Correction

Abstract

This note provides correction to some numerical results in Krivitsky P. N., Coletti, P., and Hens, N. (2023), “A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks,” Journal of the American Statistical Association, 118, 2213–2224.

While working on the rejoinder to discussion of Krivitsky, Coletti, and Hen (2023b), we identified an error in our calculation of the covariance matrix of the parameter estimates, resulting primarily in all standard errors being underestimated, most slightly but some by an order of magnitude. Table 1 here corrects Table 1 in the article and indicates where significance levels were affected. Table 2 corrects the ${\chi }^2$ omnibus tests reported in the text and Table 3 the contrast tests. Where P-values were affected, this is indicated.

Table 1 Parameter estimates and corrected standard errors for Model 1 and Model 2.

Relationship effect	Coefficient (S.E.)
× Network-level effect	Model 1	Model 2
edges × $\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}(n_s)$	–14.28 (3.78)^⋆⋆⋆	–13.78 (3.69)^⋆⋆⋆
× ${\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}}^2(n_s)$	5.69 (1.71)^⋆⋆⋆	5.47 (1.66)^⋆⋆∘
if Brussels post code	0.08 (0.19)	–0.02 (0.21)
× $\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}(\text{pop}.\text{ dens}.\text{ inpostcode})$		0.04 (0.03)
if on weekend	0.14 (0.06)^⋆	0.13 (0.06)^⋆
2-stars	1.91 (4.95)^∘	1.14 (4.55)
× $\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}(n_s)$	–2.15 (5.87)^∘∘∘	–1.22 (5.38)^∘∘
× ${\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}}^2(n_s)$	0.34 (1.72)^∘∘	0.07 (1.58)
triangles	5.55 (11.55)^∘∘∘	7.30 (10.72)^∘∘∘
× $\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}(n_s)$	–3.46 (14.29)^∘	–5.65 (13.28)^∘∘∘
× ${\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}}^2(n_s)$	0.93 (4.38)	1.60 (4.09)^∘
Young Child with Young Child	8.60 (1.88)^⋆⋆⋆	8.66 (1.83)^⋆⋆⋆
Young Child with Preadolescent	9.10 (1.88)^⋆⋆⋆	9.15 (1.84)^⋆⋆⋆
Preadolescent with Preadolescent	8.17 (1.85)^⋆⋆⋆	8.24 (1.81)^⋆⋆⋆
Adolescent with Adolescent	7.70 (1.84)^⋆⋆⋆	7.75 (1.80)^⋆⋆⋆
Young Child with Young Adult	9.64 (2.07)^⋆⋆⋆	9.67 (2.05)^⋆⋆⋆
Preadolescent with Young Adult	7.25 (1.85)^⋆⋆⋆	7.28 (1.81)^⋆⋆⋆
Adolescent with Young Adult	7.73 (1.80)^⋆⋆⋆	7.82 (1.77)^⋆⋆⋆
Young Adult with Young Adult	7.66 (1.85)^⋆⋆⋆	7.70 (1.81)^⋆⋆⋆
Young Child with Older Female Adult	10.26 (1.85)^⋆⋆⋆	10.32 (1.81)^⋆⋆⋆
Preadolescent with Older Female Adult	9.67 (1.85)^⋆⋆⋆	9.73 (1.80)^⋆⋆⋆
Adolescent with Older Female Adult	8.90 (1.84)^⋆⋆⋆	8.96 (1.80)^⋆⋆⋆
Older Female Adult with Older Female Adult	7.45 (1.87)^⋆⋆⋆	7.50 (1.83)^⋆⋆⋆
Young Child with Older Male Adult	9.09 (1.87)^⋆⋆⋆	9.14 (1.82)^⋆⋆⋆
Preadolescent with Older Male Adult	8.76 (1.83)^⋆⋆⋆	8.83 (1.79)^⋆⋆⋆
Adolescent with Older Male Adult	8.20 (1.85)^⋆⋆⋆	8.26 (1.80)^⋆⋆⋆
Older Female Adult with Older Male Adult	10.11 (1.84)^⋆⋆⋆	10.17 (1.80)^⋆⋆⋆
if child absent	–1.22 (0.30)^⋆⋆⋆	–1.20 (0.30)^⋆⋆⋆
Older Male Adult with Older Male Adult	6.59 (1.87)^⋆⋆⋆	6.66 (1.82)^⋆⋆⋆
Older Female Adult with Senior	8.12 (1.82)^⋆⋆⋆	8.20 (1.78)^⋆⋆⋆
Older Male Adult with Senior	7.51 (1.86)^⋆⋆⋆	7.58 (1.81)^⋆⋆⋆
Senior with Senior	7.82 (1.81)^⋆⋆⋆	7.89 (1.77)^⋆⋆⋆
Adolescent with Young Child or Preadolescent	8.07 (1.85)^⋆⋆⋆	8.13 (1.80)^⋆⋆⋆
Young Adult with Older Adult	8.02 (1.84)^⋆⋆⋆	8.07 (1.80)^⋆⋆⋆
Young Child or Preadolescent with Senior	8.29 (1.93)^⋆⋆⋆	8.34 (1.89)^⋆⋆⋆
Adolescent or Young Adult with Senior	9.93 (2.09)^⋆⋆⋆	10.01 (2.08)^⋆⋆⋆

Significance: ^⋆⋆⋆ $\le 0.001<$ ^⋆⋆ $\le 0.01{<}^{\star }\le 0.05$

The circles (${}^{°}$) indicate the significance levels originally reported over and above the correct ones.

Table 2 Selected omnibus tests for Model 1.

Effects	Wald ${\chi }^2$ (df)	$P\text{‐val}.$
any 2-star	20.9 (3)	<0.001
any triangle	98.7 (3)	<0.001
any $\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}(n_s)$ or ${\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}}^2(n_s)$	78.9 (6)	<0.001
any ${\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}}^2(n_s)$	17.7 (3)	0.001^a
2-star or triangle ${\hspace{0.17em}\mathrm{\text{log}}\hspace{0.17em}}^2(n_s)$	9.4 (2)	0.009^a

^a—originally reported to be < 0.001

Table 3 Selected contrasts for Model 1.

Contrast	Estimate (S.E.)	$P\text{‐val}.$
Older Female vs. Male Adults with Young Children	$1.16(0.47)$	0.013
Older Female vs. Male Adults with Preadolescents	$0.91(0.29)$	0.002
Older Female vs. Male Adults with Adolescents	$0.70(0.25)$	0.006
Older Female > Male Adults with Seniors (one-tailed)	$0.61(0.31)$	0.026^a

^a—originally reported to be 0.025

Fortuitously, although statistical significance of some individual coefficients was affected, the conclusions of omnibus tests and contrasts were not. The reasons for this are discussed in the rejoinder (Krivitsky, Coletti, and Hens 2023a).

Supplementary materials included with the article reflect these corrections.