Posts from April 2021 (18)

There’s a new research paper out from the Christchurch Health and Development Study, which recruited a group of people when they were born, in mid-1977, and has been following them ever since.  Those of the participants who were parents have been asked about physical discipline of their children on four occasions: when they were 25, 30, 35 and 40.  Obviously, over time, the number who are parents has increased (from about 150 to over 600), and the children have (on average) gotten older — when the parents were 25, most of the kids would have been pre-school; the group now includes a few very young children but many who are teenagers.

The good feature of birth cohorts like the Christchurch study is that you get to see the same people throughout the course of their lives; the bad feature is that at any given time everyone is exactly the same age.  In statistician jargon, age is completely confounded with period: you are completely unable to distinguish effects of ageing from time trends. When you see that the proportion of parents reporting hitting their kids has gone down from 77% to 42% over the 15 years, you can’t tell, at all, whether this is an effect of these specific parents getting older and more experienced or an effect of parents in general being less likely to hit their kids.  It’s hard (though not impossible) even to tell if it’s an effect of the kids being older.

As you’d hope, the research paper, in the NZ Medical Journal (paywalled) is very clear on this

…explanations include: increasing maturity of the parenting sample over time (less reactive, more experienced, older parents); a cultural shift towards the unacceptability of violence towards children over the period of the study; and the law change in 2007, which prohibited physical punishment and violence towards children. Given the nature of its design, it is not possible for the current study to distinguish between these explanations.However, it does not seem unreasonable to conjecture that all three processes are likely to have played a role.

And indeed it doesn’t seem unreasonable, as long as you recognise that the not seeming unreasonable isn’t a conclusion from the data and relies entirely on external plausibility.  The researchers do conclude that there’s still a lot of physical punishment going on, and that efforts are needed to stop it; the former is well-supported by the data and the latter is a policy response, not a scientific conclusion. That’s all good.

So let’s look at the reporting (some of this may have changed before or after I read it, of course)

• Radio NZ: Number of parents smacking children drops by half in 15 years. No caveat about the study design meaning this conclusion is basically unsupported. Gets the journal name wrong.
• 1 News: More than 40% of parents still use physical discipline years after law change, latest data shows. The story is better than the headline, and the Children’s Commissioner is quoted as saying “It’s representative of one cohort born in 1977, one group in one year in one generation, but there has been a discernible drop over the years.” I’d be happier if it was clearer from the beginning that this doesn’t claim to be representative of NZ in general over time.
• NZ Herald. Parents’ physical punishment of children decreasing, but still common – report. Slightly better headline; much clearer in the story. “…the rate of physical punishment against children was higher when parents were younger, and then decreased with age… because of the way the study was designed, it couldn’t pinpoint how much the rates reduced because of the law change.”
• Otago Daily Times. Parents still smacking, study finds. Good. “The authors warned that their method of studying a cohort of people over time meant they could not gauge what the attitude of new parents in 2021 might be to physical punishment. However, the research did suggest rates of smacking or hitting children were high enough to be a public health concern.”
• Stuff. Physical punishment of children still ‘fairly common’, despite anti-smacking law change – study.  There’s no caveat about the study design, and the story says “New research, published in the New Zealand Medical Journal on Friday, examined how the prevalence of child physical punishment changed in the 15-year period between 2002 and 2017 – before and after the legislation came into force.”, which isn’t true. And that’s not a link to the research paper.
• Newshub. Who’s most likely to use physical discipline against their kids revealed. The headline’s a bit dodgy given the non-representative group of parents, but the caveats are good “Because the study followed a cohort of parents who aged 15 years over the course of the study, “it is unclear what rates of physical punishment of children would be in studies of contemporary young parents”.

Team Ratings for Round 23

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 146 matches played, 99 of which were correctly predicted, a success rate of 67.8%.
Here are the predictions for last week’s games.

Predictions for Round 23

Here are the predictions for Round 23. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Week 11

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 38 matches played, 25 of which were correctly predicted, a success rate of 65.8%.
Here are the predictions for last week’s games.

Predictions for Week 11

Here are the predictions for Week 11. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 18

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 95 matches played, 60 of which were correctly predicted, a success rate of 63.2%.
Here are the predictions for last week’s games.

Predictions for Round 18

Here are the predictions for Round 18. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 8

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 56 matches played, 38 of which were correctly predicted, a success rate of 67.9%.
Here are the predictions for last week’s games.

Predictions for Round 8

Here are the predictions for Round 8. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

The epidemic modelling group at Te Pūnaha Matatini (who work a few floors above me) won the Prime Minister’s Science Prize for their work on modelling the Covid epidemic in New Zealand.   There have been some descriptions in the media of their models, but not so much of what it is that mathematical modelling involves.

A good mathematical model captures some aspect of the way the real process works, but leaves out enough of the detail that it’s feasible to study and learn about the model more easily.  The limits to detail might be data available or computer time or mathematical complexity or just not understanding part the way the process works.  Weather models, for example, have improved over the years by using more powerful computers and more detailed input data, enabling them to take into account more features of the real weather system and more details of Earth’s actual geography.

The simplest epidemic models are the SIR and SEIR families.  These generate the familiar epidemic curves that we’ve all seen so often: exponential on the way up, then falling away more slowly. They are also responsible for the reproduction number “R”, the average number of people each case infects.  The simple models have no randomness in them, and they know nothing about the New Zealand population except its size.  There’s a rate at which cases come into contact with new people, and a rate at which contacts lead to new infections, and that’s all the model knows.  These models are described by simple differential equations; they can be projected into the future very easily, and the unknown rates can be estimated from data.   If you want a quick estimate of how many people are likely to  be in hospital at the epidemic peak, and how soon, you can run this model and gaze in horror at the output.  In fact, many of the properties of the epidemic curve can be worked out just by straightforward maths, without requiring sophisticated computer simulation.  The SEIR models, however, are completely unable to model Covid elimination — they represent the epidemic by continuously varying quantities, not whole numbers with uncertainty.  If you put a lockdown on and then take it off, the SEIR model will always think there’s some tiny fraction of a case lurking somewhere to act as a seed for a new wave.  In fact, there’s a notorious example of a mathematical model for rabies elimination in the UK that predicted a new rabies wave from a modelled remnant of 10^-18 infected foxes — a billion billionth of a fox, or one ‘attofox’.

The next step is models that treat people not precisely as individuals but at least as whole units, and acknowledge the randomness in the number of new infections for each existing case.  These models let you estimate how confident you are about elimination, since it’s not feasible to do enough community testing to prove elimination that way.   After elimination, these models also let you estimate how big a border incursion is likely to be by the time it’s detected, and how this depends on testing strategy, on vaccination, and on properties of new viral variants.  As a price, the models take more computer time and require more information — not just the average number of people infected by each case, but the way this number varies.

None of the models so far capture anything about how people in different parts of New Zealand are different.  In some areas, people travel further to work or school, or for leisure. In some areas people live in large households; in others, small households. In some areas a lot of people work at the border; in others, very few do.  Decisions about local vs regional lockdowns need a model that knows how many people travel outside their local area, and to where.  A model with this sort of information can also inform vaccination policy: vaccinating border works will prevent them getting sick, but what will it do to the range of plausible outbreaks in the future?  Models with this level of detail require a huge amount of data on the whole country, and serious computing resources; getting them designed and programmed correctly is also a major software effort.  The model has an entire imaginary New Zealand population wandering around inside the computer; you’re all individuals!

A mathematical modelling effort on this scale involves working from both ends on the problem: what is the simplest model that will inform the policy question, and what is the most detailed model you have the time and resources and expertise to implement?  Usually, it also involves a more organised approach to funding and job security and so on, but this was an emergency.  As the Education Act points out, one reason we have universities is as a repository of knowledge and expertise; when we need the expertise, we tend to need it right now.

Team Ratings for Round 22

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 143 matches played, 96 of which were correctly predicted, a success rate of 67.1%.
Here are the predictions for last week’s games.

Predictions for Round 22

Here are the predictions for Round 22. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Week 10

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 34 matches played, 23 of which were correctly predicted, a success rate of 67.6%.
Here are the predictions for last week’s games.

Predictions for Week 10

Here are the predictions for Week 10. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 17

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 89 matches played, 56 of which were correctly predicted, a success rate of 62.9%.
Here are the predictions for last week’s games.

Predictions for Round 17

Here are the predictions for Round 17. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 7

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 48 matches played, 33 of which were correctly predicted, a success rate of 68.8%.
Here are the predictions for last week’s games.

Predictions for Round 7

Here are the predictions for Round 7. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.