@@ -239,7 +239,7 @@ For each district $i$, the Local Moran's I statistics is:
$$I_i = \frac{(Y_i-\bar{Y})}{\sum_{i=1}^N(Y_i-\bar{Y})^2}\sum_{j=1}^Nw_{ij}(Y_j - \bar{Y}) \text{ with } I = \sum_{i=1}^NI_i/N$$
:::
The `localmoran()`function from the package `spdep` treats the variable of interest as if it was normally distributed. In some cases, this assumption could be reasonable for incidence rate, especially when the areal units of analysis have sufficiently large population count suggesting that the values have similar level of variances. Unfortunately, the local Moran's test has not been implemented for Poisson distribution (population not large enough in some districts) in `spdep` package. However, Bivand **et al.** [@bivand2008applied] provided some code to manually perform the analysis using Poisson distribution and this code was further implemented in the course "[Spatial Epidemiology](https://mkram01.github.io/EPI563-SpatialEPI/index.html)".
The `localmoran()`function from the package `spdep` treats the variable of interest as if it was normally distributed. In some cases, this assumption could be reasonable for incidence rate, especially when the areal units of analysis have sufficiently large population count suggesting that the values have similar level of variances. Unfortunately, the local Moran's test has not been implemented for Poisson distribution (population not large enough in some districts) in `spdep` package. However, Bivand *et al.* [@bivand2008applied] provided some code to manually perform the analysis using Poisson distribution and this code was further implemented in the course "[Spatial Epidemiology](https://mkram01.github.io/EPI563-SpatialEPI/index.html)".
@@ -344,7 +344,7 @@ Under the kulldorff test, the statistics hypotheses are:
- **H0**: the risk is constant over the area, i.e., there is a spatial homogeneity of the incidence.
- **H1**: a particular window have higher incidence than the rest of the area , i.e., there is a spatial heterogeneity of incidence.
- **H1**: the observed window have higher incidence than the rest of the area , i.e., there is a spatial heterogeneity of incidence.
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Briefly, the kulldorff scan statistics scan the area for clusters using several steps:
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@@ -357,7 +357,7 @@ Briefly, the kulldorff scan statistics scan the area for clusters using several
4. These 3 steps are repeated for each location and each possible windows-radii.
While we test the significance of a large number of observation windows, one can raise concern about multiple testing and Type I error. This approach however suggest that we are not interest in a set of signifiant cluster but only in a most-likely cluster. This **a priori** restriction eliminate concern for multpile comparison since the test is simplified to a statistically significance of one single most-likely cluster.
While we test the significance of a large number of observation windows, one can raise concern about multiple testing and Type I error. This approach however suggest that we are not interest in a set of signifiant cluster but only in a most-likely cluster. This *a priori* restriction eliminate concern for multpile comparison since the test is simplified to a statistically significance of one single most-likely cluster.
Because we tested all-possible locations and window-radius, we can also choose to look at secondary clusters. In this case, you should keep in mind that increasing the number of secondary cluster you select, increases the risk for Type I error.