Proportional
Reduction in Error (PRE) measures
-
indicate how much better
could we predict the distribution of the d.v. if we knew the distribution
of the i.v.
-
better prediction, less error
in prediction
4 components
1) rule for predicting
case's value on d.v. based on distribution of d.v. alone
2) rule for predicting
case's value on d.v. based on case's value on i.v.
3) definition of prediction
error
4) definition of measure
-
range between 0 and 1 (0
= no reduction in error, 1 = perfect prediction/error eliminated)
-
interpretation of values:
0
to .1 = weak
.1
to .4 = moderate
.4+
= strong
-
Goodman and Kruskal's tau:
asymmetric - for predicting the dependent variable from the independent
variable
Ordinal measures of
association
-
range between -1 (perfect
negative association) and +1 (perfect positive association); 0 indicates
no relationship
-
PRE interpretation - absolute
value
-
gamma - symmetric - can be
computed no matter which variable is independent/dependent
-
same order (concordant) and
inverse order (discordant) pairs
same order (Ns) = one observation
is higher on both variables than other observation
-
inverse order (Nd) = observation
higher on one variable is lower on other variable
-
tied pairs - observations
are tied on independent and/or dependent variable
gamma = (Ns - Nd) /
(Ns + Nd)
2 x 2 tables
binary/dichotomous variables
(yes/no re reference value)
risk = number of cases in
particular category of variable / n
odds = number of cases in
one category divided by number of cases in other category
relative risk (RR) = % in
reference category of d.v. for one category of i.v. divided by % in reference
category of d.v. for
other category of i.v.
odds ratio (OR) = odds of
falling
in reference category
to not
falling in reference
category for
one category of i.v.
divided by odds for other category of i.v.
e.g., Turner et al. (1998)
experiment
-
probability sample of U.S.
adolescent males
-
random assignment to respond
via:
-
audio computer assisted self-interview
(ACASI), or
-
paper and pencil self-administered
questionnaire (SAQ)
-
test impact of response mode
on reporting sensitive behaviors
Ever had sex with
a prostitute?
| mode |
no |
yes |
total |
| ACASI |
1283 |
33 |
1316 |
| SAQ |
354 |
2 |
356 |
| total |
1637 |
35 |
1672 |
steps in computing RR/OR:
1) determine which variable
is i.v.
2) determine which risk
or odds is of interest
3) compute risk/odds for
each category of i.v.
4) determine order of
i.v. category comparison (which vs. which?)
5) divide risk/odds for
one category of i.v. by the risk/odds for the other (ratios)
Had sex with 5+ persons
in lifetime?
| mode |
no |
yes |
total |
| ACASI |
1069 |
247 |
1316 |
| SAQ |
300 |
56 |
356 |
| total |
1369 |
303 |
1672 |
problems with interpreting
RR:
-
missing baseline risk (Utts)
Elaboration examples (1991
NHIS race x health):
intervening relationship
- income mediates
-
i.v. associated w/ intervening
variable
-
intervening var. associated
w/ d.v.
-
partial tables - relationship
decreases
conditional relationship
- relationship varies by age?
-
no large difference in association
for different age groups - no interaction