1 Finding patterns of convergence and divergence within the convergEU package
The convergEU package allows to obtain patterns of change along time for indicators in the European Union (EU) by invoking the ms_pattern_ori function:
The ms_pattern_ori function allows for obtaining patterns for both lowBest and highBest types of indicators. More specifically, in this function the following patterns are defined through numerical labels and corresponding string labels:
- 1: Catching up
- 2: Flattening
- 3: Inversion
- 4: Outperforming
- 5: Slower pace
- 6: Diving
- 7: Defending better
- 8: Escaping
- 9: Falling away
- 10: Underperforming
- 11: Recovering
- 12: Reacting better
- 13: Paralleling better over
- 14: Paralleling equal over
- 15: Paralleling worse over
- 16: Paralleling worse under
- 17: Paralleling equal under
- 18: Paralleling better under
- 19: Crossing
- 20: Crossing reversed
- 21: Other (Inspection)
It is important to note that for finding patterns for indicators of type “low is better”, we assume that higher the indicator value, worse the considered socio/economic feature in a given member state (MS). Instead of creating new labels to tag patterns of this class of indicators, we transform the original indicator after noting that the absolute positioning of values is not relevant while judging for the presence of a given pattern. Thus, the indicators of type “low is better” are transformed, and the distance from the maximum value for each original observation is calculated. If the original index decreases then the transformed value increases, and the pattern recognition scheme applies in the same way as for indicators of type “high is better”.
The graphical plots for the defined patterns depending on the type of indicators (lowBest or highBest) are available by invoking the patt_legend function:
When considering indicators of type highBest, the graphical representation of the patterns is as follows:
while for the lowBest type of indicators the plot of the patterns is:
For further details on the defined patterns we refer to the Eurofound report “Monitoring convergence in the European Union Upward convergence in the EU: Concepts, measurements and indicators” (2018, p. 25-26).
For illustrating practically the points discussed above, let’s consider a first example related to the emp_20_64_MS dataset for which the indicator is of type highBest. Thus, for obtaining the patterns for this type of indicator,we invoke the ms_pattern_ori function as follows:
The output of the ms_pattern_ori function consists of the usual three list components: “$res” that contains the results, “$msg” that possibly carries messages for the user and “$err” which is a string containing an error message, if an error occurs:
The “$res” component of the output contains the numerical labels for the patterns as well as their string labels:
mypattemp<-myemp$res$mat_label_tags
mypattempn<-myemp$res$mat_without_summaries
mypattempn
#> # A tibble: 28 × 17
#> Country `2002/2003` `2003/2004` `2004/2005` `2005/2006` `2006/2007`
#> <chr> <int> <int> <int> <int> <int>
#> 1 AT 4 3 4 4 4
#> 2 BE 6 1 1 21 1
#> 3 BG 1 1 1 1 1
#> 4 CY 4 4 3 4 2
#> 5 CZ 3 3 4 2 2
#> 6 DE 3 19 20 4 4
#> 7 DK 3 4 3 4 3
#> 8 EE 4 4 4 4 2
#> 9 EL 1 1 5 1 5
#> 10 ES 1 1 1 1 5
#> # ℹ 18 more rows
#> # ℹ 11 more variables: `2007/2008` <int>, `2008/2009` <int>, `2009/2010` <int>,
#> # `2010/2011` <int>, `2011/2012` <int>, `2012/2013` <int>, `2013/2014` <int>,
#> # `2014/2015` <int>, `2015/2016` <int>, `2016/2017` <int>, `2017/2018` <int>
mypattemp
#> # A tibble: 28 × 17
#> Country `2002/2003` `2003/2004` `2004/2005` `2005/2006` `2006/2007`
#> <chr> <chr> <chr> <chr> <chr> <chr>
#> 1 AT Outperforming Inversion Outperforming Outperform… Outperform…
#> 2 BE Diving Catching up Catching up Other (Ins… Catching up
#> 3 BG Catching up Catching up Catching up Catching up Catching up
#> 4 CY Outperforming Outperforming Inversion Outperform… Flattening
#> 5 CZ Inversion Inversion Outperforming Flattening Flattening
#> 6 DE Inversion Crossing Crossing reversed Outperform… Outperform…
#> 7 DK Inversion Outperforming Inversion Outperform… Inversion
#> 8 EE Outperforming Outperforming Outperforming Outperform… Flattening
#> 9 EL Catching up Catching up Slower pace Catching up Slower pace
#> 10 ES Catching up Catching up Catching up Catching up Slower pace
#> # ℹ 18 more rows
#> # ℹ 11 more variables: `2007/2008` <chr>, `2008/2009` <chr>, `2009/2010` <chr>,
#> # `2010/2011` <chr>, `2011/2012` <chr>, `2012/2013` <chr>, `2013/2014` <chr>,
#> # `2014/2015` <chr>, `2015/2016` <chr>, `2016/2017` <chr>, `2017/2018` <chr>Let’s illustrate more in detail one of the obtained patterns; to this end, we consider the time period 2006-2007 and the country France (“FR”) for which the obtained pattern is “Slower pace”:
with the following graphical plot of the calculated pattern where the
dashed blue line refers to the France and the black solid line refers to
the EU:
The interpretation of the “Slower pace” pattern is straightforward as
illustrated in the Eurofound report “Monitoring convergence in the
European Union Upward convergence in the EU: Concepts, measurements and
indicators” (2018, p. 25).
A second example relates to an indicator of type “low is better”. To this end, let’s consider the indicator Unemployment rate by sex, age and educational attainment - annual averages for which the data are stored in the une_educ_a.xls file (Subsection 4.2, Tutorial for analyzing convergence with the convergEU package). First, we import the data from the xls file as explained in details in the Tutorial (Subsection 4.2):
# library(readxl)
file_name <- system.file("vign/une_educ_a.xls", package = "convergEU")
myxls2<-read_excel(file_name,
sheet="Data",range = "A12:AP22", na=":")
myxls2 <- dplyr::mutate(myxls2, `TIME/GEO` = as.numeric(`TIME/GEO`))where “une_educ_a.xls” specifies the path (eventually including disk unit or folders) in which the xls file is stored. Then, the cluster EU27_2020 of MS is chosen, the data are checked for unsuited features, and missing values imputation is performed as follows:
EU27estr<-convergEU_glb()$EU27_2020$memberStates$codeMS
myxls<- dplyr::select(myxls2,`TIME/GEO`,all_of(EU27estr))
check_data(myxls)
#> $res
#> NULL
#>
#> $msg
#> NULL
#>
#> $err
#> [1] "Error: one or more missing values in the dataframe."
myxls3<- dplyr::rename(myxls,time=`TIME/GEO`)
myxlsf <- impute_dataset(myxls3, timeName ="time",
countries=convergEU_glb()$EU27_2020$memberStates$codeMS,
headMiss = c("cut", "constant")[2],
tailMiss = c("cut", "constant")[2])$res
check_data(myxlsf)
#> $res
#> [1] TRUE
#>
#> $msg
#> NULL
#>
#> $err
#> NULLin order to obtain the final dataset myxlsf for calculating patterns.
The indicator une_educ_a is of type “low is better”; thus, the syntax to find the patterns is as follows:
where the “$res” component of the output contains the numerical labels for the patterns as well as their string labels:
mypattl<-myres$res$mat_label_tags
mypattn<-myres$res$mat_without_summaries
mypattn
#> # A tibble: 27 × 10
#> Country `2009/2010` `2010/2011` `2011/2012` `2012/2013` `2013/2014`
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 BE 7 8 7 10 3
#> 2 DK 10 7 7 8 2
#> 3 FR 20 21 21 21 21
#> 4 DE 8 8 8 8 2
#> 5 EL 10 10 19 9 1
#> 6 IE 9 9 9 11 1
#> 7 IT 7 7 10 10 3
#> 8 LU 8 10 7 10 21
#> 9 NL 7 8 10 10 3
#> 10 PT 7 10 10 10 4
#> # ℹ 17 more rows
#> # ℹ 4 more variables: `2014/2015` <dbl>, `2015/2016` <dbl>, `2016/2017` <dbl>,
#> # `2017/2018` <dbl>
mypattl
#> # A tibble: 27 × 10
#> Country `2009/2010` `2010/2011` `2011/2012` `2012/2013` `2013/2014`
#> <chr> <chr> <chr> <chr> <chr> <chr>
#> 1 BE Defending better Escaping Defending … Underperfo… Inversion
#> 2 DK Underperforming Defending bett… Defending … Escaping Flattening
#> 3 FR Crossing reversed Other (Inspect… Other (Ins… Other (Ins… Other (Ins…
#> 4 DE Escaping Escaping Escaping Escaping Flattening
#> 5 EL Underperforming Underperforming Crossing Falling aw… Catching up
#> 6 IE Falling away Falling away Falling aw… Recovering Catching up
#> 7 IT Defending better Defending bett… Underperfo… Underperfo… Inversion
#> 8 LU Escaping Underperforming Defending … Underperfo… Other (Ins…
#> 9 NL Defending better Escaping Underperfo… Underperfo… Inversion
#> 10 PT Defending better Underperforming Underperfo… Underperfo… Outperform…
#> # ℹ 17 more rows
#> # ℹ 4 more variables: `2014/2015` <chr>, `2015/2016` <chr>, `2016/2017` <chr>,
#> # `2017/2018` <chr>For this indicator, let’s take the time period 2015-2016 and the MS Finland (“FI”) for which the obtained pattern is again “Slower pace”:
In this case, given that the indicator is of type “low is better”,
the plot for the “Slower pace” pattern is:
where the dashed blue line refers to Finland and the black solid line
refers to the EU. Recall that differently from the previous indicator of
type “high is better”, for this type of indicator the results for the
“Slower pace” pattern should be interpreted according to the assumption
that “higher the indicator value, worse the considered socio/economic
feature in a member country”.
To further illustrate other possible patterns, consider again the first example related to the emp_20_64_MS dataset (indicators of type “high is better”). For example, let’s take the time period 2011-2012 and the MS Portugal (“PT”) for which the pattern is “Crossing”:
where the corresponding plot for this pattern is:
Similarly, for the member country Lithuania (“LT”) in the same time
period, the obtained pattern is now “Crossing reversed” and the plot for
this pattern is:
