# Download Estimation of Victimization Prevalence Using Data from the by Diane Griffin Saphire (auth.) PDF

By Diane Griffin Saphire (auth.)

The nationwide Crime Survey is a pattern survey of housing devices carried out by way of the U.S. Bureau of the Census. All eligible occupants of a sampled unit are interviewed each six months (for as much as seven interviews) approximately victimizations that they've skilled through the prior six months. during this monograph a number of longitudinal analyses are played utilizing a subsample of the knowledge overlaying the years 1973 via 1975. specifically. a number of tools of estimating the share of devices which are crime-free for a given 12 months. denoted by means of eight. are mentioned. First. numerous advert hoc. in preference to model-based. estimators of eight are mentioned. together with these utilized by the Bureau of Justice data. we discover types lower than which those estimators are constant for eight. One such version matches the information rather well. A superpopulation method of the estimation of eight is then taken. assuming that the nonresponse and sampling mechanisms are ignorable. 3 versions are healthy to the information: i) a homogeneous Bernoulli version. less than which victimization is autonomous from month to month ii) a correlated Bernoulli version. less than which victimization in any months has optimistic correlation p. and iii) a two-state Markov version with states "victimized" and "crime-free". The correlated Bernoulli version is located to be very insufficient. the opposite versions healthy the 1975 info good. yet have fairly terrible matches to the 1973 and 1974 facts. Rotation crew biases are conjectured to be the reason for those terrible fits.

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**Extra resources for Estimation of Victimization Prevalence Using Data from the National Crime Survey**

**Example text**

We need the following lemma. a. II (a. •••• a) in some neighborhood in the i=a I I e a e Lemma 2: hyperplane specified by 1: a. = 1. then i=a Proof: I w. I = 1-0. ••• e. Rewriting the expression in terms of a l' .... a 11 we find that d 1: w. a. i=. I I d + W {1 - e 1: i=-a aJ I =1 - 0 Taking derivatives with respect to a k yields Thus w. = wb = ... = we = w, and e 1: Wa. i=. I e =1 - B w1: a. = 1 - 0 i=a I (3-36) 59 1 - 8. w • Applying Lemma 2 to equation (3-35). 8H1-8) g,(a,8) + g2(a,8) iv) g(c,8) 1 - 8 , and thus g(b,8) g,(a,8) + g2(a,8) 2 g,(a,8) + g2(a,8) 2 The restrictions on g(d,8) and g(e,8) are clearly unreasonable at least from an intuitive point of view.

The number of months covered by an interview). 25 4. Use as an estimator 8, = nymber of interview months for crime-free HU's total number of interview months (2-1) If an HU has reported a victimization in any month of the given year, then we are sure that it was not crime-free. Suppose that for such an HU we have 5 months of information, and that we could somehow obtain the missing 7 months of information. Regardless of how many of these 7 months were crime-free and how many were not, this HU would still contribute nothing to the numerator of 91 and 12 to the denominator.

Z12 J - (t) 0 (w:- w 12) - 8(z. - z12) J J 0 = w 12 Next. let c - 8z 12 • =0 =0 =0 Thus Wj - 8z j =c and 12 1: (c + 8z i)a i i=1 12 =8 . a. a. a. i=l I I I =0 =8 (3-9) 42 c =0 Therefore w. - Bz. lz. I I = B. • (3-10) 12 . B) = B. This implies that the probability that an HU that contributes exactly i months of information will be crime-free during those regardless of i -- not a very reasonable model! i months is constantly B. Thus we have shown that. if we are willing to assume that HUs are victimized independently.