Growth of the Church
|If we extrapolate the fitted force of growth lines from the previous section and calculate the resulting size of the church, the membership grows approximately linearly for the next 15 or so years and then begins to slow down. Including the 1989 anomaly in the fitted growth line the church will max out at 17.5 million members. Excluding the 1989 anomaly the membership will peak at 18.5 million. Chart 8 shows these patterns.|
(5.1) we suggested that the force of growth of the church is of the form
This was the appropriate model to use to test the hypothesis that the growth of the church is exponential. Now that we have rejected that hypothesis, we need to consider if this is a functional form that we should extrapolate.
The biggest drawback of this form is that its slope remains constant as approaches zero. This seems a bit unlikelyintuitively it is more appealing for the growth rate to asymptotically approach zero. Consider the following function form:
This meets the criteria of the declining rate of growth gently approaching zero, and is the simplest form with that property to regress. The law of parsimony would suggest that we look at how this fits.
|Interestingly, using this functional form the estimates of and with and without the 1989 anomalous datum are quite close, with F statistics of 7.86 and 13.4 respectively. Chart 9 shows the growth of the church according to this model and table 4 shows the ANOVA (for the regression including the 1989 anomaly). Chart 10 shows a graph of the error terms. From 1983 to 1990 there is some strong autocorrelation. This might be explained by the unexplained growth of 1989 and 1990 being corrections for understated growth in the previous years. From 1991 to 2000 there is no apparent autocorrelation or heteroscedasticity; at least in the later years the model fits the data well and appears to meet the necessary assumptions of constant, uncorrelated errors.|
Using membership data from 1844 to the present Duwayne Anderson fit the total membership of the church to a logistics curve.1 Chart 11 compares my predictions to Anderson's and Stark's.
If you have a question or would like to discuss these topics, I suggest that you go to a Mormon-related bulletin board. If you'd like to <i>contact me</i> with comments or feedback, you may send an email to firstname.lastname@example.org.CompanyEmail