I needed help from friends about Pearson residuals in Logistic Regression:
a) The Pearson residual is the difference between the observed and estimated probabilities divided by the binomial standard deviation of the estimated probability. Therefore standardizing the residuals.
From Menard, Scott (2002). Applied logistic regression analysis, 2nd Edition. Thousand Oaks, CA: Sage Publications. Series: Quantitative Applications in the Social Sciences, No. 106. First ed., 1995. See Chapter 4.4
b) Pearson residuals are given by:
From Kutner (2013). Applied Linear Statistical Models.1 McGraw Hill India, 5th edition. See page 591
In my understanding the two formulas are different.