Residuals are calculated using the formula
$$r_i = \frac{y_i - \hat{y}_i}{\sqrt{\hat{y}_i}}$$
which treats each element of the citation counts vector as a Poisson variate.
If the expected value is zero, NA is returned.
(You can decide for yourself whether to omit these observations, treat them as zero or use some other approach.)
profile_residuals(expected, observed)
| expected | Predicted vector of citations, based on some model |
|---|---|
| observed | Vector of observed citations from the journal of interest |
A numeric vector of standardised residuals, the same length as expected and observed
We might want to make a generic S3 function like stats::residuals().
Deviance residuals may be added later. For now we have Pearson residuals only.
Agresti, Alan (2002). Categorical Data Analysis (2nd ed., pp. 366--367). New York, NY: Wiley.
Other functions for residual analysis of communities: community_residuals,
fitted_citations
# Compare citations of 'Biometrika' to those of all stats journals Bka_counts <- citations[, 'Bka'] average_profile <- rowSums(citations) / sum(citations) expected_counts <- average_profile * sum(Bka_counts) profile_residuals(expected_counts, Bka_counts)#> AmS AISM AoS ANZS Bern BioJ #> -1.76297802 -0.98156976 4.96238240 -0.29637222 -0.92793177 -0.14562603 #> Bcs Bka Biost CJS CSSC CSTM #> -0.17154994 9.07090148 1.06660040 -0.74002496 -2.09141147 -3.34070833 #> CmpSt CSDA EES Envr ISR JABES #> -0.51850701 -3.71977308 -1.51864806 -1.38097669 -1.57856126 -1.45627202 #> JASA JAS JBS JCGS JMA JNS #> 3.69607101 -1.96056621 -2.28523373 0.05265299 -1.20560201 -1.51738180 #> JRSS-A JRSS-B JRSS-C JSCS JSPI JSS #> -1.21646075 2.28783497 1.32243924 -1.65180107 -1.65722041 -1.16262346 #> JTSA LDA Mtka SJS StataJ StCmp #> -1.96056621 1.59083358 -1.05972726 1.37141341 -1.71537471 -0.26205310 #> Stats StMed SMMR StMod StNee StPap #> -0.52327667 -3.38149096 -0.93014454 -1.48332583 -1.25061467 -1.47436305 #> SPL StSci StSin Tech Test #> -2.55171850 1.49377439 2.94127377 -1.88943431 0.26771858