such as all factors with eigenvalues > 1 or > 0.7, or all factors whose eigenvalues are above average. A more elaborate criterion comes from Horn’s parallel analysis. In general, several criteria should be consulted and a middle ground should be found, because none of these are perfect or individually sufficient.

Rotation

Just because we’ve extracted the ideal amount of factors (based on whichever criteria we chose) does not mean these factors are currently ideal to describe the data. We use rotation to optimize that fit. There are two types of rotation: orthogonal and oblique. Orthogonal rotation techniques will rotate the factors to fit the data as best they can while remaining independent, i.e. no correlation between any factors will be allowed. This is much easier to interpret, but also seems rather unrealistic, at least when psychological data is involved. When are concepts we’re interested in researching together ever entirely uncorrelated? Oblique rotation methods, on the other hand, allow for correlations between factors.

The most popular orthogonal rotation technique (which Field also recommends as a default and which R uses as a default if you select nothing else) is Varimax, in which the average factor loadings are redistributed in order to create one very large factor and a few smaller ones. Overall, it tries to even out the distribution. Another popular one is Quartimax, in which individual variables are being forced to highly correlate with one factor; the aim of this technique is to explain each variable through as few factors as possible.

The oblique counterpart of Varimax is Oblimin. Short for “minimal obliqueness”, this method allows you to predetermine the correlations between factors in order to produce an improved factor solution while not being any more oblique than is absolutely necessary. Another popular oblique rotation is Promax, which strives for a good structure with minimal correlations between factors. It does so by taking an orthogonal solution and then adjusting (increasing) the factor loadings.

The steps of FA according to Field

This is just a short summary of the practical section of Field’s Chapter 17.

  1. Preparation
    1. Raw Data vs. Correlation Matrix: if we have a massive amount of cases (at least 100.000) we should run the analysis on a correlation matrix; otherwise, running it on the raw data will be fine.
    2. Correlation matrix: the first step is to scan the matrix for any correlations larger than 0.9, which could cause problems with multicollinearity. We should also look for variables that have many correlations smaller than 0.3 and consider excluding them. Basically, we want our variables to neither correlate too little nor too much.
    3. Bartlett’s test: this works on both the raw data and the correlation matrix, using cortest.bartlett(), and we want it to be significant. A significant Bartlett’s test means that our matrix is not an identity matrix (in which FA would not be possible).
    4. KMO test: this gives us a value between 0 and 1 which will indicate whether our sample size and data are adequate for FA. There is a kmo() function which needs to be installed separately, and the results should be judged according to the following scale:
      0.5 – 0.7: mediocre
      0.7 – 0.8: good
      0.8 – 0.9: great
      > 0.9: superb
      Even if the overall-KMO is fine, we need to look at the KMO’s for the individual variables to make sure that none of those are below 0.5. If we do find one below 0.5, we should try excluding it and rerunning the analysis.
  2. Factor extraction
    1. First model: Field uses the principal() function for this step, because PCA and FA often yield similar results (while not being the same kind of method). This initial model contains the same number of factors as there are variables. We thus transform our raw data into its underlying factors. The R-Output gives us factor loadings, communalities, uniqueness and the eigenvalues in terms of the amount of variance explained relative to the total. The PCA here assumes that all variance is common variance, which is why in this initial output, all commonalities equal 1.
    2. Extraction: now it’s time to decide how many factors we wish to retain in the model. This is where the criteria I’ve mentioned above (scree plot, Kaiser’s criterion etc.) come in.
    3. Second model: having decided upon a number of factors to extract, we re-run the analysis specifying that number (pc2 <- principal(<raw data frame or matrix>, nfactors = <number of factors we’ve chosen>, rotate = “none”)). This output will contain fewer factors than the previous one (duh!), and they will be unchanged except for the communalities and uniquenesses.
    4. Re-evaluation of extraction: at this point, we take a step back, take another look at Kaiser’s criterion and evaluate whether we still think the same number of factors should be extracted. This criterion is accurate when there fewer than 30 variables and communalities after extraction are > .7 or when N > 250 and the average communality is > .6. Another way to check whether we extracted the correct number of factors is by comparing the reproduced correlation matrix (obtainable via the factor.model() function) to the correlation matrix in the data. When checking the residuals, we need to make sure that fewer than 50% of them are > 0.05; also, the model fit displayed in that output should be > .9.
    5. These steps are repeated as needed.
  3. Rotation
    Finally, the factor solution is rotated to facilitate interpretation, using either of the methods described above. If we believe, based on theoretical assumptions, that our factors should be unrelated, we should pick an orthogonal rotation option; otherwise, we should choose an oblique rotation method.
    Looking at the post-rotation output, we’ll find that the factor loadings have changed but the communalities and uniquenesses have remained the same. The eigenvalues will also have changed: they will now be more even.

Finally, all that’s left to do is look at the mathematical factors the analysis produced and try to assign meaning to them. We do this by looking at all the variables loading highly on one factor and thinking about what they have in common.

 

I believe that’s an overview of the most important basics of PCA and EFA, and it’s already quite long, so in lieu of a summary, here’s a statistics-based comic that I think you’ll appreciate:

 

Consecutive Vowels

 

 

 

Two times I nearly quit Law School and one time I finally understood why I didn’t

On surviving Law School, a culture of not being good enough and celebrating selection, and remembering why I started.

What brought me to Law School was one simple wish: I wanted the ability to be strong for people who were currently not in a position to do so for themselves. A wish so simple it almost sounds cheesy (though I maintain it’s not naive), and yet when you take the leap and actually enter Law School, you move very far away from that goal very quickly.

It is worth making the introductory comment here that I study Law in Germany, a country which may have found the weirdest and most criticisable way to organise law studies yet. There are, in particular, 3 reasons for me to make this claim:

  1. The System
    If you choose law school and everything goes according to the standard plan, you’re in for 9 semesters of studying. Of those, about 5 – 6 semesters are completely irrelevant to your final grade. That’s right: you can do really well for two thirds of your studies and still have no guarantee that you end up with a degree the first time round. Essentially, it works like this: You spend those 5 – 6 semesters passing a bunch of exams, doing internships and fulfulling some other requirements; once you have checked all the requirements off, you are allowed to register for the State Exam. Your final grade will consist of a “Specialization Exam” (33 %) and the “State Exam” (66 %) – the former being two written assignments and oral exams at your university, the latter being one week from hell during which you take 6 exams about 6 randomly chosen and – depending on your luck – potentially very specific bits of everything you ever learned about the law; plus, should you pass those written exams (which only about two thirds end up passing), you will have to deal with another day of oral exams. Everyone has a bad day once in a while; make that two or three and place them during that exam week and whoops, there goes your future. Well, more or less – but I’ll get to that below.
  2. The Grading Scale
    The grading system for Law is (to my knowledge) unique in Germany, meaning no other discipline is exposed to this intense bullshit. The scale goes from 0 – 18 points; the passing point is at 4 points and if that’s the moment where you go “what the hell that’s so easy! I have to score 60 % to pass an exam!” then I regret to inform you that in most exams, the average is somewhere around 5 – 6.5 points and the failure rates usually around 30 % or higher (I once took an exam where the average was 3.5 points and scoring 5 points placed me among the top 15 % – and the professor complained that when she gave out that same exam 10 years ago, the average was so much better with a whooping 4.5 points). I don’t know who came up with the grading system, nor do I know who saw this 18 point scale and decided that the top third of it just wouldn’t be used – ever -, but I’m sure there’s a special place in hell for them. And the system alone – this beautifully crafted way to continuously make students feel like they are miles away from good enough for anyone or anything – isn’t even the worst part; what makes it worse is the way grades come to be: semi-arbitrarily. Law exams are essay-type exams, which are always harder to grade than a clear-cut multiple-choice exam; they’re even harder to grade when there are 300 of them to grade and you have to hire random law-graduates who get paid per exam and therefore have to speed up if they want to achieve minimum wage per hour. Just recently the case of a student who handed in his written assignment twice and accidentally received two very different grades – an okay-ish 5 points and an amazing 9 points – made the actual news. Your grade depends as much on your acutal legal knowledge as it depends on into which correctors hands your exam falls, at what time that happens, how tired he is at that point, how good the correction instructions were that were handed to him by the professor, how annoyed or hungry he is, how much he likes your handwriting and how much his life is pissing him off at the moment. And as if that’s not bad enough, it still get’s worse. The worst part is:
  3. How Much We Care About The Grades
    Yes, the system is basically designed to keep your chances of achieving good grades – grades that in a normal system would reflect your skills accurately – to a minimum; yes, the grades are – while not entirely baseless – subject to large arbitrary influences and everyone, and I mean everyone who is a part of this system, everyone who ever studied Law, knows this; and yes, we care about them to an unhealthy extent anyway. Remember that scene at the beginning of “Les Miserables” where we meet the main character, Jean Valjean, and Javert keeps addressing all the prisoners by their prison-registry numbers instead of their names? If I ever were addressed by a fellow-jurist by my current GPA rather than my name, I would not even be surprised enough to bat an eye. From day one we are told how much these ridiculous numbers define us and our future – we are told that, if you want to be a judge, you need to make the magic 9-point-mark, and if you just barely pass your final exam, you’ll get stuck in an insurance company for life; we are told there’s no point in applying for certain things, certain jobs, below certain point-marks – no matter the additional experience you may be bringing to the table. People ask each other about their grades, some even select company based on grades, people hide books in the library and tear out pages for no one else to be able to read them and people remember the statistics from the last exam by heart so they can eternally compare themselves to each other.

 

Not all people, of course; it goes without saying that, as within any discipline, Law has some great and chill people. But this is the general climate – one of competition and comparison, one of never being good enough and one of disdain for the weak. The conditions are harsh, yet there is collective pride of just that – as if arbitrarily making it harder to pass exams, let alone achieve good grades, made the discipline and its students somehow superior to others.

When I came to Law school, I wanted to be strong for people who were currently not in a position to be strong for themselves. I wanted to learn about issues related to human rights and civil rights, I wanted to learn how to defend people whose rights were endangered and how to make the State a little more just for everyone. Instead, I spent a lot of time dealing with a lot of very basic theory and abstract knowledge (as opposed to actual cases; the German system is not as jurisdiction-oriented as, say, the British system with all its case-law, so the first time I actually dealt with real cases in depth was after about 3.5 years, in a lecture within my area of specialization), and I used up all of my strength just to keep myself up and running rather than lending it to people in bad positions, because any display of weakness seemed out of place.

The first time I came seriously close to quitting was between my third and fourth semester. This was simultaneously also between the fifth and sixth semester of my Bachelor’s in Psychology, which means that the stress from my Bachelor’s thesis and applying for Master’s programmes came as a charming little addition to the whole thing. One might have thought that I was fine, seeing as I’d never failed an exam at that point and my grades were quite average, which shouldn’t have bothered me considering I was doing a whole other degree “on the side”. The thing is, our expectations aren’t always so logical; while the outside perspective might have been “oh wow, two degrees simultaneously and the grades are still fine, that’s impressive!”, all I could think was that I was getting nowhere. There was just so much new stuff to learn, there were so many Law lectures and exams and you were supposed to prepare for the lectures and then repeat what you learned after the lectures, all that while preparing for the exams (side note: you hear many lectures that are not relevant to the exams you are taking that same semester, but become relevant in later semesters, which makes for a difficult balancing exercise) – I felt like I was climbing a sand dune; like I kept sliding back down no matter how hard I tried to get up there. I felt like the whole thing was crushing me and there was no one who would understand, and I just wanted it to stop.

What made me push through this was not the heroic thought of why I’d come to Law school in the first place, not strength or discipline or any other great quality, so much as one simple reason: petty defiance. The day I went to enroll for Law in addition to Psychology, I encountered the most ill-tempered employee the matriculation-office had to offer. From the moment I entered her office until the moment I left it, she basically didn’t interrupt her rant about, in short, how unpleasant it was that I was interrupting her afternoon and wasting her time with such a silly request as wanting to enroll for two subjects in parallel, because people like me never pulled through with stuff like this; she informed me I would try this for a few semesters, then admit to myself that it was too hard and just pick one, which would make this a waste of her time. I left that office swearing to myself that even if it turned out to suck, I would graduate, and with an excellent grade too, just to shove it into her arrogant face. Three semesters later I was still petty enough to have not let go of that and to make it my reason to persevere – and as stupid a reason as that is, it was good enough: I stuck around. 8 semesters later, I now appreciate that this woman had a stressul day, a stressful job, and some people probably did waste her time – and I’m actually very glad that she was having such an exceptionally (I hope for her family) grumpy day, because as silly as that was, it got me through my first rough patch.

The second time I nearly quit was between my sixth and seventh semester of law – around one and a half years later, and yet it felt like an eternity. The situation was similar in that I had pushed myself over the edge with a serious overload of work; I’d pushed through too much for too long and now I was just exhausted. What was different was that this time, I had stumbled into a proper quarter-life-crisis; I was just tired, so tired, and I didn’t know what for anymore – I’d lost view of where I was going with these degrees, I kept pushing myself without anything in sight that made it worth pushing for. I was at a point where I had to admit that I loved Law, but I hated being a Law student; I had rushed through all my requirements and started preparatory courses for the State Exam (while working on my Master’s in Psychology) and I just couldn’t do it anymore – I couldn’t stay up until 2 a.m. to prepare a case for class the next morning one more night, I couldn’t sit through one more lecture and repress my panic at the realization that everyone else knew more than me, and I couldn’t spend one more break trying to ignore the group next to me chatting about how many hours they’d studied yesterday and how many cases they were going to catch up on today. I couldn’t stand any of it for another day without having a clear view of a good reason.

This time, it took me more strenght, or more of an effort, to push through than the first time. The decision to walk away from something is often terrifying – leaving a steady job from which we’ve gotten everything there was to get and which is now sucking us dry, walking away from a person who’s very close to us, but doesn’t treat us the way we deserve: sometimes, our self-respect dictates we do something that seems dreadful and yet is inevitable, because if we don’t look after ourselves, no one else will. And that’s what I did – I walked away from Law for a whole semester. I was scared – scared I might fall behind drastically because of this, and even more scared that I might just never find the strength to come back to it; yet I knew that if I didn’t take this step now, if I didn’t take my distance and invest the time to find a really good reason to go on, I wouldn’t make it either way, and I’d be potentially looking at consequences that were worse than just a Law-school drop-out. So that’s what I did – I spent the semester doing some electives for Psychology, pursuing different interests that I’d never previously had the time for, and invested a lot of time into volunteering; by the end of it, I’d found a good reason – I’d found my way back to where I started. And not only that, I rediscovered my love for Law, in spite of its irritating study system. I returned after this semester hungry for new knowledge and eager to take on the final challenge in order to finally arrive at the destination I’d aimed for since day one: being able to be strong for those who currently couldn’t be.

That semester I made use of my new-found motivation by starting my area of specialization – for the first time, an assignment I handed in would be relevant for my actual final grade. Shit was getting serious. I still felt like a kind of average student – I didn’t have any special skills, but I now had my determination, and it was stronger than ever. This close to the end, there was no way I was backing down: I was going to finish this degree, in spite of my skills or lack thereof, and then I would finally do what I’d come here to do in the first place. I handed in my assignment and waited; when the day of the oral exam finally came around, I was so nervous that I was more focused on not being sick inside the exam room than on my actual presentation. Afterwards, I waited around nervously for the interviewers to agree upon my grade, praying to all of the deities to let me pass and not make me redo the whole assignment, until finally the moment had come. I sat down and anxiously eyed the lecturer’s expressionless face as he, after a moment, opened his mouth and informed me that –

not only I had passed the exam, but they were unanimously so impressed with both the scientific quality of my assignment and my style of writing, as well as with the comprehensive understanding of the topic that I had acquired during this time, that they wanted me as a student research assistant at their department.

I was in utter shock. For four years, I had been mediocre at best, a student with no particular talent for anything, no individual worth – and suddenly, I was being told I had special skills? A worth beyond my grades? And then I realized: there was a reason I was still here, and it wasn’t just defiance or stubbornness, not even just perseverance or dedication. I was here after all this time because I belonged; because I wanted to do something and I had not only the dedication but the skills to get there.

Law, like perhaps no other discipline (though of course, I can’t know that for sure, but I know no other discipline with a similar bad reputation), has managed to create a system and a culture that keep telling us we aren’t good enough, we’re nothing beyond our grades and we never will be good enough because the system is designed to keep the highest grades out of reach. It is a system that removes any individuality from us students because it does its best to limit our perception to one specific set of numbers; and if your personal skills – although they may make you an excellent fit for certain areas of law/jobs in the legal spectrum – don’t align perfectly with the skills it takes to achieve good grades in this bizarre system, you may not see them for a long time. It is a system that pushes us to feel bad about ourselves until we are fortunate enough to discover those individual skills by ourselves – or have them discovered by someone else, in my case; in a way, this is how we beat the system. Not in a grand toppling-maneuver, but little by little, day by day and student by student who finally discovers their worth outside and beyond the system and is rewarded for it.

I finally understood why I’d never quit: because this system couldn’t break me, nor could it break my love for Law for what it was – nor could it ever keep me from doing what I came here to do in the first place.

I burst into tears while peeling potatos

On the loss of a grandparent, the long-term process of grief and the hardest thing I’ve had to get over.

When my grandmother died two years ago, I was distraught. It happened quite suddenly, which was good for her because she didn’t have to suffer for a long time and she was comepletely at peace; she was ready. I was not. I spent days and nights sobbing just before and after the event, and eventually I was just exhausted. I was tired of feeling – this way, or anything for that matter.

And all that time, I had a little voice in my head that told me “Why are you being such a baby? You’re overreacting. She was your grandmother – everyone’s grandmother dies, and everyone has to deal with it; it’s not tragic, it’s normal. So pull yourself together.” Eventually, I did what nowadays everyone ends up doing when they’re stuck with a problem – I googled it.

I don’t remember the exact searches, but I figure it was something along the lines of “how to get over grief” and “how to deal with grandparent’s death.” I realized I was not alone – in particular, one sentence stuck with me until now: “The loss of a grandparent was the hardest thing I’d ever had to deal with up until then.” It was an incredible relief to find that others struggled with this, too, and I wasn’t just being a baby about it.

I wasn’t raised by my grandma or anything – she lived on a farm and we lived in the suburbs, so we went to visit her every few weeks and I spent my childhood summers there. We’re a really big family as well, so everyone’s not as close as very small families tend to be. But still, I looked up to her and she was important to me – grandmothers are like that fixed star of unconditional love that’s always there, even if you can’t always see it, and you can rely on it when everything else is foggy and confusing. Since she’s been gone, I’ve been pondering the character traits I might have gotten from her a lot more than I used to. She was a caring and kind woman, resolute and determined, practical and brave; she was always very active, and when she noticed an injustice she tried to make it right. There’s a lot I hope to have gotten from her.

Her death struck me all the harder because I didn’t get to say goodbye, and it was my own fault. I was halfway through exam season when the news came that she was not doing well. I planned to go home immediately after the last exam and help take care of her. Then one day I came home from an exam and saw an email from my aunt, stating that she’d gotten worse and it was probably time to say our goodbyes. This was a Monday, and the last exam of my bachelor’s was on Tuesday the next week. 8 days. I wanted to leave immediately and figure out the exam thing somehow on the way. My parents advised me against it – my mum thought surely this would drag on for a while, as it had with so many of her relatives. Surely, she’d be fine for another week, and she’d want me to finish this before I came home. I decided she was right – just 8 days. I would stay, I would finish it and then go home immediately after. 8 days.

She lasted 3.

She died on Thursday that week, and I couldn’t believe I had prioritized an exam over this. I hated myself.

 

Back then, when I was googling grief and getting over death because I couldn’t help myself and couldn’t bear it anymore, I kept wondering: when does it stop? How much longer do I have to sit through this? It doesn’t stop; it changes. Some days I don’t think of her; some days I do, because I’m remembering a sweet childhood moment, or a funny story, or something she told me, and I smile. Sometimes I’m acting a certain way, and I think “I got that from her, and I’m proud of that; she would have liked that.” And then some days are like today: I’m thinking about her because it’s her death’s anniversary next Sunday, and as I’m standing in the kitchen, peeling potatos, the memory suddenly hits me of how many times I used to watch her do that. So banal, such a simple memory, and yet the feeling of missing her punches me in the stomach and I’m surprised to find myself bursting into tears.

The difference is, now I don’t think I’m being a baby; it’s fine. Sometimes she makes me cry, sometimes she makes me smile and laugh, and sometimes she still points me in the right direction when I’m at a loss as to what to do. That’s life, and as long as it’s this way, she’ll never be completely gone.

Should you be teaching? Hell yeah, probably

When I was 17, a local refugee shelter was looking for a volunteer teacher for those who could, for some reason or other, not attend the state-run German classes at present. The first person I taught there had a pretty good reason: a tiny newborn baby boy named Marvellous who was simply too distracting to just bring him to class with her. And man, am I glad for that baby – not just because he was adorable and it was fun to play with him while teaching, but mostly because this experience got me into doing something I still enjoy to this day. Currently, I teach a level B1 class on a weekly basis for a student organization that works towards helping refugees overcome language barriers.

Of course, the students aren’t the only ones who take away something from class; here are some things I learned teaching my native language:


1. Not understanding each other right away isn’t a big deal.

At first, you’ll be so nervous. You’ll try to prepare an explanation for certain things (at which point you’ll realize how hard that can be, see below), and because you’re not trained to change your explanation ad hoc, you’ll be knocked out of your stride when that prepared explanation doesn’t work because the other person is missing certain vocabulary or the sentence-structure is making it hard to follow. If you’re a bit awkward like me, you’ll look at their blank facial expression of confusion and think “oh no, they didn’t understand that! Quick, come up with something else…oh, come on! You look like an idiot right now! Dig yourself a grave as deep as possible and never emerge again!” The same will happen when they’re trying to say something and you just don’t understand – usually because of pronunciation. You’re sitting there, playing the shit-what-word-could-that-be game as you panic, “Guess it, come on! You look like an idiot right now (AGAIN)!”

But the thing is, that goes away quickly; for one, you get better at coming up with ad hoc explanations, you become more flexible and simultaneously, the person you’re teaching will get better at the language. That is, your communication both with that person and with other learners of your language improves – jackpot, right? But it’s not just that; you soon realize that they’re as embarrassed as you are, and then something great happens – the embarrassment goes away and you just start having fun with it. Teaching and learning turn into a fun exchange with quiz show elements.

2. Miming and drawing are your friends.

Yes, this is it – this is the experience that playing “Activity” with your family and friends for so many hours prepared you for. You’ll find that making the class fun will make the whole thing more enjoyable and more successful for everyone involved – and before you know it you’ll be drawing a horse tied to a church steeple to illustrate a story that you’re reading together or jumping up and down and around the classroom to visualise the correct use of semicolons (totally never happened to me…*cough*…they’ll remember this forever though).

3. You have way more knowledge than you can put into words.

“What is ____?” and “What does _____ mean?” will be the most common phrases you hear (paired with “Ah, thank you!” of course), and while you may think “oh I’ll be fine, it’s my native language after all!” you will quickly realize how many words you use and understand without being able to accurately define them off the top of your head. And often, it’s not the large complicated ones, but the short, harmless-looking words, the seemingly benign fillers that turn out to change the sentence in such a nuanced way that you have real trouble pinning down the meaning of that specific word. Two words I surprisingly struggled with in German were “nämlich” in sentences like “Ich kann nicht kommen, ich habe nämlich etwas vor” (which translates to something like “I can’t come; the thing is, I’ve got other plans”, only neither “because” nor “the thing is” are accurate translations for “nämlich” and I haven’t figured out anything about this other than that it implies causality) and “doch” in sentences expressing irreal wishes, such as “Hätte ich doch eine Jacke angezogen!” – “If only I’d put on a jacket!” On a sidenote, if anyone has a good way of explaining either of those, go ahead and let me know, because I still haven’t figured it out and my students are still waiting. In relation to that:

4. Your native language is weird.

Like, hella weird. They all are. And you never notice, because you never think about it, until someone asks you those oddly specific questions. Whether it be those little words that suddenly seem impossible to define and replace with a synonym even though you know exactly what information they convey, the hellishly complex rules of German subjunctive usage, the fact that it feels like half of the letters in French are silent and the other half are pronounced as anything but that letter, or the ridiculous rules for when to use the female singular and plural in Arabic – no matter which language you speak, you’ll keep encountering all these little things that make no sense, and you’ll keep realizing how weird it is and wondering how you never questioned all these things. And that’s beautiful. You’ll think about things you never thought about before and discover things together – you’ll get to know your native language much better as you go along, and you’ll love it. Plus, it’ll occasionally be really funny. Which brings me to the next point:

5. Some mistakes are funny as fuck, and it’s okay to laugh.

In Arabic, if you mispronounce “good morning”, you’ll greet your friend with “morning of dick!” (in certain dialects). In German, if you mispronounce “night” you’re saying “naked”, and if you mispronounce “to hear” you’re saying “whores”. Language is funny, and one of the great things about teaching is explaining the mistake to your students, laughing your asses off collectively, and then fixing the mistake. Sometimes, mistakes will reoccur (the night – naked thing is quite difficult for many people because it requires a sound that is not part of many languages), but often, the whole class laughing about it will help someone to remember and not repeat that mistake. Personally, I’ll never wish anyone a “morning of dick!” again.

6. If you think you should work on your flexibility and spontaneity, this is for you.

In some ways, teaching can be like impro-theatre. Sure, you’ll make a concept and think your lesson through beforehand, but you won’t see all the questions coming and when they do, you have to react right there and then. You’ll learn to get better at impromptu explanations and answering questions spontaneously, you’ll get more flexible in that you change and adapt your explanation according to what your students need – and, perhaps most importantly, you’ll learn to let go of your strict plan. Well, perhaps not let go entirely – you will still need to plan, but you will quickly learn to accept that sometimes, things don’t work out that way, and how to change plans without letting it bother you or your students and without completely losing sight of your goals. If you’re someone who gets very upset when their routine is disturbed, or who makes very strict plans and then flips out when something interferes with them, this could really help you in terms of personal development.

7. There’s nothing greater than leaving the room knowing you made a difference.

I have a pretty stressful week…every week. I have a lot going on – usually I like it, sometimes I don’t, but the one thing I always enjoy without fail is my weekly German class. Rarely am I so consistently present in a situation for 90 minutes straight as I am during that class, and rarely do I do anything where I can observe so directly how it affects and helps people. When I leave that classroom, I do so knowing that my students now have more knowledge than they had when they came in, they’re better prepared for exams or other goals they may be pursuing, and we all had fun together. Just today, one of them gave me a thank-you hug. We as a species like instant gratification, particularly of the social kind, so tasks where you can observe the outcome directly and even get some social recognition out of it are a pretty safe bet when it comes to looking for something that’ll make you happy. If your job is stressful and quite different from that, teaching can be a great way to balance the stress.

In conclusion: should you be teaching? Absolutely! If you have even the faintest hint of curiousity about it, be sure to do some research about organizations that support refugees in your community; there are usually several of them that are always looking for teachers for language classes. It’s a great, low-threshold opportunity to try something new from which both you and the people around you will benefit!

My dad’s a good person. Also, he’s developed genocidal tendencies.

On radicalization, the struggle of strongly disagreeing on fundamental matters with family members, and what prompted me to start a blog.

What a grim “hello world!” post to make, right?

I’m a psychologist; a psychology student, to use precise terminology – though at this point, I’m merely one exam and one thesis (which will, incidentally, be on radicalization – but that’s for another time) away from officially being allowed to call myself that. If you are one, too, then chances are that, just like me, you’ve learned a lot about group dynamics, group identity and perception and the mechanisms behind intergroup conflict. You know the theories, you know the research, you’re aware that intergroup conflict is a complex process and manifold factors play into it, and if you’re like me in that you see a solution for every problem rather than a problem for every solution, you try to apply that knowledge whenever you encounter such conflict in the broadest sense. When I witness a conflict between two groups (which happens all the time, since intergroup conflict is pervasive throughout society – be it grave issues like racism or minuscule things like a petty feud between two academic disciplines at university), I try to figure out the reasons behind it and the psychological mechanisms that perpetuate it beyond the purely objective reason. It is only when you have thoroughly deliberated on those factors that you can try to come up with an effective solution, which is what I want to do with my research.

This scientific approach can put a comfortable distance between you and whichever conflict it is you’re observing – a distance which, to some extent, then shields you from the moral disgust that overcomes you when listening to aggressive, racist rants and other horrifying things people say when they’re fully immersed in a conflict. It’s an instrument that you suddenly have in your formerly powerless hands; where you used to have nothing but your reactive emotions that had nowhere to go, you now have a tool that allows you to approach the matter systematically, understand how it comes about (a little), and change how it goes down (again, a little).

Except that whole distance-thing doesn’t work nearly as well when the upsetting behaviour you’re confronted with is coming from a person you’re close to, such as a family member. My dad’s a good person. I wouldn’t say that our relationship is particularly complicated – you grow up looking up to your father until some day, for the first time, he won’t have an answer to your question and utter those disheartening words: “I don’t know; google it.” You realize that he’s by no means omniscient after all, you develop opinions and learn that they will sometimes be the polar opposite of his opinions, you move on with your life and you’re fine. Pretty standard. Except some time later, you figure out that there are some things you can’t just have an “opinion” on – they’re fundamental values, often matters of life and death, and when you disagree on them, you can’t just shrug it off like when you disagree on what constitutes good music or acceptable tidying habits. I’m probably about as liberal as it gets, and I grew up thinking of my father as an open-minded and level-headed person. I often found us to be agreeing on social issues, and when that was not the case, he usually argued fairly, so it was possible to respectfully disagree. Of late, however, the tone has shifted considerably.

Things that he has become convinced of over the course of the last two-ish years and has repeatedly and avidly argued include:

  • he thinks Arabic men are inherently incapable of treating women respectfully and are, in fact, so dangerous that they should not only be avoided, but barred from entering Europe
  • he also thinks Muslims are coming to Europe to have as many children as possible so that, when the time comes (whatever that means), they’ll be enough to take over Europe and eradicate the current population
  • regarding the European external borders, he is convinced they need to be closed completely, because there are no war refugees coming to Europe, just people who are trying to destroy it (see above); if anyone is to be let in, he demands it should only be women and children, no men (also see above)
  • related to that, he is firmly convinced that anyone who gets on a shabby boat to take them over the Mediterranean to Europe is not doing so out of utter despair and in the full knowledge that they may not live to see the shore, but rather in the knowledge that nothing will happen to them because if their boat sinks, they’ll be comfortably pulled out of the water and taken to shore to receive their free pass to Europe
  • also, he believes the Chinese were really on to something with their one-child policy, except they weren’t taking it far enough – enforced sterilization of entire countries and continents would be a solution more to his taste

Horrifying as these things are to write down (and I greatly struggled to do so; I feel the need to apologize to my laptop for using it to put together such disgusting sentences, and it’s not even sentient), they’re even worse to seriously have to argue over with someone you’re close to and respect – not least because there’s a massive conflict of conscience here between being loyal to your family and not wanting to put family members on the spot like this, and not wanting to let someone get away with statements like these just because they’re family. When nine out of ten times, you’re talking about work, the weather, a movie you saw or general family matters and you’re having a pleasant time, and then the tenth time you’re yelling at each other as you struggle to convey the value of respecting basic human rights and human dignity and to dismantle their irrational fears and generalizations, you’re in for some internal conflict, to put it mildly. When you spend a quite large chunk of your time working for and with people who came to this country as refugees, it’s even more upsetting to hear someone speak so dismissively and unempathetically of their plight; when you study and work with Muslims and there are people from Arab countries amongst your closest friends, it’s that much harder to comprehend how someone you respect can lump them all into one group and suspect that group of wanting to destroy his continent, culture and life.

When we think of radicalization, we usually think of it as a broadly political or religious phenomenon – we think of the damage it does to the public, to society, when people terrorize others in the name of their firmly-held beliefs, be it the belief that they of all people know what some god or other wants, or the belief in their racial superiority. But the damage starts at home; radicalization does not just tear apart society, but also families. Not everyone is as upset about this as me, though: one Muslim friend of mine will even ask me for news from my dad every once in a while, as he gets a good laugh out of hearing his perfectly harmless self getting demonized like that. Other friends strongly empathise with me and some, in some form or other, even have similar problems in their families. But what can we do? For now, the only option I have seems to be to relentlessly argue and counter, to try my hardest to remain patient and to continue attempting to change his mind about things little by little – exhausting as that is.

Finally, why would I write this down and why the hell would this be what motivates me to start blogging?

Well – for one, it was immensely helpful for me to discover that friends shared similar, if not the exact same extreme problems in their families, and I’ve gotten compassion as well as some good advice on how to approach these things; so I figured by chance, someone struggling with similar issues might read this and it might help them as well. As for how this constitutes a (good) starting point for an academic blog: throughout my ten semesters of studying psychology (yes, I’m a little behind the standard schedule, shoot me), I’ve had five research assistant jobs and numerous aha-moments where I developed a research-interest for something in class or during a project and briefly thought I’d found the thing I wanted to do. However, most of these things ended up not being the thing, because they had two shared features: they fascinated me, but didn’t contribute to improving the world as directly, permanently or importantly as I hoped I could one day.

That is, until I became familiar with the topic of intergroup conflict through an intriguing job and my bachelor’s thesis and ultimately, through a number of factors and experiences such as those with my father, decided on the topic of radicalization for my future research. I suppose you could call that academic daddy issues, if you were trying to be funny. And seeing as I will soon be starting to work on my thesis about just that and will certainly have a lot to learn and to think and babble about, what better time to venture an attempt at blogging? I hope to learn so much about this topic that eventually, I’ll be able to contribute to effectively preventing the radicalization of some people and to permanently de-radicalizing others, which entails changing the minds of people like my father. While doing that, I’ll attempt to provide an interesting, occasionally even entertaining read.

So, hello world, I suppose.