maandag 10 december 2012

Stata: various

Below is a selection of practical stuff not worth spending a full post about

Display lead values

Some administrative sources or classification codes use fixed length numbers, which have leading zero's for the first so many numbers. To allow for this in Stata (effectively converting the number into a string), walk through the following page:

vrijdag 7 december 2012

Polarization: TINA?

One big question that runs through my research is the contraposition of wage inequality and wage equality. At first, it seems like a very simple, nearly trivial point. Let me expand on it.

We all know that wages, by employer's request, have the tendency to move towards marginal productivity. However difficult to calculate, the difference between a brilliant order of one engineer and a stupid order of another one is more important than between a brilliant operation of one manual worker and a stupid operation of another worker. Hence, the good engineer gets paid a lot. This is in accordance with the demand for bright people in management, while manual workers have a whole army of unemployed equally unschooled workers that cause a surplus offer. Therefore, for each segment in the workforce, there is an optimal wage.

Ever since 2006, however, the world has discovered externalities. Externalities come in between seemingly Pareto efficient deals, such as the one discribed above. Would it be possible that two segments in the workforce are both better off if government intervenes? Wilkinson & Pickett believe so: inequality has a price. That price is to be paid by all, also by the rich. In so far that the underclass or precariat causes trouble, this price goes up. This is no moral position at all, I confess, but it may be a very convincing one. The upper segments will profit from having a lower wage, if it smoothens differences in society. Of course, the underclass gets leveled up, which may equally improve happiness and even provide chances for development. In the end, there will be a Pareto efficient equilibrium in some degree of wage inequality way less than the one based on marginal productivity.

Now there is a paradoxical complication in this reasoning: what is the optimal choice when the underclass causes trouble. One can suppress the consequences or the causes, and be indifferent between both options. For example, the upper class can demand a higher wage to compensate for increasing insecurity and the need to have private surveillance. This will actually be the first idea from a free riding micro perspective. It will fail for two reasons:
- The need to be surrounded by guards implies the cost of individual freedom in all cases. In a way, one could however still say that one can be bribed to accept this cost.
- Wages rise far above marginal productivity, which should be compensated by wages far below marginal productivity for lower skilled workers. This will however create ever more trouble, so that this solution is not stable.

In my view, therefore, there is a rational foundation for more equality, which may be the subject of specification in further research. I hope social sciences one day will be able to bring one and one together on this matter.

woensdag 5 december 2012

Latin abbreviations

APA has provided this list, where you'll find that a.o.:
  • E.g. = exempli gratia = for example
  • I.e. = id est = that is
  • Cf. = confer = compare with
  • Etc. = et cetera = and so on
  • Well... et cetera.
Moreover, we should use al of these abbreviation only within parentheses (and footnotes maybe). Except for et al. (et alii), which is used all over the place. And mind you, when you use these abbreviations, there is no need to italicize!

Some more words of warning from the gentle folks at Sussex. Not.
And from Europe! Here.

vrijdag 23 november 2012

Online graphical calculators

Good news for people who want quick graphs: there is now a Google graphical calculator.

We already loved graph.tk, which delivers these kind of beauties:


Well, Google's graph thing may not be as slick, it is quite handy as you can enter multiple functions on one line from the search box. This for example gives us the Batman equation.

It doesn't replace your Matlab copy, as the output is below publication quality, but for a quick check it is brilliant and fun.


maandag 1 oktober 2012

World salaries

http://www.worldsalaries.org/

Seems like a huge exercise to combine so many sources, comparing wages by sector, occupation and country. Not customizable at all, sometimes outdated. Props for precisely quoting sources.

For amusement only.

vrijdag 21 september 2012

Labour Stats goes through a linguistic crisis

I thought about changing the name of this blog to 'Labor Stats'. Decent American spelling. It is said to be more logical. But just how logical do languages have to be? Does logic imply internal consistency, respecting etymology or rather streamlining common practice? Then which spelling is preferable: Merriam-Webster, Cambridge Dictionary, Oxford English Dictionary, BBC practice, MS Worst?

Having studied classical languages, I first considered etymology and the infamous -ising/-izing debate. The Greek ending is -idzein, Latin -izare. So why making it French when it isn't? Even old English uses the -izing form, although mixed with the s-spelling. There are other similar cases. Color is Latin too, it means colour. Why not simply write it the way it has always been (like the Americans do)? Merriam-Webster is on your side.

Second: internal consistency. Humour leads to humorous. We could spell it humor right away. It is more logical, easier for foreigners. In particular I like the use of the suffix -ize for everything you 'make'. That keeps you from writing analize, unless you have perverse motives. It is analyse or analyze. There's a preference for the former, because it comes from analysis-ize, largely omitting the suffix. Common British spelling (en-UK) thinks about it differently.

Etymology and consistency. Jolly good, but we may not forget that language is an independent cultural object. Even strict grammar and spelling rules cannot enter the living room of people and decided what dialect they speak, words they take up. During some period of time, French has influenced English. It has changed words English already had, and introduced words that have a history before they were French. These words had a history before they were Latin or Greek too. It is a cultural bias to assume civilization started 1000 BC. Maybe writing did, but then again this must have been more evolutionary than revolutionary. If you study classical languages, you quickly learn a new vocabulary for every Greek poet you read. Don't try to find the original writings, cause you will not even understand most signs.

This is exactly why I keep Labour in Labour Stats. It looks familiar, it has history and it's not that far from logical. If English would evolve towards 'labor', I would not mind at all, but for the time being labour ends on -our, error on -or and labourer on -er. It has been different before and it will be in the future, but the changes are minor and reflect the history of a word.

Then again, when the European Union tries to -ise English, primarily to please the French, I will first oppose. For me, the Oxford English Dictionary is a way more important authority that nicely balances logic, etymology and consistency. It interacts with language as it is used, without standardizing fads. Here is someone who agrees.

P.S. Don't try to make Microsoft Office talk Oxford English. You just bumped into the limits of closed source software.

dinsdag 11 september 2012

Making the Pay Gap look good (Tableau)

Here's a nice illustration of the capabilities of Tableau Software. Quite useful for the stakeholders in some projects I did.
http://www.tableausoftware.com/public/gallery/making-pay-gap-look-good



Now everybody's impressed. But actually Tableau does not help you that much. It is a nice tool, but the quintessential thing about making graphs and tables is to give a message. These Tableau tables just provide a way to explore, yet that is what researchers are paid for. Using the interactive Tableau charts, you basically provide a fun tool to viewers. I agree there is a lot of demand for useless stuff too.

I liked the Pay Gap visualization anyway, but let's look at far worse graphs:
http://www.tableausoftware.com/public/gallery/best-dutch-restaurants --> Is this a restaurant guide or a statistical tool? Main conclusion is that fancy restaurants are more likely to be found near the coast and the capital. Oh no...

Or this graph, which has wonderful colours, except you don't know what they stand for. Also, they do linear regression on sight, suggesting a discrete point where effects pop in. Could be an exponential effect though. http://www.tableausoftware.com/public/gallery/game-reviews

Yet, let us finish on a good note. While being easy to make with any statistical program, this graph and the interactive menus confront us with some astonishing insight. Very appropriate point of view.
http://www.tableausoftware.com/public/gallery/great-divide


donderdag 6 september 2012

Arme West-Vlamingen

Een tijdje geleden vroeg een journaliste mij uitleg bij een opvallende statistiek. Uit de loonstructuurenquête bleek dat de West-Vlamingen minder verdienen dan de meeste Walen (!). Ik vind het artikel waarop ze zich baseerde niet onmiddellijk terug, maar hier staat iets gelijkaardigs.

Na wat uitleg over arbeidsmobiliteit en de methodologie (de SES-enquête houdt de lonen bij op basis van de werkplaats en enkel voor bedrijven met meer dan tien werknemers) besloot ik dat de rijkdom in West-Vlaanderen allicht niet bij de werknemers zit.

Deze vakantie ontmoette ik dan een arme Amerikaan uit Montana. Dus dacht ik het regionaal GDP/BBP van Montana te vergelijken met dat van West-Vlaanderen. Montana, met ca. 900 000 inwoners, haalt 36 miljard USD. West-Vlaanderen, met 1 160 000 inwoners, 34 miljard EUR (in 2009). Close match, ook per capita. Maar dit rapport van Eurostat toont meteen ook aan dat het regionaal BBP van West-Vlaanderen helemaal niet lager is dan dit van Oost-Vlaanderen en Limburg. Antwerpen, Vlaams & Waals-Brabant scheren weliswaar hogere toppen, maar zo arm zijn die West-Vlamingen dus niet. Ik denk dat dit het bewijs is voor mijn fameuze quote.

Even more graphics ... Excel to the rescue?

After a while, you get bored of Excel so much that you eventually forget it is capable of doing some good things too. That is, with the right plug ins.

The must-have plug in is Daniel's XL Toolbox. It has some statistical options that may save you some bucks on the basic SPSS package. I particularly like the option to make charts publication ready.

Not really a plug-in, but simply stunning, is Juice Labs' Chart Chooser. An online gallery of templates you can download to get started with better-than-average graphs. The guys made Chart Cleaner in the past, which improve your charts, BUT it forces you to enable macros.

The people at Juice Labs have some more goods in store, amongst which I am simply stunned by the Excel Geocoding Tool. What this allows you to do is to have a field describing an address or a town (don't try regions or countries), and then with one press on the button obtain the longitude and the latitude. There is even a link to Google Maps. What's the deal? Well, I'm thinking of the Stata tmap user command. This plots borders on your graph, and with the geocoding tool, you can overlay regional capital town names, for instance, or add values on exactly that spot. I realize the tmap geographic projection is not the best in the world, but at least this procedure is logical, and I like that.

woensdag 5 september 2012

More graphics ... javascript and html

As I see it, three teams compete for the King of Charts title:
  • Illustrators
  • Programmers
  • Statisticians
However powerful our statistical languages, we're still far from the code that drives the Internet. A few websites of our online friends provide javascript code for very neat graphical output.
  • Google Chart Tools: you must love the investment Google does in products that won't bring money in the short run. Very good graphics, intuitive syntax. There is even this playground.
  • Fusion charts: it's free for schools and it does charts... but kind of an overload to me
  • Highcharts: didn't really bother, yet the graphs look good
All in all, I believe these programmer tools are pretty useless for now. For instance, I manage to make a geochart with the Google syntax, but it's not possible to display city names unless you hover over the dots. Nice online, but not what we'd print out. Too bad, as Google's simplicity and respect for the ISO country codes is what we need.

Cornell on statistical packages and Ethan Fosse's blog

This guy, Ethan Fosse, is a sociologist who uses R. Instead of Stata. Picture this. He does know a lot about graphics but I particularly liked this corner of the blog where he points to unsolved questions in sociology. Rising inequality in any field is one such question that intriges me too. Interesting readings. Found it through this R blog (Revolutions), when I was actually looking for sociologist using Stata. And yes, it's what people at Cornell recommend to learn first. I quote:


General Purpose Software

Quantitative data analysis in sociology is dominated by three all-purpose programs, Stata, SPSS, and SAS. All three are available on Cornell's Athena computer cluster, and all three are excellent.
We typically recommend that graduate students learn Stata first. SPSS has some attractive features, but it has been losing ground to the other two for the past 15 years. Although SAS is the most comprehensive, it has a relatively inefficient programming language. Stata is almost as comprehensive as SAS, and it has a much more efficient programming language. And, if you need one of the special routines that SAS offers but Stata does not, you will often end up using a more specialized computer program anyway because even SAS is not quite as good as the specialized software (see below). Nonetheless, SAS is particularly well-suited for very large datasets, and SAS is also the dominant package for the federal government. If you work with many types of government data, you will find that the best supporting documentation is written for SAS users.
UCLA statistical computing has the best (we think) on-line set of resources for these three programs. See http://www.ats.ucla.edu/stat/. Also, Cornell's CISER offers tutorials for all three programs. Seehttp://www.ciser.cornell.edu/ASPs/workshops.aspx.



Infographics

To us, researchers, two opposites demand always pop up:

  • Be precise
  • Make science look fun
In order to lean a bit more towards the latter, people created infographics and infographics tools. It's like the kind of graphs you read in newspapers or on posters. You may get close to the chart itself if you're really handy with Stata, but it takes way to much time for the simple chart you get. There are many tools that may do that easier and better. There are also much more artistic contribution you'll read about on the cool infographics blog. And be sure to check out this Swiss website on data visualizations.

The drawback: which tool will do what you want and exactly what you want? Basically, you need to be able to customize and add data. That brings you terribly close to Stata, doesn't it. Yet sometimes, these tools will really make it happen:
  • Tableau: it's the more sophisticated package, available in a free ("public"), paid desktop and server version. You get it. Consultancy stuff. Basically it's all about two axis and a third dimension expressed in colours or size of dots. Also has annoying interactive dashboards we do not need.
  • Many eyes: it's IBM software, so it should eventually find its way into SPSS. Nice charts, hard way to get there though. Worth a try and looks professional.
  • Infogr.am: I haven't really figured out. It makes nice graphs, most importantly including the matrix charts I love (coloured little people representing counts). It's beta and buggy at the moment, and quite inflexible. Like how on earth do you change the shapes in the matrix chart? I do not know.

  • Pik to chart: this is only the lay-out part: nice fonts, few charts really.
Word clouds and social media
  • wordle: looks very good
  • visual.ly: the sole purpose of this website is to show off your work. Boring. Oh, there are a few tools to combine with your Facebook or Twitter website. Fancy stuff. Far from what we do.

Network visualizations
  • Gephi: network visualizations. I don't do that. Much like Graph Viz, but I suppose more intuitive.

(I got the overview here, here and mostly here, still plenty of tools I haven't tried yet)

Olympic Games of graphics - Junk Chart

This is one hell of a good graphical overview, on the NYT website. Just take a look and be amazed.

http://www.nytimes.com/interactive/2012/08/05/sports/olympics/the-100-meter-dash-one-race-every-medalist-ever.html

They invested a lot of money it seems, as here you have the same engine applied to Swimming.



And that's just an introduction to a wonderful blog about charts, called Junk Charts. The discussion of the Olympic charts is found here. And this is a nice appreciation of Kenworthy's work.

vrijdag 31 augustus 2012

Probability bar graph

Here's Nicholas J. Cox tutorial on how to get a histogram with varying bin widths. It's a nice way to get to understand probability densities.

http://www.stata.com/support/faqs/graphics/histograms-with-varying-bin-widths/

Demonocrazy

http://demonocracy.info/

This is what descriptive statistics should look like.

State debt of India, in 2 billion dollars trucks.


Stata regression prefixes

Lagged values
l.var = l1.var = variable at t-1
l2.var = variable at t-2
l(1/3).var = l1.var l2.var l3.var
etc.

Leading values
f.var = f1.var = variable at t+1
f2.var = variable at t+2

Differences
d.var = var[t] - var[t-1]
d2.var = ( var[t] - var[t-1] ) - (var[t-1] - var[t-2])

Seasonal differences
s.var = var[t] - var[t-1]
s4.var = var[t] - var[t-4]

Principal Global Indicators

http://www.principalglobalindicators.org

Fantastische website die gegevens van Eurostat, ECB, OESO e.a. samenbrengt.

Landencodes (country codes)

Nummerplaten, WK-voetbal, statistieken, ... landennamen worden op verschillende manieren afgekort. En nu eens is Griekenland EL (wat trouwens komt van Hellas), dan weer GR. Duitsland is DE (Deutschland), maar Albanië AL, terwijl het land in de eigen taal Shqipëria heet.

Dus hebben we nood aan standaarden. En standaarden, daarvoor moet je bij de ISO zijn. Van vijzen over branddeuren tot landencodes. De standaard is ISO 3166. Het officiële document kost een aardige stuiver, maar gelukkig hebben we de piraten van Wikipedia, waar de twee- en drielettercodering gewoon gratis te vinden is.

Rest ons enkel consistent deze afkortingen te gebruiken.

donderdag 30 augustus 2012

Belgische administratie

Rijksdienst voor sociale zekerheid (RSZ)
http://www.rsz.fgov.be/nl/home

Sociale zekerheid portaalsite
https://www.socialsecurity.be/site_nl/home_default.htm

dinsdag 14 augustus 2012

Shige's Research Blog: Mplus vs. Stata for Heavy Computation

Golden tip (from 2006)

Do the basic stuff with basic Stata and the heavy stuff with Mplus, which has the same price no matter how many cores your processor has.

Shige's Research Blog: Mplus vs. Stata for Heavy Computation

vrijdag 10 augustus 2012

Gender studies

Ingstituut voor de Gelijkheid van Vrouwen en Mannen
http://igvm-iefh.belgium.be/nl/

Vrouwen hebben alles, dus ook een specifieke wiki-website.
http://www.wikigender.org

Decenniumdoelen 2017

Waarom ze een decennium laten verstrijken in 2017 is mij een raadsel, maar hier alvast een aardige campagne voor kwalitatief en duurzaam werk.

http://www.decenniumdoelen.be/

Eurobarometer

De Eurobarometer is zo'n typische jack of all trades. Als het goed uitkomt zit er een module in die twee of drie pertinente vragen uit je thema stelt, maar zelden meer dan dat. Toch ben ik een fan, om te beginnen omdat je de data gratis krijgt. Het gaat het snelst als je een ICPSR abonnement hebt, maar voor de anderen is er GESIS. Veel plezier!

http://info1.gesis.org/dbksearch19/SDESC2.asp?no=5481&search=eurobarometer&search2=&DB=e&tab=0&notabs=&nf=1&af=&ll=10

Mobiliteitsgegevens

In onze fantastische bureaucratie is er ook een dienst die zich bezighoudt met het verzamelen van mobiliteitsgegevens, c.q. pendelafstand. Dit is een uitermate interessante statistiek voor milieu-wetenschappers maar ook voor arbeidsmarktvorsers. Helaas zijn de data niet zomaar op te vragen, want in principe worden ze enkel ter beschikking gesteld in functie van het beheer van mobiliteit. Helaas paashaas.

https://www.mobilit.fgov.be/nl/indexReframed.htm?newURL=/nl/mobil/mobaccn/diagnosn.htm

Indexcijfer van de conventionele lonen (ICL)

http://www.werk.belgie.be/moduleDefault.aspx?id=7390

Verzameld door FOD WASO. Deze statistiek werd ook gebruikt door de CRB voor het maken van prognoses omtrent de loonstijging voor het Technisch Verslag.


Loonakkoorden

Een overzicht van recente loonakkoorden is te vinden via de sociale secretariaten of via FOD WASO.

Minimumloon

In België beslissen cao's gesloten in de Nationale Arbeidsraad over het gewaarborgd minimum maandinkomen. Opvallend is dat dit voor jonge werknemers minder is. Dit lijkt in strijd met het Europese verbod op leeftijdsbarema's maar heeft de hervormingen van de loonakkoorden doorstaan.

Meer info op de site van FOD WASO.

http://www.werk.belgie.be/detailA_Z.aspx?id=1024

Wage Indicator

Wage Indicator is een Nederlands initiatief dat probeert via websurveys internationale loongegevens te verzamelen. Dit project krijgt de steun van de ILO. Het idee is fantastisch: als 'vuurtoren' geeft de website informatie over loonverschillen en de waarde van een werknemer. Lonen zijn bovendien moeilijk te verzamelen gegevens, dus zeer gegeerd. Het team dat de database beheert vertrekt vanuit een sociale motivatie. Helaas spelen de wetten van de markt ook hier, en moet een serieuze som neergeteld worden om de data te gebruiken. Ook zijn de enquêtes niet openbaar of open source, waardoor je op hun kwaliteitscontrole moet vertrouwen. Dit zijn inherente zwaktes die de de automatische verbetering van het product in de weg staan. Er is niettemin reeds vrij veel output, hoewel op academisch vlak nog terein te winnen valt.

http://www.wageindicator.org

Loonnorm

Sinds 1996 is er in België een 'loonnorm', een akkoord tussen vakbonden en werkgevers dat tweejaarlijks een maximale loonsstijging bepaalt. In de praktijk is dit gewoon een omzetting van het advies dat de Centrale Raad voor het Bedrijfsleven (CRB) geeft in het voorbereidend Technisch Verslag. Ook komt het al eens voor dat er geen akkoord bereikt wordt, en dan legt de regering dit op. Sowieso is het wachten op de regering om het akkoord kracht van wet te geven, wat in dit laatste geval per definitie gebeurt.

De filosofie achter de loonnorm is georganiseerde loonmatiging. Op die manier proberen we gelijke pas te houden met de loonevolutie in de buurlanden die ook onze belangrijkste handelspartners zijn: Duitsland, Frankrijk en Nederland. Het uiteindelijke doel is het behoud van de concurrentiepositie en de bevordering van de werkgelegenheid.

In de mate dat de economieën van de hierboven genoemende handelspartners gelijk zijn aan die van België, valt er iets te zeggen voor zo'n geagregeerde aanpak. Hebben we echter met divergerende structuren te maken (voorbeeld: lage loonarbeid in Duitsland), dan houdt het geen steek. Maar ook intern evolueren verschillende sectoren op een ander tempo. Die beweging wordt afgevlakt: in de dienstensector moest men in 2010 op de rem gaan staan terwijl bedrijven zeer graag meer loon zouden uitbetalen. Het argument dat je dan kan maken voor een loonnorm, nl. het voorkomen van verdere dualisering op de arbeidsmarkt, komt niet overeen met de oorspronkelijke doelstelling. De loonnorm is met andere woorden een vreemd gedrocht dat finesse mist.

Meer informatie vind je op de site van FOD WASO. Hou er rekening mee dat deze pagina geüpdated wordt, en er zo al eens informatie verdwijnt.


EGP via ISCO

De sociologie heeft niet erg veel kant en klare concepten, maar om beroepen te groeperen is er wél een systeem: de EGP-schaal (Erikson–Goldthorpe–Portocarero).

Nu is het altijd een gedoe om deze schaal te construeren op basis van de beschikbare data. Gelukkig hebben we Harry Ganzeboom, die beroepenclassificaties bestudeert.

Op onderstaande links staan zijn beschouwingen en tools, voor statagebruikers is er het handige isko programma, te downloaden via - ssc install isko -

Happy analysing ! 

http://home.fsw.vu.nl/hbg.ganzeboom/isco08/
http://home.fsw.vu.nl/hbg.ganzeboom/ismf/index.htm

Sociale secretariaten

In België bestaat er een gek systeem genaamd sociale secretariaten. Dit zijn dienstverlenende bedrijven die andere bedrijven bijstaan wat betreft de personeelsadministratie. Ze berekenen de lonen, loonstijgingen, vakantiedagen, etc. en houden de rechten van de werknemers in de gaten. Persoonlijk vind ik dat deze sector in zijn geheel vervangen zou moeten worden door gedegen informatica en informatie verstrekt door de betrokken ministeries. Maar zover zijn we dus nog niet.

Een lijst met alle sociale secretariaten vind je op de site van FOD WASO.

De sociale secretariaten houden ongelofelijk veel gegevens bij, maar voor onderzoekers blijft de honingpot te vaak gesloten. Het meest frustrerende is dat alle gegevens verschillende malen vergaard worden. Dubbel werk dus, dat zich daarenboven ook nog eens in private handen bevindt.

Af en toe kan het zijn dat een sociaal secretariaat haar kennis openbaart. Op die manier kunnen we vaak overzichtelijker (een comparatief begrip) de conventionele loonevolutie opvolgen. De manier waarop FOD WASO de cao's indexeert is immers op vandaag (augustus 2012) nog niet geperfectioneerd.

Hieronder enkele links naar websites van sociale secretariaten die hiervoor geconsulteerd zijn geweest in het verleden.

http://www.sd.be/site/website/be/nl/5000A/50C00C/50C20C/50C26C/
http://www.sd.be/site/website/be/nl/5000A/50C00C/50C20C/50C26C/IndexEnLoon?period=102007
http://www.clbvzw.be/loonsverhogingen_april_2008.htm
http://www.acerta.be/xq/ASP/taal.NL/site.1/qx/home.htm
http://www.sodalis.be/index1.asp?pageID=59&menuID=34
http://www.groups.be/index.htm
http://www.groups.be/1_400.htm

woensdag 4 januari 2012

Heteroskedasticiteit

deze post is herzien op 11-2-2013

Theorie

Homoskedasticiteit is een centrale assumptie in OLS, en betekent de fout niet varieert volgens de waarden van het model, dat is wenselijk (als in 'homofilie'). Bij heteroskedasticiteit wordt hier dus aan gezondigd. Deze assumptie kan met andere technieken (GMM, ML) weggenomen worden.

Testen

Er zijn twee populaire testen voor heteroskedasticiteit: Brausch-Pagan en White. Het idee is gelijkaardig: bij Brausch-Pagan gaan we de gekwadrateerde fout $ ( y - \hat{y})^2 $ (de restvariantie) regresseren op een quadratische functie van de voorspelde waarde $ \hat{y} $.

Bij White regresseren we op alle andere (unieke) verklarende variabelen in het model. De R² van dit model geeft aan of er heteroskedasticiteit is. Idealiter is R² hier zeer laag. De teststatistiek voor de nulhypothese is:

nR² -> Chi²(m), met m = aantal variabelen in het model

Referenties

  • White test: Hayashi 2000, p. 131