Two functions allow empirical researchers to partition clustered data on one or two dimensions and to derive solutions for the pooled data and for each partition.
partition_min() is available for producing
conservative or parsimonious models;partition_min_inter() should be used for
intermediate models. For programming purposes, we opted for a
separate function for the intermediate solution.We first illustrate how one can decompose panel data on two
dimensions. In a between-unit perspective, the panel is
partitioned into multiple cross sections with the time
argument that specifies the cross section ID. In a within-unit
perspective, the data is decomposed into multiple time series with the
units argument that specifies the unit (or time series) ID.
The arguments of the functions are:
n_cut: Frequency threshold for pooled dataincl_cut: Inclusion threshold (a.k.a. consistency
threshold) for pooled datasolution (only for partition_min()):
Either C for conservative solution (a.k.a. complex
solution) or P for parsimonious solutionBE_cons and WI_cons: Inclusion thresholds
for cross sections and time series. The length of the numeric vector
should equal the number of units and time series.BE_ncut and WI_ncut: Frequency thresholds
for the cross sections and time series. The length of the numeric vector
should equal the number of units and time series.We first illustrate the parsimonious solution with dataset from Thiem (2011).
# load data (see data description for details)
data(Thiem2011)
# partition data into time series (within-unit) and cross sections (between-unit)
Thiem_pars <- partition_min(
dataset = Thiem2011,
units = "country", time = "year",
cond = c("fedismfs", "homogtyfs", "powdifffs", "comptvnsfs",
"pubsupfs", "ecodpcefs"),
out = "memberfs",
n_cut = 6, incl_cut = 0.8,
solution = "P", # parsimonious solution
BE_cons = c(0.9, 0.8, 0.7, 0.8, 0.85, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8),
BE_ncut = rep(1, 11),
WI_cons = c(0.75, 0.8, 0.9, 0.8, 0.85, rep(0.75, 10)),
WI_ncut = rep(1, 15))
kable(Thiem_pars)| type | partition | solution | model | consistency | coverage |
|---|---|---|---|---|---|
| pooled | - | comptvnsfs+fedismfs * pubsupfs | 1 | 0.8976935 | 0.7113797 |
| pooled | - | comptvnsfs+fedismfs * ecodpcefs | 2 | 0.8949502 | 0.7158019 |
| pooled | - | comptvnsfs+homogtyfs * pubsupfs | 3 | 0.8780259 | 0.7342767 |
| between | 1996 | fedismfs * comptvnsfs | 1 | 0.9030303 | 0.3748428 |
| between | 1996 | comptvnsfs * pubsupfs | 2 | 0.9885057 | 0.4327044 |
| between | 1997 | ~powdifffs | 1 | 0.9064748 | 0.6339623 |
| between | 1997 | comptvnsfs | 2 | 0.8910675 | 0.5144654 |
| between | 1997 | pubsupfs * ~ecodpcefs | 3 | 0.8672769 | 0.4767296 |
| between | 1998 | comptvnsfs | 1 | 0.9288703 | 0.6090535 |
| between | 1999 | ~powdifffs+fedismfs * ecodpcefs | 1 | 0.8876404 | 0.7623643 |
| between | 1999 | ~powdifffs+fedismfs * ~homogtyfs+homogtyfs * pubsupfs * ecodpcefs | 2 | 0.8961039 | 0.7490953 |
| between | 2000 | comptvnsfs+fedismfs * pubsupfs | 1 | 0.9684685 | 0.6508577 |
| between | 2000 | comptvnsfs+fedismfs * ecodpcefs | 2 | 0.9417476 | 0.6851665 |
| between | 2000 | comptvnsfs+fedismfs * ~homogtyfs+homogtyfs * pubsupfs | 3 | 0.9708333 | 0.7053481 |
| between | 2001 | fedismfs+comptvnsfs | 1 | 0.9028436 | 0.7689203 |
| between | 2002 | fedismfs+~powdifffs+pubsupfs | 1 | 0.8149780 | 0.7467205 |
| between | 2002 | fedismfs+comptvnsfs+pubsupfs | 2 | 0.8214665 | 0.7800202 |
| between | 2003 | pubsupfs+~ecodpcefs | 1 | 0.7985213 | 0.8529121 |
| between | 2004 | fedismfs+~ecodpcefs | 1 | 0.9184290 | 0.8260870 |
| between | 2004 | pubsupfs+~ecodpcefs | 2 | 0.9081726 | 0.8958333 |
| between | 2005 | pubsupfs+~ecodpcefs | 1 | 0.9002695 | 0.9076087 |
| between | 2005 | fedismfs+homogtyfs+ecodpcefs | 2 | 0.8868101 | 0.8586957 |
| between | 2006 | comptvnsfs+~pubsupfs | 1 | 0.8982118 | 0.7829736 |
| between | 2006 | ~pubsupfs+fedismfs * ~ecodpcefs | 2 | 0.8335725 | 0.6966427 |
| within | AT | All truth table rows inconsistent | - | NA | NA |
| within | BE | No variation in all conditions | - | NA | NA |
| within | DE | All truth table rows consistent | - | NA | NA |
| within | DK | ~pubsupfs | 1 | 0.8297389 | 0.9798928 |
| within | DK | ~ecodpcefs | 2 | 0.9469154 | 0.8847185 |
| within | ES | All truth table rows consistent | - | NA | NA |
| within | FI | No variation in all conditions | - | NA | NA |
| within | FR | All truth table rows consistent | - | NA | NA |
| within | GR | All truth table rows inconsistent | - | NA | NA |
| within | IE | All truth table rows inconsistent | - | NA | NA |
| within | IT | No variation in all conditions | - | NA | NA |
| within | LU | homogtyfs | 1 | 0.7629630 | 0.8131579 |
| within | NL | All truth table rows consistent | - | NA | NA |
| within | PT | All truth table rows inconsistent | - | NA | NA |
| within | SE | All truth table rows inconsistent | - | NA | NA |
| within | UK | All truth table rows consistent | - | NA | NA |
The output of partition_min() is a dataframe summarizing
the solutions for the pooled data and the partitions and the consistency
and coverage values for the solution. The column model
shows whether model ambiguity is given for the pooled data or individual
partitions if one can derive any model from the data in the
first place.
There are different reasons why one might not be able to derive a partition-specific solution:
When one the reason applies, it is listed in the column
solution.
The intermediate solution is derived with
partition_min_inter(). The only command that is new
compared to partition_min() is intermediate
that is available for specifying the directional expectations.
The data structure for Schwarz 2016 is
an unbalanced panel with eight countries, ten years and 74 observations
in total. We assume that one is only interested in the between-unit
dimension and wants to derive one solution per cross section. For this
reason, the argument for the within-unit dimension (unit)
is not specified.
# load data (see data description for details)
data(Schwarz2016)
# partition data into cross sections
Schwarz_inter <- partition_min_inter(
Schwarz2016,
time = "year",
cond = c("poltrans", "ecotrans", "reform", "conflict", "attention"),
out = "enlarge",
n_cut = 1, incl_cut = 0.8,
WI_cons = rep(0.8, 8), BE_cons = c(0.75, 0.75, 0.75, 0.75, 0.75,
0.8, 0.8, 0.8, 0.8, 0.8),
WI_ncut = rep(1, 8), BE_ncut = rep(1, 10),
intermediate = c("1", "1", "1", "1", "1"))
kable(Schwarz_inter)| type | partition | solution | model | consistency | coverage |
|---|---|---|---|---|---|
| pooled | - | poltrans * ecotrans * reform+poltrans * reform * conflict * attention | 1 | 0.8008497 | 0.7783001 |
| between | 04 | All inconsistent | - | NA | NA |
| between | 05 | All inconsistent | - | NA | NA |
| between | 06 | All inconsistent | - | NA | NA |
| between | 07 | poltrans * ecotrans * reform+poltrans * reform * ~conflict | 1 | 0.7552752 | 0.8692104 |
| between | 08 | poltrans * ecotrans * reform * conflict | 1 | 0.7626173 | 0.8482275 |
| between | 09 | All consistent | - | NA | NA |
| between | 10 | poltrans * ecotrans * reform * attention+poltrans * reform * conflict * attention | 1 | 0.8760953 | 0.8125806 |
| between | 11 | poltrans * conflict * attention+poltrans * ecotrans * reform * attention | 1 | 0.8195671 | 0.9566749 |
| between | 12 | poltrans * conflict+poltrans * ecotrans * reform | 1 | 0.8411864 | 0.8865839 |
| between | 13 | All consistent | - | NA | NA |
Clustered data can be partitioned on a single dimension if there is
only one dimension as an in multilevel data where lower-level units are
nested in higher-level units. The analysis is then similar to the
partition of panel data along one dimension. We use the dataset by Grauvogel and von Soest
(2014) for illustrating the analysis of multilevel data. The study
analyzes the effect of sanctions on authoritarian regimes. The data
distinguishes between the source of the sanction (Sender)
and the target country (Target). All sanctions have been
imposed by the EU, UN or US, which means that target countries are
nested in three different senders. We partition the data on the
dimension of senders to see how solutions differ across senders.
# load data (see data description for details)
data(Grauvogel2014)
# partition data by sender country (higher-level unit)
GS_pars <- partition_min(
dataset = Grauvogel2014,
units = "Sender",
cond = c("Comprehensiveness", "Linkage", "Vulnerability",
"Repression", "Claims"),
out = "Persistence",
n_cut = 1, incl_cut = 0.75,
solution = "P",
BE_cons = rep(0.75, 3),
BE_ncut = rep(1, 3))
kable(GS_pars)| type | partition | solution | model | consistency | coverage |
|---|---|---|---|---|---|
| pooled | - | ~Comprehensiveness * Claims+~Linkage * Claims+~Repression * Claims+~Comprehensiveness * ~Linkage * ~Repression+Comprehensiveness * ~Vulnerability * Repression | 1 | 0.7758164 | 0.7336208 |
| pooled | - | ~Comprehensiveness * Claims+~Linkage * Claims+~Repression * Claims+~Comprehensiveness * ~Linkage * ~Repression+Linkage * ~Vulnerability * Repression | 2 | 0.7776948 | 0.7245792 |
| within | EU | Vulnerability+~Comprehensiveness * ~Repression+Linkage * Claims | 1 | 0.6293355 | 0.9145825 |
| within | EU | Vulnerability+~Linkage * ~Repression+Linkage * Claims | 2 | 0.6327684 | 0.9049634 |
| within | EU | Vulnerability+Linkage * Repression+~Repression * Claims | 3 | 0.6310549 | 0.9022701 |
| within | EU | Vulnerability+Linkage * Claims+~Repression * Claims | 4 | 0.6320277 | 0.9126587 |
| within | EU | Vulnerability+~Comprehensiveness * Linkage+~Comprehensiveness * ~Repression+Comprehensiveness * Claims | 5 | 0.6273610 | 0.8945748 |
| within | EU | Vulnerability+~Comprehensiveness * Linkage+Comprehensiveness * Repression+~Repression * Claims | 6 | 0.6238361 | 0.9022701 |
| within | EU | Vulnerability+~Comprehensiveness * Linkage+Comprehensiveness * Claims+~Linkage * ~Repression | 7 | 0.6253391 | 0.8868796 |
| within | EU | Vulnerability+~Comprehensiveness * Linkage+Comprehensiveness * Claims+~Repression * Claims | 8 | 0.6261682 | 0.9022701 |
| within | EU | Vulnerability+~Comprehensiveness * ~Repression+Comprehensiveness * Claims+Linkage * Repression | 9 | 0.6303763 | 0.9022701 |
| within | UN | Comprehensiveness+Linkage+Claims | 1 | 0.7458176 | 0.9207195 |
| within | US | Comprehensiveness * ~Linkage * ~Vulnerability+Linkage * ~Repression * Claims+~Vulnerability * Repression * Claims | 1 | 0.7864914 | 0.5616704 |
| within | US | Comprehensiveness * ~Vulnerability * Claims+Linkage * ~Repression * Claims+~Vulnerability * Repression * Claims | 2 | 0.7866918 | 0.5396568 |
| within | US | Comprehensiveness * ~Linkage * ~Vulnerability+Linkage * ~Vulnerability * Claims+~Vulnerability * Repression * Claims+Comprehensiveness * Linkage * Vulnerability * ~Repression | 3 | 0.7960289 | 0.5710586 |
| within | US | Comprehensiveness * ~Vulnerability * Claims+Linkage * ~Vulnerability * Claims+~Vulnerability * Repression * Claims+Comprehensiveness * Linkage * Vulnerability * ~Repression | 4 | 0.7975690 | 0.5522823 |
Yihui Xie (2021): knitr: A General-Purpose Package for Dynamic Report Generation in R. R package version 1.33.
Yihui Xie (2015): Dynamic Documents with R and knitr. 2nd edition. Chapman and Hall/CRC. ISBN 978-1498716963
Yihui Xie (2014): knitr: A Comprehensive Tool for Reproducible Research in R. In Victoria Stodden, Friedrich Leisch and Roger D. Peng, editors, Implementing Reproducible Computational Research. Chapman and Hall/CRC. ISBN 978-1466561595