Explain How We Can Interpret Probit Coefficients Using the Observed-Value

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Examlex · Accepted Answer

The Answer is Calculate fitted value and then calculated a second set of fitted values if X1 was increased by one std deviation for all observations, and compare average difference between the two values
(a) For each observation, calculate

P _ { 1 i }

as the standard fitted probability from the probit results.

P _ { 1 i } = \Phi \left( \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } X _ { 1 i } + \hat { \beta } _ { 2 } X _ { 2 i } + \hat { \beta } _ { 3 } X _ { 3 i } + \ldots \right)

(b) For each observation, calculate

P _ { 2 i }

as the fitted probability when the value of

X _ { 1 i }

is increased by one standard deviation

\left( \sigma _ { X _ { 1 } } \right)

for each observation

P _ { 2 i } = \Phi \left( \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } \left( X _ { 1 i } + \sigma _ { X _ { 1 } } \right) + \hat { \beta } _ { 2 } X _ { 2 i } + \hat { \beta } _ { 3 } X _ { 3 i } + \ldots \right)

(c) The simulated effect of increasing

X _ { 1 }

by one standard deviation is the average difference

P _ { 2 i } - P _ { 1 i }

across all observations.

Explain How We Can Interpret Probit Coefficients Using the Observed-Value

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Explain How We Can Interpret Probit Coefficients Using the Observed-Value

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