on linear (or other) values across time. In this model, each case, i, has a distinct intercept and
slope.
The mean intercept and slope are of major interest in this analysis. Taking averages
provides the average starting point (across states) of women’s political representation in 1982,
and the average rate of change in women’s political representation over time. This leads to two
additional equations,
i
i
α
α
ζ
µ
α
+
=
(2)
i
i
β
β
ζ
µ
β
+
=
(3)
Where μ
α
and μ
β
are the mean intercept and mean slope across all cases (here, the average
intercept and slope across states). The first equation represents a state’s individual intercept (α
i
)
as a function of national average intercept (μ
α
) and a disturbance (ζ
αi
). The second represents a
state’s slope (β
i
) as a function of the national average slope (μ
β
) and a disturbance (ζ
βi
).
Only one of the models theorized above is a linear model (the null model without gender
salience or political context). In the other models, we use splines to distinguish time periods with
different expected levels of growth in women’s political participation. That is, splines allow us to
model and estimate unique slopes within distinct periods.
We estimated all models in AMOS 6.0. We use four fit statistics to assess model fit: the
chi-square test statistic, the Incremental Fit Index (IFI) (Bollen 1989), the Normed Fit Index
(NFI) (Bentler and Bonett 1980), and the root mean squared error of approximation (RMSEA)
(Steiger and Lind 1980). A non-significant chi-square test statistic indicates good fit. Both the
IFI and NFI are scaled so that values closer to 1.0 indicate better model fit. Typically, values
above .90 are considered acceptable and .95 considered optimal. In contrast, the RMSEA is
oppositely scaled so that the closer values are to 0, the better the fit of the model. Values below .
05 are considered to indicate optimal fit (Browne and Cudeck 1993).
RESULTS
Table 1 contains the results from our analyses. Model 1 presents the results from the
linear model. In Models 2 through 4, we add splines to capture gender salience, political context,
or both. In Table 1 vertical lines divide the observation period into theorized intervals and the
slope parameter from each spline is reported in its respective interval. Shading distinguishes
12
Convention