blocking_factor {CurricularAnalytics}

Calculate blocking factor

Description

A helper function for calculating the blocking factor for each node and the total blocking factor of a curriculum graph.

Usage

blocking_factor(node_list, edge_list)

Arguments

node_list

Dataframe with an 'id' column for each node and a 'term' column specifying which term the course is to be taken in.

edge_list

Dataframe with two columns 'from' and 'to' specifying directed edges starting at 'from' nodes directed towards 'to' nodes. Entries must use node ids from node_list.

Details

Blocking quantifies when a failing a course would result in being blocked from registering for future courses. More formally the blocking factor of a node v_i is defined as

b_c(v_i) = \sum_{v_j \in V} I(v_i,v_j)

where I is the indicator function:

=\begin{cases}1, & \text{if } v_i \to v_j \\ 0, & \text{if }v_i \not\to v_j\end{cases}

The blocking factor for an entire curriculum graph G_c is defined as

b(G_c)=\sum_{v_i \in V} b_c(v_i)

Value

A list that contains the following:

bynode

A dataframe containing the blocking factor of each node

total

The total blocking factor of the curriculum graph

Author(s)

Daniel Krasnov

References

Heileman, Gregory L, Chaouki T Abdallah, Ahmad Slim, and Michael Hickman. 2018. “Curricular Analytics: A Framework for Quantifying the Impact of Curricular Reforms and Pedagogical Innovations.” arXiv Preprint arXiv:1811.09676.

Examples

edge_list <- data.frame(from = c(1, 3), to = c(3, 4))
node_list <-
data.frame(
id = 1:4,
label = c("MATH 100", "DATA 101", "MATH 101", "MATH 221"),
term = c(1, 1, 2, 2)
)
bf_list <- blocking_factor(node_list,edge_list)
print(bf_list)
# Output:
# $bynode
# id bf
# 2  1  2
# 3  2  0
# 4  3  1
# 5  4  0
# $total
# [1] 3