p-value missing for `fit_power_law()`

[krlmlr]

What happens?

fit_power_law() no longer returns a KS.p component.

To Reproduce

igraph 1.6.0

options(conflicts.policy = list(warn = FALSE))
library(igraph)
g <- sample_pa(1000) # increase this number to have a better estimate
d <- degree(g, mode = "in")
fit_power_law(d + 1, 10)
#> $continuous
#> [1] FALSE
#> 
#> $alpha
#> [1] 2.738748
#> 
#> $xmin
#> [1] 10
#> 
#> $logLik
#> [1] -62.25711
#> 
#> $KS.stat
#> [1] 0.1037705
#> 
#> $KS.p
#> [1] 0.986668

^{Created on 2024-01-23 with reprex v2.1.0}

igraph 2.0.0

options(conflicts.policy = list(warn = FALSE))
library(igraph)
g <- sample_pa(1000) # increase this number to have a better estimate
d <- degree(g, mode = "in")
fit_power_law(d + 1, 10)
#> $continuous
#> [1] FALSE
#> 
#> $alpha
#> [1] 3.226469
#> 
#> $xmin
#> [1] 10
#> 
#> $logLik
#> [1] -63.90509
#> 
#> $KS.stat
#> [1] 0.07306791

^{Created on 2024-01-23 with reprex v2.1.0}

[bockthom]

Are there any news on this issue? I have seen that you declared this bug as "breaking change" of igraph 2.0.0 in your NEWS.md ("fit_power_law() no longer returns a KS.p component.")

However, without KS.p component, the function fit_power_law() is useless, at least, in the situations in which I need to use this function for power-law fitting. So, declaring this a "breaking change" is not a solution to the problem. Did you already investigate what had happened and why the component is missing now? Could you please fix this problem as soon as possible in your next release? I guess I am not the only user who needs the KS.p component of power-law fitting.
Thanks in advance!

[krlmlr]

The underlying C core function no longer returns this component. My attempts to use the new igraph_plfit_result_calculate_p_value() didn't give satisfactory results, so I gave up.

@jhollway: You mentioned in stocnet/migraph#284 that you could compute the p-value yourself. Would you like to share a pointer?

@szhorvat @ntamas: Appreciate your support here too.

[ntamas]

In theory it should be simple:

• igraph_power_law_fit() gives you an igraph_plfit_result_t object, which is the result of the fitting procedure.
• igraph_igraph_plfit_result_calculate_p_value() requires the result object as an input, along with a precision (say, 0.001), and then it gives you the p-value in an output argument.

[krlmlr]

I remember testing with the example given here, and the p-value came out as zero.

@Antonov548: can you please give it another try?

[ntamas]

That is an entirely valid p-value, depending on the input.

Try data/discrete_data.txt from https://github.com/ntamas/plfit as an input. When using the exact p-value calculation method, the p-value should turn out to be around 0.63 (alpha = 2.5833, xmin = 2, L = -9155.6).

[krlmlr]

I ran with the example in the OP, there the p-value comes out as 0.98. Are you expecting consistency in the p-values between igraph 1.6.0 and igraph >= 2.0.0?

[szhorvat]

No, the calculation changed between igraph 0.9 and 0.10. The previous calculation was faster but poorer.

See https://github.com/igraph/igraph/blob/master/CHANGELOG.md :

igraph_power_law_fit() does not calculate the p-value automatically any more because the previous estimation method did not match the results from the original paper of Clauset, Shalizi and Newman (2009) and the implementation of the method outlined in the paper runs slower than the previous naive estimate. A separate function named igraph_plfit_result_calculate_p_value() is now provided for calculating the p-value. The automatic selection of the x_min cutoff also uses a different method than earlier versions. As a consequence, results might be slightly different if you used tests where the x_min cutoff was selected automatically. The new behaviour is now consistent with the defaults of the underlying plfit library.

[ntamas]

I ran with the example in the OP, there the p-value comes out as 0.98

I can get 0.98 only with the current implementation of plfit if I use the older approximation method and also force the system to treat the incoming sample as continuous instead of discrete.

Discrete input, exact method

❯ src/plfit ../data/discrete_data.txt -p exact
../data/discrete_data.txt:
	Discrete MLE
	alpha =      2.58330
	xmin  =      2.00000
	L     =  -9155.61701
	D     =      0.00433
	p     =      0.62280

Continuous input, exact method

❯ src/plfit ../data/discrete_data.txt -p exact -c
../data/discrete_data.txt:
	Continuous MLE
	alpha =      2.75401
	xmin  =     25.00000
	L     =   -295.89683
	D     =      0.05713
	p     =      0.62200

Discrete input, old approximation

❯ src/plfit ../data/discrete_data.txt -p approximate
../data/discrete_data.txt:
	Discrete MLE
	alpha =      2.58330
	xmin  =      2.00000
	L     =  -9155.61701
	D     =      0.00433
	p     =      0.99995 (approximation)

Continuous input, old approximation

❯ src/plfit ../data/discrete_data.txt -p approximate -c
../data/discrete_data.txt:
	Continuous MLE
	alpha =      2.75401
	xmin  =     25.00000
	L     =   -295.89683
	D     =      0.05713
	p     =      0.97629 (approximation)

Which of these results (if any) are you getting @krlmlr ?

[maelle]

@krlmlr are the next steps

• your trying again
• and then... the change being documented?