Markdown show methods for our types

[palday]

Closes #273.

Needs tests.

I've marked this for v3.2 in the NEWS file and will do the necessary backport as soon as this is merged.

There's no method for CoefTable because that would be type piracy. I'll make an upstream PR.

The Markdown tables for the models are compact. This is intentional -- I think this is journal/publication friendlier and also makes them true Markdown tables. If we decide to add in LaTeX methods, this will also be convenient. The measures of fit (log likelihood, deviance, AIC, BIC) can be extracted separately and if someone really wants to fight with a journal, then they can assemble the pieces from the VarCorr and CoefTable methods.

OptSummary was low-hanging fruit, so I've included it. PCA seems fiddly won't be a single table anyway, so I've omitted it. (I also don't expect most people to include that in published work, so it really didn't seem like the effort.)

BlockDescription

rows	subj	fixed
36	BlkDiag
2	Dense	Dense

rows	subj	item	fixed
316	Diagonal
24	Dense	Diag/Dense
6	Dense	Dense	Dense

LikelihoodRatioTest

	model-dof	deviance	χ²	χ²-dof	P(>χ²)
reaction ~ 1 + days + (1 | subj)	4	1794
reaction ~ 1 + days + (1 + days | subj)	6	1752	42	2	<1e-09

MixedModel

	Est.	SE	z	p	σ_subj
(Intercept)	251.4051	9.506187	26.45	<1e-99	36.0121
days	10.4673	0.801735	13.06	<1e-38
Residual	30.89543

	Est.	SE	z	p	σ_subj
(Intercept)	251.4051	6.63226	37.91	<1e-99	23.78047
days	10.4673	1.50224	6.97	<1e-11	5.71683
Residual	25.59182

	Est.	SE	z	p	σ_subj	σ_item
(Intercept)	0.1955555	0.405190	0.48	0.6294	1.339766	0.495305
anger	0.0575541	0.016758	3.43	0.0006
gender: M	0.3207844	0.191266	1.68	0.0935
btype: scold	-1.0582595	0.256805	-4.12	<1e-04
btype: shout	-2.1047525	0.258529	-8.14	<1e-15
situ: self	-1.0549790	0.210303	-5.02	<1e-06

OptSummary

Initialization
Initial parameter vector	[1.0, 0.0, 1.0]
Initial objective value	1784.642296192471
Optimizer settings
Optimizer (from NLopt)	LN_BOBYQA
Lower bounds	[0.0, -Inf, 0.0]
ftol_rel	1.0e-12
ftol_abs	1.0e-8
xtol_rel	0.0
xtol_abs	[1.0e-10, 1.0e-10, 1.0e-10]
initial_step	[0.75, 1.0, 0.75]
maxfeval	-1
Result
Function evaluations	1
Final parameter vector	[0.9292, 0.0182, 0.2226]
Final objective value	1751.9393
Return code	FTOL_REACHED

VarCorr

	Column	Variance	Std.Dev.	Corr.
subj	(Intercept)	565.51069	23.78047
	days	32.68212	5.71683	+0.08
Residual		654.94145	25.59182

[codecov]

Codecov Report

Merging #474 (ccf8569) into master (2e23253) will increase coverage by 0.65%.
The diff coverage is 98.33%.

@@            Coverage Diff             @@
##           master     #474      +/-   ##
==========================================
+ Coverage   92.84%   93.49%   +0.65%     
==========================================
  Files          26       27       +1     
  Lines        1746     1906     +160     
==========================================
+ Hits         1621     1782     +161     
+ Misses        125      124       -1     

Impacted Files	Coverage Δ
src/MixedModels.jl	100.00% <ø> (ø)
src/blockdescription.jl	100.00% <ø> (ø)
src/randomeffectsterm.jl	96.72% <95.45%> (+2.60%)	⬆️
src/mdshow.jl	98.62% <98.62%> (ø)
src/generalizedlinearmixedmodel.jl	88.23% <100.00%> (+0.44%)	⬆️
src/likelihoodratiotest.jl	98.68% <100.00%> (+0.01%)	⬆️
src/linearmixedmodel.jl	94.30% <100.00%> (-0.02%)	⬇️
src/mixedmodel.jl	83.33% <100.00%> (+1.51%)	⬆️
src/optsummary.jl	100.00% <100.00%> (ø)
src/pca.jl	97.95% <100.00%> (+2.04%)	⬆️
... and 3 more

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[dmbates]

This looks fine to me. Thanks very much for doing this - formatting output is one of my least favorite parts of coding - probably tracing back to needing to write Fortran FORMAT statements in my youth.