# Health Practitioner Bonuses and Their Impact on the Availability and Utilization of Primary Care Services. Method of Calculating the Predicted Proportion of Office-based Physicians Accepting New Medicaid Patience as a Function of the Medicaid-to-Medicare Fee Index

Consider that:

• I0 is the observed value of the Medicaid-to-Medicare fee index 2008.

• I1 is the new value of the Medicaid-to-Medicare fee index (e.g. I1 could be 1 percent or 10 percent or x percent higher than I0 where x is a chosen value).

• P0 is the observed proportion of office-based physicians accepting Medicaid patients in 2011.

• P1 is the predicted proportion of office-based physicians accepting Medicaid patients after the x percent increase in Medicaid-to-Medicare fee index.

• M1 is the estimated marginal effect of the Medicaid-to-Medicare fee ratio (2008) = 0.4 (reported in the study).

B1 is the estimated logit coefficient of the Medicaid-to-Medicare fee ratio (2008).

Given the fact that marginal is equal to the estimated logit coefficient times P times (1-P) where P is the mean proportion of office-based physicians accepting Medicaid patients in the sample, equation (12) shows the estimated logit coefficient of the Medicaid-to-Medicare fee ratio (2008).

(12)

Since Decker (2012) reports that P is 0.694, this implies B1 is equal to 0.4/(0.694*(1-0.694)) which is approximately equal to 1.88.

Let’s name the part of the estimated logit model which incorporates the effect of other independent variables (other than Medicaid-to-Medicare fee ratio) and the intercept term in the model as “Other Effects” or OE. Equation (13) below shows the expression of “Other Effects” (OE) based on a given value of P0 and a known value of B1 (where “ln” is the natural log).

(13)

Then based on the estimated logit model, we can predict the log-odds of the proportion of office-based physicians accepting new Medicaid patients for a new value of the Medicaid-to-Medicare index (say, I1). Equation (14) shows the log-odds of the proportion of office-based physicians accepting new Medicaid patients.

(14)

Therefore, equation (15) shows the implied predicted proportion of office-based physicians accepting new Medicaid patients (where “exp” is the exponential function operation).

(15)

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