The name is absent

If Ω(a:, Xk) is the odds of some outcome (for example, working versus not working) for a given set of independent variables,
e transformation

_eβ_{k =} Ω(z,a⅛ + 1)

Ω(<r,a⅛)

is the factor or multiplicative change in the predicted odds when Xj. changes by one unit. Thus we have the factor change : for
a unit change in ¾ the odds are expected to change by a factor of exp(∕⅞), holding all other variables constant.

The effect of a change of a standard deviation change *7,. in x_k will equal exp (∕⅞ × s⅛), thus giving rise to the standardized
factor change : for a standard deviation change in a⅛, the odds are expected to change by a factor of exp(∕‰ × s_k), holding all
other variables constant.

For the binary logit model estimated by logit or logistic, the odds are for outcome “not-0” versus outcome 0’. Often
the dependent variable is coded as 1 and 0 so it becomes the odds of a 1 compared to a 0. The coefficients in the ordinal
logit model estimated by ologit can also be interpreted in terms of factor change in the odds. In this model, the odds are for
“outcomes greater than some value” compared to “outcomes less than some value”, for example, the odds for categories 3 or 4
compared to categories 1 and 2.

Instead of a multiplicative or factor change in the outcome, some people prefer the percent change given by

100 [exp (βk × δ') — 1]

which is listed by Iistcoef with the percent option.

Count models

The poisson and nbreg models are loglinear in the mean of the expected count. For example in the Poisson model,

E(y I x) = e^βo e^β1x1e^β2x2

Accordingly, exp (∕⅞) can be interpreted as follows. For a unit change in a⅛, the expected count changes by a factor of exp(∕⅞),
holding all other variables constant.

For a standard deviation change s>_s in x⅛, the factor change coefficient exp (βk × s⅛) can be interpreted as follows. For a
standard deviation change in x_k, the expected count changes by a factor of exp(∕⅜ × s⅛), holding all other variables constant.

Alternatively, the percentage change in the expected count for a S unit change in x⅛, holding other variables constant, can
be computed as

100 × [exp(∕⅞ ×<5)-l]

Zero-inflated models

The zero-inflated models zip and zinb combine a binary model predicting those who always have 0 outcomes and those
who might not have zeros and a count model that applies to those who could have non-zero outcomes. If the binary portion of
the model is assumed to be a logit, interpretation of the binary portion can be made in terms of the odds of always being 0
versus not always being 0. The count portion can be interpreted as a standard count model. Iistcoef transforms coefficients
accordingly and the help option provides information on the correct interpretation.

Alternative contrasts for mlogit

mlogit estimates the multinomial logit in which the estimated coefficients are for the comparison of a given outcome
to a base category. For complete interpretation it is useful to examine the coefficients for all possible comparisons, including
comparisons between categories in which neither outcome is the base category. While this could be done by specifying a different
basecategory, all possible comparisons are computed by Iistcoef. Since this can involve a large number of coefficients
when there are more than three dependent categories, the pvalue options can be useful for finding the most important effects.

Acknowledgment

We thank David Drukker at Stata Corporation for his suggestions.

References

Long, J. S. 1997. Regression Models for Categorical and Limited Dependent Variables. Thousand Oaks, CA: Sage.

Long, J. S. and J. Freese. 2000. sg145: Scalar measures of fit for regression models. Stata Technical Bulletin 56: 34-40.

Rogers, W. H. 1995. sqv10: Expanded multinomial comparisons. Stata Technical Bulletin 23: 26-28. Reprinted in Stata Technical Bulletin Reprints,
vol. 4, pp. 181 -183.

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