create function to generate simple sentence summarizing results for all key paramters

[StefanoMezzini]

I'm thinking something like an unordered list at the beginning of each report with something like one of the following:

• The evidence in favour of $\beta_1 > 0$ was equivalent to 10 consecutive heads in a single attempt.
• The probability of compound x remaining below the maximum allowed concentration until 2030 was equivalent to flipping 2 heads out of 2 coin flips.
• The estimated risk of population collapse is approximately equivalent to flipping 3 tails out of 3 consecutive coin flips.

[joethorley]

Nice. I like the idea.

I think positive or greater than a threshold if positive rather than $>$.

I think effect x rather than $\beta_1$

and maybe just 10 heads in a row as a single attempt is implicit?

[joethorley]

I think this function should live in the poisreport or subreport packages.

[StefanoMezzini]

I think specifying the single attempt can help clarify the effort rather than the occurrence of a coincidence, kind of like the "monkeys at a typewriter" argument, but I am happy to remove it if you think it's clear without it. I mainly fear that some may imagine flipping a coin repeatedly until they get 10 heads and get a distorted view of probability.

Maybe we should add it to {subreport} to allow others to use it, since {poisreport} is private?

[joethorley]

Yes good point on adding to subreport as poisreport as private.

Let's poll @nehill197 and @sebdalgarno and @aylapear for whether they think we should say

"Evidence was equivalent to throwing 10 consecutive heads in a single attempt"

vs

"Evidence was equivalent to throwing 10 consecutive heads"

vs

"Evidence was equivalent to throwing 10 heads in a row"

vs

"Evidence was equivalent to throwing 10 heads in a row on a fair coin"

vs

Something else?

[sebdalgarno]

cool idea - I like the simplest "Evidence was equivalent to throwing 10 heads in a row".
a couple questions:

• where in the report does this go? In Results (under each model subheader) but above the tables/figures subheaders?
• should we summarize SD of random effects (i.e. "evidence to support variation between x")
• should we also report magnitude on original scale? i.e. "Estimated change in x of 10 for each unit y"

[joethorley]

Stefano was thinking at the start of each report - kind of like a exec summary for an analytic appendix which I thought was a good idea.

I don't know how often clients are really interested in the magnitude of random effects?

yes good idea on potentially reporting magnitude on original scale as a good default. A more general solution to deal with transforms and non-linearity might be to report the "change in response as a predictor increases from its mean value by 1 SD"?

[joethorley]

I guess more robust still would be to report the change in response as a predictor increases from its median value to its 75th quantile so something like

Response y increased (or decreased) from xx1 to xx2 as predictor y increased from yy1 (median) to yy2 (75th quantile).

[StefanoMezzini]

The SD of the REs could be situationally useful, but I don't think we should have it as a default. I was thinking we would set this up so that the function generates bullet-point list for all parameter names passed to the function.

Yes, I think the change should generally be reported on the original or response scale, and the sentence should follow the model format (e.g., additive or multiplicative change). We may want to use something like "had x times greater/smaller odds" if we are modelling probabilities on the logit scale.

Response y increased (or decreased) from xx1 to xx2 as predictor y increased from yy1 (median) to yy2 (75th quantile).

This implicitly suggests a linear increase, so I think a unit change (x% increase every unit increase in the predictor) would be more appropriate.

[joethorley]

Good idea on odds for logistic and perhaps we could use percent change for things on the log scale?

My concern with (x% increase every unit increase in the predictor) only works when linear increase with identity link function with is quite rare.

[StefanoMezzini]

The % change only restricts to linear models if you intend it as an additive increase. Instead, if you mean it as a multiplicative/proportional change and transform to the response scale, it can work fine with log-link functions, too (including odds from a logit link):

$$y_x / y_{x+1} = \frac{\exp(\beta_0 + \beta_1 x)}{\exp(\beta_0 + \beta_1 (x + 1)} = \exp\left[\beta_0 + \beta_1 x - \beta_0 + \beta_1 (x + 1)\right] = \exp\left[\beta_1 (x - x + 1)\right] = e^{\beta_1}.$$

So, in this case, $$e^{\beta_1}$$ is the multiplicative change in the response for a unit change from $$x$$ to $$x+1$$.

[aylapear]

I like this one the best "Evidence was equivalent to throwing 10 heads in a row" as I find it clear and simple.

[nehill197]

I agree with Ayla and Seb!