| Title: | Scott-Knott for Forensic Glass Analysis |
|---|---|
| Description: | In forensics, it is common and effective practice to analyse glass fragments from the scene and suspects to gain evidence of placing a suspect at the crime scene. This kind of analysis involves comparing the physical and chemical attributes of glass fragments that exist on both the person and at the crime scene, and assessing the significance in a likeness that they share. The package implements the Scott-Knott Modification 2 algorithm (SKM2) (Christopher M. Triggs and James M. Curran and John S. Buckleton and Kevan A.J. Walsh (1997) <doi:10.1016/S0379-0738(96)02037-3> "The grouping problem in forensic glass analysis: a divisive approach", Forensic Science International, 85(1), 1--14) for small sample glass fragment analysis using the refractive index (ri) of a set of glass samples. It also includes an experimental multivariate analog to the Scott-Knott algorithm for similar analysis on glass samples with multiple chemical concentration variables and multiple samples of the same item; testing against the Hotellings T^2 distribution (J.M. Curran and C.M. Triggs and J.R. Almirall and J.S. Buckleton and K.A.J. Walsh (1997) <doi:10.1016/S1355-0306(97)72197-X> "The interpretation of elemental composition measurements from forensic glass evidence", Science & Justice, 37(4), 241--244). |
| Authors: | Toby Hayward [aut, cre] (Main developer and maintainer of the package.), James Curran [aut, ctb] (Supervised and contributed to the development of the package.), Lewis Kendall-Jones [ctb] (Wrote and supported the development of the C++ code.) |
| Maintainer: | Toby Hayward <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.1.1 |
| Built: | 2024-11-07 04:26:27 UTC |
| Source: | https://github.com/tobyhayward13/sci118uoa_forensicglassanalysis |
For a given significance value, this function uses critical values determined from simulated data formed on 1 million arrays, and returns the quantile estimated at that significance level. For values of k > 20, it assumes a chi squared distribution with k/(pi - 2) degrees of freedom.
calculate_lambda_threshold(k, alpha)calculate_lambda_threshold(k, alpha)
k |
Number of indices. |
alpha |
Level of significance. |
A 100(1-alpha)% quantile estimate from the distribution of Lambda.
Calculates the B0 value for a given numeric vector of values; assuming they're appropriate values corresponding to glass fragment refractive indices.
find_B0(arr)find_B0(arr)
arr |
vector of refractive indices. |
A numeric corresponding to the maximum between-sum-of-squares estimate from the sample.
Calculates the "T0" value (the split corresponding to the maximum value of T^2) for a given list of data sets corresponding to glass fragment features assuming they're appropriate values corresponding to glass fragment features.
find_T0(data, i = 1, j = length(data))find_T0(data, i = 1, j = length(data))
data |
list of glass fragment chemical (or otherwise) features. |
i |
Starting element (default = 1) |
j |
Ending element (default = length(array)) |
A numeric corresponding to the maximum between-sum-of-squares estimate from the sample.
Calculate Hotelling's T^2 Statistic for two independent multivariate samples.
find_T2(d1, d2)find_T2(d1, d2)
d1 |
matrix or data.frame type object containing the multivariate data for the first sample. |
d2 |
matrix or data.frame type object containing the multivariate data for the second sample. |
T^2 value for the two objects.
Returns a vector of randomly generated refractive indices from a expected normal distribution of glass fragments.
generate_indices(n = 10, .sd_multi = 1)generate_indices(n = 10, .sd_multi = 1)
n |
Number of refractive indices to generate. |
.sd_multi |
Scale factor of the standard deviation. Greater values imply more variance in the random sample. |
A vector of randomly generated RIs.
test_ris = generate_indices(8) partition(test_ris) test_ris_varied = generate_indices(.sd_multi = 5) partition(test_ris_varied)test_ris = generate_indices(8) partition(test_ris) test_ris_varied = generate_indices(.sd_multi = 5) partition(test_ris_varied)
Glass composition data for seven elements from 200 glass items.
data(glass)data(glass)
a 'data.frame' with 2400 rows and 9 columns.
factor
200 levels - which item the measurements came from
factor
4 levels - which of the four fragments from each item the observations were made upon
numeric
log of sodium concentration to oxygen concentration
numeric
log of magnesium concentration to oxygen concentration
numeric
log of aluminium concentration to oxygen concentration
numeric
log of silicon concentration to oxygen concentration
numeric
log of potassium concentration to oxygen concentration
numeric
log of calcium concentration to oxygen concentration
numeric
log of iron concentration to oxygen concentration
These data are from Grzegorz (Greg) Zadora at the [Institute of Forensic Research](http://ies.krakow.pl/) in Krakow, Poland. They are the log of the ratios of each element to oxygen, so logNaO is the log(10) of the Sodium to Oxygen ratio, and logAlO is the log of the Aluminium to Oxygen ratio. The instrumental method was SEM-EDX.
The 'item' indicates the object the glass came from. The levels for each item are unique to that item. The 'fragment' can be considered a sub-item. When collecting these observations Greg took a glass object, say a jam jar, he would then break it, and extract four fragments. Each fragment would be measured three times upon different parts of that fragment. The fragment labels are repeated, so, for example, fragment "f1" from item "s2" has nothing whatsoever to do with fragment "f1" from item "s101".
For two level models use 'item' as the lower level - three level models can use the additional information from the individual fragments.
Grzegorz Zadora [Institute of Forensic Research](http://ies.krakow.pl/), Krakow, Poland.
Aitken, C.G.G. Zadora, G. & Lucy, D. (2007) A Two-Level Model for Evidence Evaluation. Journal of Forensic Sciences: 52(2); 412-419.
Glass Fragment Elemental Composition Data on 15 variables.
data(glass2)data(glass2)
a 'data.frame' with 16 rows and 16 columns.
factor
761 levels - which item the measurements came from
numeric
log of lithium concentration
numeric
log of magnesium concentration
numeric
log of aluminium concentration
numeric
log of potassium concentration
numeric
log of titanium concentration
numeric
log of manganese concentration
numeric
log of iron concentration
numeric
log of rubidium concentration
numeric
log of strontium concentration
numeric
log of zirconium concentration
numeric
log of barium concentration
numeric
log of lanthanum concentration
numeric
log of cerium concentration
numeric
log of neodymium concentration
numeric
log of lead concentration
Log transformed example casework data
Almirall, Jose; Akmeemana, Anuradha, 2022, "casework.tab", Shiny Glass Application, https://doi.org/10.34703/gzx1-9v95/OB8BS9/CP6WXP, FIU Research Data Portal, V2, UNF:6:jQxEQCGZVvlWtc6owbtp+A== [fileUNF]
Anuradha Akmeemana, R. C., Jose Almirall, The Calculation of Calibrated Likelihood Ratios (LRs) for Glass Using a Multivariate Kernel Density Model: Introducing a User-Friendly Graphical User Interface (GUI). In American Academy of Forensic Science, Anaheim, CA, 2020.
For internal use only. Determines if a node in the Partition tree has a child.
has.children(part)has.children(part)
part |
Node in partition Tree. |
Logical determining if the node has any children.
Meant for internal use only.
order_euclid(alist)order_euclid(alist)
alist |
A list of data frames. |
A list of data frames.
Partitions the array of assumed glass fragment refractive indices into statistically significant groups.
partition(array, alpha = 0.05, .debug = FALSE)partition(array, alpha = 0.05, .debug = FALSE)
array |
Vector of refractive indices. |
alpha |
Significance parameter "[0,1]". Higher values are more likely to partition the array further. |
.debug |
Runs debugging. |
sk_partition_tree
set.seed(123) ris = generate_indices(8, 4) part = partition(ris) plot(part) part$groupsset.seed(123) ris = generate_indices(8, 4) part = partition(ris) plot(part) part$groups
Partitions the array of assumed glass fragment chemical compositions and features into statistically significant groups.
partition.multi(data, alpha = 0.05, .debug = FALSE)partition.multi(data, alpha = 0.05, .debug = FALSE)
data |
A list of data.frames or matrices corresponding to individual observations of glass fragment features. |
alpha |
Significance parameter "[0,1]". Higher values are more likely to partition the array further. |
.debug |
Runs debugging. |
A list of groupings and the tree formed.
test.data = prepare_data(glass, 1)[1:3] part = partition.multi(test.data) plot(part) set.seed(123) test.data.random = prepare_data(glass, 1) test.data.random = test.data.random[sample(1:length(test.data.random), 5)] part = partition.multi(test.data.random) part$groupstest.data = prepare_data(glass, 1)[1:3] part = partition.multi(test.data) plot(part) set.seed(123) test.data.random = prepare_data(glass, 1) test.data.random = test.data.random[sample(1:length(test.data.random), 5)] part = partition.multi(test.data.random) part$groups
S3method for plotting the resulting tree formed by the partitioning algorithms in the SK4FGA package.
## S3 method for class 'sk_partition_tree' plot(x, ...)## S3 method for class 'sk_partition_tree' plot(x, ...)
x |
Output from the function "partition()" |
... |
Extra details for the plot. Unused. |
Plot of the decision tree that is formed by the sk_partition_tree object returned by partition and partition.multi.
data = generate_indices() part = partition(data) plot.sk_partition_tree(part) data(glass) data.multi = prepare_data(glass, 1)[1:3] part = partition.multi(data.multi) plot(part)data = generate_indices() part = partition(data) plot.sk_partition_tree(part) data(glass) data.multi = prepare_data(glass, 1)[1:3] part = partition.multi(data.multi) plot(part)
Prepare a data file that is in standard form for partition.multi.
prepare_data(data, label = NA)prepare_data(data, label = NA)
data |
Inputted data.frame. |
label |
Column corresponding to the label to be grouped by. |
A list of split data.
Calculate the Probability for a given T^2 statistic.
ptsquared(t, n1, n2, p)ptsquared(t, n1, n2, p)
t |
T^2 statistic. |
n1 |
Number of observations in first sample. |
n2 |
Number of observations in second sample. |
p |
Number of parameters. |
A probability corresponding to a given T^2 statistic and for given arguments.
Ungroups the tree object in the output from partition()
ungroup.partition(tree)ungroup.partition(tree)
tree |
tree object returned from partition() |
A list object containing the indices of the
FIU Vehicle Glass Database V2.0
data(vehicle.glass)data(vehicle.glass)
a 'data.frame' with 6858 rows and 16 columns.
factor
761 levels - which item the measurements came from
numeric
log of lithium concentration
numeric
log of magnesium concentration
numeric
log of aluminium concentration
numeric
log of potassium concentration
numeric
log of titanium concentration
numeric
log of manganese concentration
numeric
log of iron concentration
numeric
log of rubidium concentration
numeric
log of strontium concentration
numeric
log of zirconium concentration
numeric
log of barium concentration
numeric
log of lanthanum concentration
numeric
log of cerium concentration
numeric
log of neodymium concentration
numeric
log of lead concentration
This freely available research-based database consists of 762 samples of various vehicle glass (windshield, passenger side, driver side, etc.). The samples span various makes and models, and range in year from 2004-2019. All samples were collected from the M&M salvage yard in Ruckersville, VA.
Almirall, Jose; Akmeemana, Anuradha, 2022, "FIU Vehicle Glass Database V2.0.tab", Shiny Glass Application, https://doi.org/10.34703/gzx1-9v95/OB8BS9/XGH0IO, FIU Research Data Portal, V2, UNF:6:YDbwWISU04S+UCtb7aRoBQ== [fileUNF]
Anuradha Akmeemana, R. C., Jose Almirall, The Calculation of Calibrated Likelihood Ratios (LRs) for Glass Using a Multivariate Kernel Density Model: Introducing a User-Friendly Graphical User Interface (GUI). In American Academy of Forensic Science, Anaheim, CA, 2020.