Do two approaches:

Similar to the general comparison plot, comparing aggregate levels
Correspondence analysis

# How important to engage with
# X78 = public
# X80 = industry
# X82 = Policy

# Institutional policy
# X30  = public
# X31  = industry
# X33 = policy

core_data <- df %>% 
  select(inst_public = X30, inst_industry = X31, inst_policy = X33,
         imp_public = X78, imp_industry = X80, imp_policy = X82)

## select: renamed 6 variables (inst_public, inst_industry, inst_policy, imp_public, imp_industry, …) and dropped 67 variables

core_data %>% 
  head(10) %>% 
  knitr::kable()

inst_public	inst_industry	inst_policy	imp_public	imp_industry	imp_policy
Neither important nor unimportant	Somewhat important	Neither important nor unimportant	Unimportant	Neither important nor unimportant	Unimportant
Somewhat important	Somewhat important	Somewhat unimportant	Very important	Unimportant	Important
Neither important nor unimportant	Somewhat important	Somewhat important	Neither important nor unimportant	Neither important nor unimportant	Neither important nor unimportant
Somewhat important	Very important	Neither important nor unimportant	Important	Important	Very important
Somewhat important	Somewhat important	Somewhat important	Important	Neither important nor unimportant	Neither important nor unimportant
Very important	Very important	Very important	Neither important nor unimportant	Important	Important
Neither important nor unimportant	Very important	I don’t know	Very important	Very important	Neither important nor unimportant
Neither important nor unimportant	Somewhat important	Neither important nor unimportant	Neither important nor unimportant	Neither important nor unimportant	Very unimportant
Somewhat important	Somewhat important	Somewhat important	Neither important nor unimportant	Neither important nor unimportant	Neither important nor unimportant
Somewhat important	Neither important nor unimportant	Very important	Important	Neither important nor unimportant	Very important

long_data <- core_data %>% 
  mutate(across(.fns = get_numeric_val)) %>% 
  pivot_longer(everything(), names_to = c("source", "type"),
               names_pattern = "(.*)_(.*)") %>% 
  mutate(source = recode(source, inst = "Perceived institutional view", 
                         imp = "Importance for success of research"))

## mutate: converted 'inst_public' from character to integer (10 new NA)

##         converted 'inst_industry' from character to integer (16 new NA)

##         converted 'inst_policy' from character to integer (20 new NA)

##         converted 'imp_public' from character to integer (4 new NA)

##         converted 'imp_industry' from character to integer (10 new NA)

##         converted 'imp_policy' from character to integer (14 new NA)

## pivot_longer: reorganized (inst_public, inst_industry, inst_policy, imp_public, imp_industry, …) into (source, type, value) [was 198x6, now 1188x3]

## mutate: changed 1,188 values (100%) of 'source' (0 new NA)

bootstrapped <- long_data %>% 
  group_by(source, type) %>% 
  summarise(res = list(Hmisc::smean.cl.boot(value))) %>%
  unnest_wider(res)

## group_by: 2 grouping variables (source, type)

## summarise: now 6 rows and 3 columns, one group variable remaining (source)

dodge_width <- .2
yellow <- "#E0C47C"

bootstrapped %>% 
  ggplot(aes(Mean, type, colour = source)) +
  geom_linerange(aes(xmin = Lower, xmax = Upper, group = fct_rev(source)),
                 position = position_dodge(width = dodge_width),
                 colour = "grey60") +
  geom_point(aes(colour = fct_rev(source)), size = 2.6,
             position = position_dodge(width = dodge_width)) +
  five_point_scale() +
    scale_colour_manual(values = c(
    `Importance for success of research` =  yellow, #"#B96FB0",
    `Perceived institutional view` = custom_blue #"#54984E"
  )) +
  labs(y = NULL, colour = NULL, x = NULL) +
  theme(legend.position = "top")

Aggregate levels are very similar. Biggest dis-alignment with industry, although differences still quite close and within confidence intervals for the means.

Via correspondence analysis

# simplify for plotting
make_names_simple <- function(x, keep_NA = TRUE) {
  if (keep_NA) {
    case_when(
      x == "Very important" ~ "++",
      x == "Important" ~ "+",
      x == "Somewhat important" ~ "+",
      x == "Neither important nor unimportant" ~ "=",
      x == "Unimportant" ~ "-",
      x == "Somewhat unimportant" ~ "-",
      x == "Very unimportant" ~ "--",
      x == "I don't know" ~ "?",
      x == "Not applicable" ~ "NA"
    )
  } else {
    case_when(
      x == "Very important" ~ "++",
      x == "Important" ~ "+",
      x == "Somewhat important" ~ "+",
      x == "Neither important nor unimportant" ~ "=",
      x == "Unimportant" ~ "-",
      x == "Somewhat unimportant" ~ "-",
      x == "Very unimportant" ~ "--",
      x == "I don't know" ~ "?"
    )
  }

}

mca_model <- core_data %>%
  mutate(across(everything(), make_names_simple)) %>% 
  ca::mjca()

## mutate: changed 198 values (100%) of 'inst_public' (0 new NA)

##         changed 198 values (100%) of 'inst_industry' (0 new NA)

##         changed 198 values (100%) of 'inst_policy' (0 new NA)

##         changed 198 values (100%) of 'imp_public' (0 new NA)

##         changed 198 values (100%) of 'imp_industry' (0 new NA)

##         changed 198 values (100%) of 'imp_policy' (0 new NA)

prettify <- list(
  theme(legend.position = "top",
        axis.title.x = element_text(size = rel(1.5)),
        axis.title.y = element_text(size = rel(1.5)),
        axis.text = element_text(size = rel(1.2)),
        legend.text = element_text(size = rel(1.1)))
  #scale_color_manual(values = scale_spectral) 
)

# scale_short <- c("Indicator present" = "#3588BD", 
#                     "Indicator not present" = "#C26574")

mca_model %>%
  plot_ca(font_size = 5, show.legend = TRUE) +
  coord_fixed() +
  prettify

## mutate: changed 40 values (100%) of 'rowname' (0 new NA)

##         new variable 'Profil' (character) with one unique value and 0% NA

## slice: removed all rows (100%)

## mutate: new variable 'sup_var' (factor) with 0 unique values and 100% NA

## full_join: added 3 columns (x, y, Profil)

##            > rows only in x    0

##            > rows only in y   40

##            > matched rows      0

##            >                 ====

##            > rows total       40

## replace_na: changed 40 values (100%) of 'sup_var' (40 fewer NA)

Second dimension is mainly NAs, so removing.

m2 <- core_data %>%
  mutate(across(everything(), make_names_simple, keep_NA = FALSE)) %>% 
  ca::mjca()

## mutate: changed 198 values (100%) of 'inst_public' (7 new NA)

##         changed 198 values (100%) of 'inst_industry' (12 new NA)

##         changed 198 values (100%) of 'inst_policy' (8 new NA)

##         changed 198 values (100%) of 'imp_public' (0 new NA)

##         changed 198 values (100%) of 'imp_industry' (10 new NA)

##         changed 198 values (100%) of 'imp_policy' (4 new NA)

m2 %>%
  plot_ca(font_size = 5, keep_labels = TRUE) +
  coord_fixed() +
  prettify

## mutate: new variable 'Profil' (character) with one unique value and 0% NA

## slice: removed all rows (100%)

## mutate: new variable 'sup_var' (factor) with 0 unique values and 100% NA

## full_join: added 3 columns (x, y, Profil)

##            > rows only in x    0

##            > rows only in y   35

##            > matched rows      0

##            >                 ====

##            > rows total       35

## replace_na: changed 35 values (100%) of 'sup_var' (35 fewer NA)

Broadly speaking: categories agree to each other, all of them are similar. Only exception: perceived institutional policies of complete unimportance are a little removed from the rest - level of unimportance is higher for these three than for the importance to own research.

The general pattern is a typical horseshoe-patter and of no substantive relevance.

A correlation analysis likely might bring out more subtle differences.

Correlation analysis

cor_base <- core_data %>% 
  mutate(across(.fns = get_numeric_val))

## mutate: converted 'inst_public' from character to integer (10 new NA)

##         converted 'inst_industry' from character to integer (16 new NA)

##         converted 'inst_policy' from character to integer (20 new NA)

##         converted 'imp_public' from character to integer (4 new NA)

##         converted 'imp_industry' from character to integer (10 new NA)

##         converted 'imp_policy' from character to integer (14 new NA)

cor_matrix <- cor_base %>% 
  cor(use = "pairwise.complete.obs", method = "spearman")
cor_matrix %>% 
  knitr::kable()

	inst_public	inst_industry	inst_policy	imp_public	imp_industry	imp_policy
inst_public	1.0000000	0.4172419	0.6633837	0.3878459	0.1526236	0.3612194
inst_industry	0.4172419	1.0000000	0.5394400	0.1588892	0.3176614	0.1602090
inst_policy	0.6633837	0.5394400	1.0000000	0.3375562	0.2536682	0.4028998
imp_public	0.3878459	0.1588892	0.3375562	1.0000000	0.4674405	0.6088790
imp_industry	0.1526236	0.3176614	0.2536682	0.4674405	1.0000000	0.3689097
imp_policy	0.3612194	0.1602090	0.4028998	0.6088790	0.3689097	1.0000000

plot_correlation <- function(cor_matrix, cluster = TRUE) {
  # code from http://www.sthda.com/english/wiki/visualize-correlation-matrix-using-correlogram
  # col <- colorRampPalette(c("#BB4444", "#EE9988", "#FFFFFF", "#77AADD", "#4477AA"))
  
  col <- colorRampPalette(c(yellow, "#FFFFFF", "#0880AB"))
  order <- ifelse(cluster, "hclust", "original")
  
  corrplot::corrplot(
    cor_matrix, method = "color", col = col(200),  
    type = "upper", order = order, 
    addCoef.col = "black", # Add coefficient of correlation
    tl.col = "black", tl.srt = 45, #Text label color and rotation
    # hide correlation coefficient on the principal diagonal
    diag = FALSE 
  )
}

plot_correlation(cor_matrix, cluster = FALSE)

Here, “inst” denotes the perceived institutional policy, and “imp” denotes the relevance to the respondents research.

Correlations in the upper right square (3x3), which shows the relationships between perceived institutional policies and the relevance to research, are generally low to moderate.

The correlations between the three types, comparing relevance to research and perceived institutional policy, are .39 (public), .32 (industry), and .4 (policy). Thus, there seems to be moderate alignment between importance for researchers and perceived institutional policies.

However, it is unclear how much alignment could be expected, and therefore, whether this finding is of any substantive interest.

All three key correlations are statistically significant (after correction for multiple comparisons via the approach developed by Benhamini & Hochberg (1995))

p_vals <- corrplot::cor.mtest(cor_base)$p
adj_p_vals <- p.adjust(p_vals, method = "fdr") %>% 
  matrix(nrow = 6) 

colnames(adj_p_vals) <- colnames(p_vals)
rownames(adj_p_vals) <- rownames(p_vals)

col <- colorRampPalette(c(yellow, "#FFFFFF", "#0880AB"))
corrplot::corrplot(
  cor_matrix, method = "color",  col = col(200),
  type = "upper", p.mat = adj_p_vals, sig.level = .05,
  addCoef.col = "black", # Add coefficient of correlation
  tl.col = "black", tl.srt = 45, #Text label color and rotation
  # hide correlation coefficient on the principal diagonal
  diag = FALSE 
)

Refs

Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B, 57, 289–300. doi: 10.1111/j.2517-6161.1995.tb02031.x. https://www.jstor.org/stable/2346101.

Importance for research vs opinions

Thomas Klebel

21 Dezember, 2022

Via correspondence analysis

Correlation analysis

Refs