HEXACO Validation: Six Factors or Five?

Description

The HEXACO model (Lee & Ashton, 2004; Ashton & Lee, 2007) describes personality with six broad factors instead of the Big Five: Honesty-Humility, Emotionality, eXtraversion, Agreeableness, Conscientiousness and Openness to Experience. The new factor is Honesty-Humility (sincerity, fairness, greed avoidance, modesty). Lexical studies in many languages found it as a sixth factor when the adjectives people use to describe each other are analysed. HEXACO Emotionality and Agreeableness are also rotated versions of Big Five Neuroticism and Agreeableness: sentimentality moves into Emotionality, and anger (low patience) moves into low Agreeableness.

This tutorial validates the IPIP-HEXACO scales (Ashton, Lee & Goldberg, 2007), a public-domain version from the International Personality Item Pool with 240 items: 10 items for each of 24 facets, 4 facets per factor. Respondents rated each statement on a 1-7 scale (1 = strongly disagree, 4 = neutral, 7 = strongly agree). Its central question is the one that separates HEXACO from the Big Five measured in the BFI-44 and IPIP-50 tutorials: do the data need a sixth factor, and what happens to Honesty-Humility when only five are allowed?

Data and cleaning

The data come from the Open-Source Psychometrics Project (HEXACO.zip, 22,786 records). The codebook does not give the keying of the items, so the scoring key in data/hexaco_key.csv was matched item by item to the official IPIP-HEXACO key, which also lists the published alpha of each facet. data/prepare_hexaco.R applies the cleaning rules below.

Besides two validity questions and the completion time, the cleaning uses the even-odd consistency index (Johnson, 2005): each facet is split into its odd- and even-numbered items, the 24 odd and 24 even half-scores are correlated within the person, and the correlation is corrected to full length with the Spearman-Brown formula. Someone who reads the items gives similar answers to the two halves of a facet (typical values around .8); someone who answers at random does not (values near 0).

Rule	Excluded	Remaining
All 240 items answered	52	22,734
Understood the instructions (at least slightly agree)	626	22,160
Answered accurately (at least slightly agree)	561	22,225
At least 2 seconds per item	442	22,344
Even-odd consistency at least .30	95	22,691
All rules together	1,541	21,245

ggplot(df_hexaco, aes(x = even_odd)) +
  geom_histogram(binwidth = 0.02, fill = "grey40", colour = "white") +
  geom_vline(xintercept = 0.30, colour = "#d6604d", linetype = "dashed") +
  labs(x = "Even-odd consistency (kept respondents)", y = "Respondents") +
  theme_bw(base_size = 10) +
  ggtitle("Even-odd consistency of the kept protocols",
          subtitle = "Dashed line: exclusion threshold (.30)")

Item List

Show the 240 items with their facet and keying

Label	Domain	Facet	Key	Item
HSinc1	Honesty-Humility	Sincerity	+	Don’t pretend to be more than I am.
HSinc2	Honesty-Humility	Sincerity	-	Use flattery to get ahead.
HSinc3	Honesty-Humility	Sincerity	-	Tell other people what they want to hear so that they will do what I want them to do.
HSinc4	Honesty-Humility	Sincerity	-	Put on a show to impress people.
HSinc5	Honesty-Humility	Sincerity	-	Switch my loyalties when I feel like it.
HSinc6	Honesty-Humility	Sincerity	-	Play a role in order to impress people.
HSinc7	Honesty-Humility	Sincerity	-	Pretend to be concerned for others.
HSinc8	Honesty-Humility	Sincerity	-	Act like different people in different situations.
HSinc9	Honesty-Humility	Sincerity	-	Find it necessary to please the people who have power.
HSinc10	Honesty-Humility	Sincerity	-	Let people push me around to help them feel important.
HFair1	Honesty-Humility	Fairness	+	Would never take things that aren’t mine.
HFair2	Honesty-Humility	Fairness	+	Would never cheat on my taxes.
HFair3	Honesty-Humility	Fairness	+	Return extra change when a cashier makes a mistake.
HFair4	Honesty-Humility	Fairness	+	Would feel very badly for a long time if I were to steal from someone.
HFair5	Honesty-Humility	Fairness	+	Try to follow the rules.
HFair6	Honesty-Humility	Fairness	-	Admire a really clever scam.
HFair7	Honesty-Humility	Fairness	-	Cheat to get ahead.
HFair8	Honesty-Humility	Fairness	-	Steal things.
HFair9	Honesty-Humility	Fairness	-	Cheat on people who have trusted me.
HFair10	Honesty-Humility	Fairness	-	Would not regret my behavior if I were to take advantage of someone impulsively.
HGree1	Honesty-Humility	Greed Avoidance	+	Would not enjoy being a famous celebrity.
HGree2	Honesty-Humility	Greed Avoidance	+	Don’t strive for elegance in my appearance.
HGree3	Honesty-Humility	Greed Avoidance	-	Love luxury.
HGree4	Honesty-Humility	Greed Avoidance	-	Have a strong need for power.
HGree5	Honesty-Humility	Greed Avoidance	-	Seek status.
HGree6	Honesty-Humility	Greed Avoidance	-	Am mainly interested in money.
HGree7	Honesty-Humility	Greed Avoidance	-	Wish to stay young forever.
HGree8	Honesty-Humility	Greed Avoidance	-	Try to impress others.
HGree9	Honesty-Humility	Greed Avoidance	-	Prefer to eat at expensive restaurants.
HGree10	Honesty-Humility	Greed Avoidance	-	Am out for my own personal gain.
HMode1	Honesty-Humility	Modesty	+	Don’t think that I’m better than other people.
HMode2	Honesty-Humility	Modesty	+	See myself as an average person.
HMode3	Honesty-Humility	Modesty	+	Am just an ordinary person.
HMode4	Honesty-Humility	Modesty	+	Consider myself an average person.
HMode5	Honesty-Humility	Modesty	-	Would like to have more power than other people.
HMode6	Honesty-Humility	Modesty	-	Believe that I am better than others.
HMode7	Honesty-Humility	Modesty	-	Like to attract attention.
HMode8	Honesty-Humility	Modesty	-	Am more capable than most others.
HMode9	Honesty-Humility	Modesty	-	Am likely to show off if I get the chance.
HMode10	Honesty-Humility	Modesty	-	Boast about my virtues.
EFear1	Emotionality	Fearfulness	+	Am a physical coward.
EFear2	Emotionality	Fearfulness	+	Begin to panic when there is danger.
EFear3	Emotionality	Fearfulness	+	Would fear walking in a high-crime part of a city.
EFear4	Emotionality	Fearfulness	+	Tremble in dangerous situations.
EFear5	Emotionality	Fearfulness	+	Would never go riding down a stretch of rapids in a canoe.
EFear6	Emotionality	Fearfulness	-	Like to do frightening things.
EFear7	Emotionality	Fearfulness	-	Face danger confidently.
EFear8	Emotionality	Fearfulness	-	Love dangerous situations.
EFear9	Emotionality	Fearfulness	-	Would be good at rescuing people from a burning building.
EFear10	Emotionality	Fearfulness	-	Am willing to take risks.
EAnxi1	Emotionality	Anxiety	+	Often worry about things that turn out to be unimportant.
EAnxi2	Emotionality	Anxiety	+	Worry about things.
EAnxi3	Emotionality	Anxiety	+	Get stressed out easily.
EAnxi4	Emotionality	Anxiety	+	Get upset by unpleasant thoughts that come into my mind.
EAnxi5	Emotionality	Anxiety	+	Panic easily.
EAnxi6	Emotionality	Anxiety	-	Rarely worry.
EAnxi7	Emotionality	Anxiety	-	Rarely feel depressed.
EAnxi8	Emotionality	Anxiety	-	Am not easily disturbed by events.
EAnxi9	Emotionality	Anxiety	-	Remain calm under pressure.
EAnxi10	Emotionality	Anxiety	-	Don’t worry about things that have already happened.
EDepe1	Emotionality	Dependence	+	Need reassurance.
EDepe2	Emotionality	Dependence	+	Let myself be influenced by others.
EDepe3	Emotionality	Dependence	+	Need the approval of others.
EDepe4	Emotionality	Dependence	+	Need protection.
EDepe5	Emotionality	Dependence	+	Often need help.
EDepe6	Emotionality	Dependence	+	Show my sadness.
EDepe7	Emotionality	Dependence	+	Suspect that my facial expressions give me away when I feel sad.
EDepe8	Emotionality	Dependence	+	Seek support.
EDepe9	Emotionality	Dependence	+	Can’t do without the company of others.
EDepe10	Emotionality	Dependence	+	Want to be liked.
ESent1	Emotionality	Sentimentality	+	Feel others’ emotions.
ESent2	Emotionality	Sentimentality	+	Immediately feel sad when hearing of an unhappy event.
ESent3	Emotionality	Sentimentality	+	Cry during movies.
ESent4	Emotionality	Sentimentality	+	Am sensitive to the needs of others.
ESent5	Emotionality	Sentimentality	+	Am deeply moved by others’ misfortunes.
ESent6	Emotionality	Sentimentality	-	Rarely cry during sad movies.
ESent7	Emotionality	Sentimentality	-	Seldom feel weepy while reading the sad part of a story.
ESent8	Emotionality	Sentimentality	-	Am seldom bothered by the apparent suffering of strangers.
ESent9	Emotionality	Sentimentality	-	Don’t understand people who get emotional.
ESent10	Emotionality	Sentimentality	-	Seldom get emotional.
XExpr1	Extraversion	Expressiveness	+	Talk a lot.
XExpr2	Extraversion	Expressiveness	+	Am never at a loss for words.
XExpr3	Extraversion	Expressiveness	+	Am the life of the party.
XExpr4	Extraversion	Expressiveness	+	Tell people about it when I’m irritated.
XExpr5	Extraversion	Expressiveness	+	Have an intense, boisterous laugh.
XExpr6	Extraversion	Expressiveness	-	Don’t talk a lot.
XExpr7	Extraversion	Expressiveness	-	Don’t like to draw attention to myself.
XExpr8	Extraversion	Expressiveness	-	Say little.
XExpr9	Extraversion	Expressiveness	-	Bottle up my feelings.
XExpr10	Extraversion	Expressiveness	-	Speak softly.
XSocB1	Extraversion	Social Boldness	+	Am good at making impromptu speeches.
XSocB2	Extraversion	Social Boldness	+	Don’t mind being the center of attention.
XSocB3	Extraversion	Social Boldness	+	Feel comfortable around people.
XSocB4	Extraversion	Social Boldness	+	Have leadership abilities.
XSocB5	Extraversion	Social Boldness	+	Have a strong personality.
XSocB6	Extraversion	Social Boldness	-	Would be afraid to give a speech in public.
XSocB7	Extraversion	Social Boldness	-	Keep in the background.
XSocB8	Extraversion	Social Boldness	-	Find it difficult to approach others.
XSocB9	Extraversion	Social Boldness	-	Hate being the center of attention.
XSocB10	Extraversion	Social Boldness	-	Have little to say.
XSoci1	Extraversion	Sociability	+	Usually like to spend my free time with people.
XSoci2	Extraversion	Sociability	+	Talk to a lot of different people at parties.
XSoci3	Extraversion	Sociability	+	Love to chat.
XSoci4	Extraversion	Sociability	+	Make friends easily.
XSoci5	Extraversion	Sociability	+	Enjoy being part of a group.
XSoci6	Extraversion	Sociability	-	Seem to derive less enjoyment from interacting with people than others do.
XSoci7	Extraversion	Sociability	-	Rarely enjoy being with people.
XSoci8	Extraversion	Sociability	-	Would not enjoy a job that involves a lot of social interaction.
XSoci9	Extraversion	Sociability	-	Am hard to get to know.
XSoci10	Extraversion	Sociability	-	Keep others at a distance.
XLive1	Extraversion	Liveliness	+	Maintain high energy throughout the day.
XLive2	Extraversion	Liveliness	+	Have great stamina.
XLive3	Extraversion	Liveliness	+	Am usually active and full of energy.
XLive4	Extraversion	Liveliness	+	Smile a lot.
XLive5	Extraversion	Liveliness	+	Feel healthy and vibrant most of the time.
XLive6	Extraversion	Liveliness	+	Laugh a lot.
XLive7	Extraversion	Liveliness	+	Feel that I have a lot of inner strength.
XLive8	Extraversion	Liveliness	+	Have a lot of fun.
XLive9	Extraversion	Liveliness	-	Tire out quickly.
XLive10	Extraversion	Liveliness	-	Often feel blue.
AForg1	Agreeableness	Forgiveness	+	Love my enemies.
AForg2	Agreeableness	Forgiveness	+	Try to forgive and forget.
AForg3	Agreeableness	Forgiveness	+	Am inclined to forgive others.
AForg4	Agreeableness	Forgiveness	+	Am nice to people I should be angry at.
AForg5	Agreeableness	Forgiveness	-	Find it hard to forgive others.
AForg6	Agreeableness	Forgiveness	-	Hold a grudge.
AForg7	Agreeableness	Forgiveness	-	Get back at people who insult me.
AForg8	Agreeableness	Forgiveness	-	Get even with others.
AForg9	Agreeableness	Forgiveness	-	Distrust people.
AForg10	Agreeableness	Forgiveness	-	Feel that most people can’t be trusted.
AGent1	Agreeableness	Gentleness	+	Rarely complain.
AGent2	Agreeableness	Gentleness	+	Take things as they come.
AGent3	Agreeableness	Gentleness	+	Accept people as they are.
AGent4	Agreeableness	Gentleness	+	Have a good word for everyone.
AGent5	Agreeableness	Gentleness	-	Become frustrated and angry with people when they don’t live up to my expectations.
AGent6	Agreeableness	Gentleness	-	Am quick to judge others.
AGent7	Agreeableness	Gentleness	-	Find fault with everything.
AGent8	Agreeableness	Gentleness	-	Speak ill of others.
AGent9	Agreeableness	Gentleness	-	Have a sharp tongue.
AGent10	Agreeableness	Gentleness	-	Criticize others’ shortcomings.
AFlex1	Agreeableness	Flexibility	+	Adjust easily.
AFlex2	Agreeableness	Flexibility	+	Am good at taking advice.
AFlex3	Agreeableness	Flexibility	-	When interacting with a group of people, am often bothered by at least one of them.
AFlex4	Agreeableness	Flexibility	-	React strongly to criticism.
AFlex5	Agreeableness	Flexibility	-	Get upset if others change the way that I have arranged things.
AFlex6	Agreeableness	Flexibility	-	Am hard to convince.
AFlex7	Agreeableness	Flexibility	-	Am annoyed by others’ mistakes.
AFlex8	Agreeableness	Flexibility	-	Can’t stand being contradicted.
AFlex9	Agreeableness	Flexibility	-	Am hard to satisfy.
AFlex10	Agreeableness	Flexibility	-	Am hard to reason with.
APati1	Agreeableness	Patience	+	Find that it takes a lot to make me feel angry at someone.
APati2	Agreeableness	Patience	+	Rarely feel angry with people.
APati3	Agreeableness	Patience	+	Am usually a patient person.
APati4	Agreeableness	Patience	+	Rarely get irritated.
APati5	Agreeableness	Patience	+	Seldom get mad.
APati6	Agreeableness	Patience	-	Am easily annoyed.
APati7	Agreeableness	Patience	-	Get angry easily.
APati8	Agreeableness	Patience	-	Get irritated easily.
APati9	Agreeableness	Patience	-	Lose my temper.
APati10	Agreeableness	Patience	-	Get upset easily.
COrga1	Conscientiousness	Organization	+	Keep things tidy.
COrga2	Conscientiousness	Organization	+	Get chores done right away.
COrga3	Conscientiousness	Organization	+	Like order.
COrga4	Conscientiousness	Organization	+	Like to tidy up.
COrga5	Conscientiousness	Organization	+	Want everything to be just right.
COrga6	Conscientiousness	Organization	-	Leave a mess in my room.
COrga7	Conscientiousness	Organization	-	Leave my belongings around.
COrga8	Conscientiousness	Organization	-	Don’t finish the things that I start.
COrga9	Conscientiousness	Organization	-	Often forget to put things back in their proper place.
COrga10	Conscientiousness	Organization	-	Am not bothered by disorder.
CDili1	Conscientiousness	Diligence	+	Push myself very hard to succeed.
CDili2	Conscientiousness	Diligence	+	Get started quickly on doing a job.
CDili3	Conscientiousness	Diligence	+	Am exacting in my work.
CDili4	Conscientiousness	Diligence	+	Work hard.
CDili5	Conscientiousness	Diligence	+	Complete tasks successfully.
CDili6	Conscientiousness	Diligence	-	Do just enough work to get by.
CDili7	Conscientiousness	Diligence	-	Stop when work becomes too difficult.
CDili8	Conscientiousness	Diligence	-	Do too little work.
CDili9	Conscientiousness	Diligence	-	Hang around doing nothing.
CDili10	Conscientiousness	Diligence	-	Quickly lose interest in the tasks I start.
CPerf1	Conscientiousness	Perfectionism	+	Pay attention to details.
CPerf2	Conscientiousness	Perfectionism	+	Continue until everything is perfect.
CPerf3	Conscientiousness	Perfectionism	+	Have an eye for detail.
CPerf4	Conscientiousness	Perfectionism	+	Want every detail taken care of.
CPerf5	Conscientiousness	Perfectionism	+	Dislike imperfect work.
CPerf6	Conscientiousness	Perfectionism	+	Want everything to add up perfectly.
CPerf7	Conscientiousness	Perfectionism	+	Detect mistakes.
CPerf8	Conscientiousness	Perfectionism	+	Demand quality.
CPerf9	Conscientiousness	Perfectionism	-	Pay too little attention to details.
CPerf10	Conscientiousness	Perfectionism	-	Prefer to just let things happen.
CPrud1	Conscientiousness	Prudence	+	Avoid mistakes.
CPrud2	Conscientiousness	Prudence	+	Make plans and stick to them.
CPrud3	Conscientiousness	Prudence	+	Do things according to a plan.
CPrud4	Conscientiousness	Prudence	-	Jump into things without thinking.
CPrud5	Conscientiousness	Prudence	-	Do things without thinking of the consequences.
CPrud6	Conscientiousness	Prudence	-	Make rash decisions.
CPrud7	Conscientiousness	Prudence	-	Act impulsively when something is bothering me.
CPrud8	Conscientiousness	Prudence	-	Make careless mistakes.
CPrud9	Conscientiousness	Prudence	-	Don’t know why I do some of the things I do.
CPrud10	Conscientiousness	Prudence	-	Make a fool of myself.
OAesA1	Openness	Aesthetic Appreciation	+	Believe in the importance of art.
OAesA2	Openness	Aesthetic Appreciation	+	Get deeply immersed in music.
OAesA3	Openness	Aesthetic Appreciation	+	See beauty in things that others might not notice.
OAesA4	Openness	Aesthetic Appreciation	+	Enjoy feeling close to the earth.
OAesA5	Openness	Aesthetic Appreciation	+	Have read the great literary classics.
OAesA6	Openness	Aesthetic Appreciation	-	Do not like art.
OAesA7	Openness	Aesthetic Appreciation	-	Seldom notice the emotional aspects of paintings and pictures.
OAesA8	Openness	Aesthetic Appreciation	-	Do not like poetry.
OAesA9	Openness	Aesthetic Appreciation	-	Do not like concerts.
OAesA10	Openness	Aesthetic Appreciation	-	Do not enjoy watching dance performances.
OInqu1	Openness	Inquisitiveness	+	Am interested in science.
OInqu2	Openness	Inquisitiveness	+	Would love to explore strange places.
OInqu3	Openness	Inquisitiveness	+	Enjoy intellectual games.
OInqu4	Openness	Inquisitiveness	+	Love to read challenging material.
OInqu5	Openness	Inquisitiveness	+	Find political discussions interesting.
OInqu6	Openness	Inquisitiveness	+	Have a rich vocabulary.
OInqu7	Openness	Inquisitiveness	-	Don’t know much about history.
OInqu8	Openness	Inquisitiveness	-	Avoid difficult reading material.
OInqu9	Openness	Inquisitiveness	-	Don’t bother worrying about political and social problems.
OInqu10	Openness	Inquisitiveness	-	Will not probe deeply into a subject.
OCrea1	Openness	Creativity	+	Have a vivid imagination.
OCrea2	Openness	Creativity	+	Come up with something new.
OCrea3	Openness	Creativity	+	Carry the conversation to a higher level.
OCrea4	Openness	Creativity	+	Am full of ideas.
OCrea5	Openness	Creativity	+	Love to think up new ways of doing things.
OCrea6	Openness	Creativity	+	Have excellent ideas.
OCrea7	Openness	Creativity	-	Do not have a good imagination.
OCrea8	Openness	Creativity	-	Have difficulty imagining things.
OCrea9	Openness	Creativity	-	Have trouble guessing how others will react.
OCrea10	Openness	Creativity	-	Seldom experience sudden intuitive insights.
OUnco1	Openness	Unconventionality	+	Am considered to be kind of eccentric.
OUnco2	Openness	Unconventionality	+	Know that my ideas sometimes surprise people.
OUnco3	Openness	Unconventionality	+	Do things that others find strange.
OUnco4	Openness	Unconventionality	+	Rebel against authority.
OUnco5	Openness	Unconventionality	+	Swim against the current.
OUnco6	Openness	Unconventionality	-	Would hate to be considered odd or strange.
OUnco7	Openness	Unconventionality	-	Enjoy being thought of as a normal mainstream person.
OUnco8	Openness	Unconventionality	-	Like to be viewed as proper and conventional.
OUnco9	Openness	Unconventionality	-	Like to be thought of as a normal kind of person.
OUnco10	Openness	Unconventionality	-	Try to avoid complex people.

Checking the Scoring Key

If an item is keyed in the wrong direction, its correlation with the rest of its facet is negative. After reverse-keying, every one of the 240 items should correlate positively with the other nine items of its facet, whatever its keying.

item_total <- do.call(rbind, lapply(facets, function(f) {
  a <- psych::alpha(df[, key$facet == f], check.keys = FALSE, warnings = FALSE)
  data.frame(item = key$item[key$facet == f], facet = f, key = key$key[key$facet == f],
             r_drop = a$item.stats$r.drop)
}))
cat(sprintf("Corrected item-total correlations: %.2f to %.2f; negative: %d of %d\n",
            min(item_total$r_drop), max(item_total$r_drop),
            sum(item_total$r_drop < 0), nrow(item_total)))

Corrected item-total correlations: 0.19 to 0.85; negative: 0 of 240

item_total$facet <- factor(item_total$facet, levels = rev(facets))
ggplot(item_total, aes(x = r_drop, y = facet, colour = key)) +
  geom_vline(xintercept = 0, colour = "grey60") +
  geom_point(size = 2, alpha = 0.8, position = position_jitter(height = 0.15, seed = 1)) +
  scale_colour_manual(values = c(`+` = "#2166ac", `-` = "#d6604d"),
                      labels = c(`+` = "+ keyed", `-` = "- keyed (reversed)"), name = NULL) +
  labs(x = "Corrected item-total correlation", y = NULL) +
  theme_bw(base_size = 9) +
  theme(legend.position = "top") +
  ggtitle("Each item against the rest of its facet")

weak <- item_total[order(item_total$r_drop), ][1:5, ]
weak$text <- key$text[match(weak$item, key$item)]
knitr::kable(weak[, c("item", "facet", "key", "r_drop", "text")], digits = 2, row.names = FALSE,
             col.names = c("Item", "Facet", "Key", "Item-total r", "Wording"))

Item	Facet	Key	Item-total r	Wording
OInqu2	Inquisitiveness	+	0.19	Would love to explore strange places.
HSinc10	Sincerity	-	0.19	Let people push me around to help them feel important.
COrga5	Organization	+	0.21	Want everything to be just right.
AGent2	Gentleness	+	0.21	Take things as they come.
OCrea9	Creativity	-	0.22	Have trouble guessing how others will react.

Reliability

Cronbach’s alpha of the 24 facets in this sample, against the alpha published with the IPIP-HEXACO key, and the alpha of the six domains (40 items each).

facet_alpha <- data.frame(
  facet     = facets,
  domain    = facet_domain[facets],
  sample    = sapply(facets, function(f) psych::alpha(df[, key$facet == f], warnings = FALSE)$total$raw_alpha),
  published = as.numeric(key$published_alpha[match(facets, key$facet)]))
cat(sprintf("Facet alpha: %.2f to %.2f (published %.2f to %.2f); mean difference %+.2f\n",
            min(facet_alpha$sample), max(facet_alpha$sample),
            min(facet_alpha$published), max(facet_alpha$published),
            mean(facet_alpha$sample - facet_alpha$published)))

Facet alpha: 0.74 to 0.93 (published 0.69 to 0.88); mean difference +0.02

alpha_long <- melt(facet_alpha, id.vars = c("facet", "domain"), variable.name = "source", value.name = "alpha")
alpha_long$facet <- factor(alpha_long$facet, levels = rev(facets))
ggplot(alpha_long, aes(x = alpha, y = facet)) +
  geom_line(aes(group = facet), colour = "grey70") +
  geom_point(aes(colour = source), size = 2.5) +
  scale_colour_manual(values = c(sample = "#d6604d", published = "#2166ac"),
                      labels = c(sample = "This sample", published = "Published (IPIP key)"), name = NULL) +
  labs(x = "Cronbach's alpha", y = NULL) +
  theme_bw(base_size = 9) +
  theme(legend.position = "top") +
  ggtitle("Facet reliability: this sample against the published values")

diff_alpha <- setNames(facet_alpha$sample - facet_alpha$published, facet_alpha$facet)
domain_alpha <- sapply(domains, function(d) psych::alpha(df[, key$domain == d], warnings = FALSE)$total$raw_alpha)
knitr::kable(data.frame(domain = domains, alpha = domain_alpha), digits = 2, row.names = FALSE,
             col.names = c("Domain (40 items)", "Alpha"))

Domain (40 items)	Alpha
Honesty-Humility	0.90
Emotionality	0.92
Extraversion	0.95
Agreeableness	0.94
Conscientiousness	0.92
Openness	0.88

17 of the 24 facets are at least as reliable here as in the published key (within .01). The largest gains are Dependence and Greed Avoidance; the largest drops are Aesthetic Appreciation and Unconventionality, both Openness facets, which are a little less homogeneous in this online sample. Every facet stays above .70.

Facet Correlation Matrix

The factor analyses below work with the 24 facet scores, the usual level for testing the structure of a hierarchical inventory: each facet score averages 10 items, so it is far more reliable than a single item.

facet_cor <- cor(facet_scores)
cor_long  <- melt(facet_cor)
cor_long$Var1 <- factor(cor_long$Var1, levels = facets)
cor_long$Var2 <- factor(cor_long$Var2, levels = rev(facets))

ggplot(cor_long, aes(x = Var1, y = Var2, fill = value)) +
  geom_tile(color = "white", linewidth = 0.2) +
  scale_fill_gradient2(low = "#2166ac", mid = "white", high = "#d6604d",
                       midpoint = 0, limits = c(-1, 1), name = "r") +
  geom_hline(yintercept = seq(4.5, 20.5, 4), colour = "grey30", linewidth = 0.3) +
  geom_vline(xintercept = seq(4.5, 20.5, 4), colour = "grey30", linewidth = 0.3) +
  theme_bw(base_size = 9) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5),
        axis.title = element_blank(), panel.grid = element_blank()) +
  ggtitle("IPIP-HEXACO facet intercorrelations\nLines separate the six domains (H, E, X, A, C, O)")

How Many Factors?

eig <- eigen(facet_cor, only.values = TRUE)$values
cat("Eigenvalues 1-8:", sprintf("%.2f", eig[1:8]), "\n")

Eigenvalues 1-8: 4.82 3.97 2.86 2.36 1.88 1.14 0.79 0.60 

cat("Eigenvalues above 1:", sum(eig > 1), "\n")

Eigenvalues above 1: 6 

set.seed(42)
pa <- fa.parallel(facet_scores, fm = "ml", fa = "fa", n.iter = 20,
                  main = "Parallel analysis scree plot (24 IPIP-HEXACO facets)")

Parallel analysis suggests that the number of factors =  7  and the number of components =  NA 

fits <- lapply(4:7, function(k) fa(facet_scores, nfactors = k, rotate = "oblimin", fm = "ml"))
fit_tab <- data.frame(factors = 4:7,
                      TLI   = sapply(fits, function(e) e$TLI),
                      RMSEA = sapply(fits, function(e) e$RMSEA[1]),
                      BIC   = sapply(fits, function(e) e$BIC))
knitr::kable(fit_tab, digits = c(0, 3, 3, 0), row.names = FALSE,
             col.names = c("Factors", "TLI", "RMSEA", "BIC"))

Factors	TLI	RMSEA	BIC
4	0.705	0.117	52250
5	0.818	0.092	28293
6	0.891	0.071	14505
7	0.926	0.059	8236

Exactly six eigenvalues are above 1, and BIC, which penalises extra factors, roughly halves from five factors to six. Fit keeps improving with a seventh factor, and parallel analysis suggests 7: with 21,245 respondents, even very small factors are detectable. The seventh eigenvalue (0.79) is below 1, though, and the seventh factor is a minor one:

L7 <- unclass(fits[[4]]$loadings)
minor <- which.min(apply(abs(L7), 2, max))          # the factor with the weakest top loading
cat("Facets loading at least |0.30| on the seventh factor:\n")

Facets loading at least |0.30| on the seventh factor:

print(round(sort(L7[abs(L7[, minor]) >= 0.30, minor]), 2))

Fearfulness    Prudence  Liveliness 
      -0.46       -0.32        0.32 

cat("Facets whose largest loading is on it:", sum(apply(abs(L7), 1, which.max) == minor), "\n")

Facets whose largest loading is on it: 1 

The seventh factor collects risk-taking across three domains: low Fearfulness, high Liveliness and low Prudence. Fearfulness splits almost evenly between it and Emotionality; every other facet keeps its largest loading on its own domain. It is a narrow factor rather than a new domain, so six remains the number the model predicts and the number of broad factors in the data.

Six Factors

efa6 <- fits[[3]]
L6 <- unclass(efa6$loadings)
colnames(L6) <- factor_label(L6)
L6 <- L6[, dom_abbr]
colnames(L6) <- domains
print(round(L6, 2))

                       Honesty-Humility Emotionality Extraversion Agreeableness Conscientiousness Openness
Sincerity                          0.74        -0.11         0.11         -0.02              0.14     0.02
Fairness                           0.41         0.38         0.01          0.18              0.30    -0.07
Greed Avoidance                    0.73        -0.04        -0.15          0.07             -0.12     0.04
Modesty                            0.49         0.19        -0.26          0.21             -0.05    -0.23
Fearfulness                        0.02         0.43        -0.29         -0.10              0.04    -0.29
Anxiety                            0.04         0.71        -0.21         -0.36             -0.05     0.02
Dependence                        -0.22         0.78         0.13          0.04             -0.11    -0.17
Sentimentality                     0.17         0.69         0.16          0.11              0.00     0.16
Expressiveness                     0.02         0.02         0.89         -0.22             -0.08     0.04
Social Boldness                   -0.09        -0.10         0.82         -0.03              0.07     0.16
Sociability                       -0.02         0.21         0.81          0.23             -0.01    -0.12
Liveliness                        -0.01        -0.16         0.60          0.26              0.15     0.05
Forgiveness                        0.08         0.21         0.07          0.71             -0.03     0.00
Gentleness                         0.19         0.07        -0.02          0.77             -0.07     0.06
Flexibility                        0.16        -0.10         0.14          0.69             -0.04     0.00
Patience                          -0.11        -0.18        -0.11          0.82              0.09     0.02
Organization                       0.00         0.00         0.02         -0.03              0.75    -0.19
Diligence                          0.15        -0.08         0.20          0.02              0.69     0.10
Perfectionism                     -0.18         0.14        -0.09         -0.20              0.68     0.20
Prudence                           0.08        -0.17        -0.12          0.14              0.69    -0.03
Aesthetic Appreciation             0.03         0.40         0.00          0.19              0.03     0.55
Inquisitiveness                   -0.03         0.01        -0.04          0.04              0.17     0.61
Creativity                        -0.06         0.02         0.11          0.11              0.11     0.67
Unconventionality                  0.05        -0.15         0.04         -0.11             -0.25     0.69

found6 <- colnames(L6)[apply(abs(L6), 1, which.max)]
cat(sprintf("\nFacets whose largest loading is on their own domain: %d of %d\n",
            sum(found6 == facet_domain[rownames(L6)]), nrow(L6)))

Facets whose largest loading is on their own domain: 24 of 24

plot_loadings(L6, "Six-factor EFA of the 24 facets (ML, oblimin)\nValues >= |0.30| shown")

phi6 <- efa6$Phi
dimnames(phi6) <- list(colnames(unclass(efa6$loadings)), colnames(unclass(efa6$loadings)))
lab6 <- factor_label(unclass(efa6$loadings))
dimnames(phi6) <- list(names(dom_abbr)[match(lab6, dom_abbr)], names(dom_abbr)[match(lab6, dom_abbr)])
knitr::kable(round(phi6[domains, domains], 2), caption = "Correlations between the six factors")

Correlations between the six factors

	Honesty-Humility	Emotionality	Extraversion	Agreeableness	Conscientiousness	Openness
Honesty-Humility	1.00	0.06	-0.13	0.39	0.05	-0.02
Emotionality	0.06	1.00	-0.02	-0.04	-0.11	-0.14
Extraversion	-0.13	-0.02	1.00	0.19	0.06	0.27
Agreeableness	0.39	-0.04	0.19	1.00	0.11	0.00
Conscientiousness	0.05	-0.11	0.06	0.11	1.00	0.11
Openness	-0.02	-0.14	0.27	0.00	0.11	1.00

Every facet loads on its own factor: a clean recovery of the HEXACO structure. Most factor correlations are small; the largest is between Honesty-Humility and Agreeableness (0.39), the two factors that the next section pulls apart.

Five Factors: Where Does Honesty-Humility Go?

The decisive test for HEXACO is to force a Big Five solution on the same facets.

L5 <- unclass(fits[[2]]$loadings)
colnames(L5) <- factor_label(L5)
L5 <- L5[, order(match(substr(colnames(L5), 1, 1), dom_abbr))]
print(round(L5, 2))

                           E     X A + H     C     O
Sincerity              -0.02 -0.14  0.47  0.17  0.13
Fairness                0.40 -0.08  0.45  0.32 -0.03
Greed Avoidance         0.04 -0.37  0.55 -0.07  0.13
Modesty                 0.21 -0.38  0.54 -0.02 -0.18
Fearfulness             0.44 -0.28 -0.06  0.03 -0.31
Anxiety                 0.76 -0.22 -0.27 -0.06  0.01
Dependence              0.71  0.24 -0.07 -0.13 -0.23
Sentimentality          0.70  0.16  0.26  0.01  0.15
Expressiveness          0.06  0.83 -0.16 -0.08  0.08
Social Boldness        -0.10  0.82 -0.09  0.07  0.18
Sociability             0.17  0.85  0.22 -0.02 -0.13
Liveliness             -0.19  0.62  0.23  0.15  0.06
Forgiveness             0.12  0.14  0.72 -0.02 -0.03
Gentleness              0.00  0.01  0.85 -0.04  0.05
Flexibility            -0.16  0.15  0.76 -0.02  0.00
Patience               -0.29  0.01  0.66  0.10 -0.03
Organization            0.00  0.03 -0.06  0.75 -0.20
Diligence              -0.06  0.16  0.09  0.70  0.12
Perfectionism           0.14 -0.02 -0.35  0.67  0.16
Prudence               -0.17 -0.12  0.14  0.70 -0.03
Aesthetic Appreciation  0.39  0.05  0.21  0.04  0.52
Inquisitiveness         0.01 -0.01  0.00  0.18  0.60
Creativity              0.02  0.15  0.04  0.12  0.65
Unconventionality      -0.11  0.00 -0.08 -0.24  0.71

plot_loadings(L5, "Five-factor EFA of the same 24 facets\nHonesty-Humility has no factor of its own")

With only five factors, the four Honesty-Humility facets (sincerity, fairness, greed avoidance, modesty) join the Agreeableness facets (forgiveness, gentleness, flexibility, patience) in one broad factor. That merged factor is close to Big Five Agreeableness, which in Big Five inventories includes straightforwardness and modesty. The other four factors hardly change. So the Big Five does not lose the Honesty-Humility content; it folds it into Agreeableness. HEXACO’s claim is that the two are distinct: being slow to anger and forgiving (Agreeableness) is not the same as being fair, modest and uninterested in wealth and status (Honesty-Humility). The six-factor solution above supports the claim: the two factors correlate 0.39, related but clearly distinct, and fit improves substantially when they are separated.

The 50 IPIP items in the IPIP-50 / OCEAN tutorial have no Honesty-Humility content at all, which is why its five factors are enough there.

The Hierarchy: From One Factor to Six

Goldberg’s (2006) “bass-ackwards” method shows how the factors emerge as more are extracted. Solutions with 1, 2, …, 6 factors are computed, factor scores are saved at each level, and the scores of each level are correlated with the scores of the next. Each line below links a factor to a factor one level down when they correlate at least .30; the line is thicker the stronger the correlation. Each box is named after the domains whose facets load on it at least .30 on average.

Z <- scale(facet_scores)
levels_k <- 1:6
solutions <- lapply(levels_k, function(k) {
  e    <- fa(facet_scores, nfactors = k, rotate = "oblimin", fm = "ml", scores = "tenBerge")
  flip <- sign(colSums(unclass(e$loadings)))          # orient factors so that most loadings are positive
  L    <- sweep(unclass(e$loadings), 2, flip, "*")
  list(label = factor_label(L), scores = Z %*% sweep(e$weights, 2, flip, "*"))
})

# Horizontal position: the six final factors in an order that keeps factors that split from each
# other side by side; each higher factor sits at the mean position of the final factors it
# correlates with (weighted by r squared), at least 0.9 apart from its neighbours
final_order <- c("H", "A", "E", "C", "X", "O")
final_pos <- match(solutions[[6]]$label, final_order)
spread <- function(x, gap = 0.9) {
  o <- order(x)
  for (i in seq_along(o)[-1]) x[o[i]] <- max(x[o[i]], x[o[i - 1]] + gap)
  x
}
nodes <- do.call(rbind, lapply(levels_k, function(k) {
  r2 <- cor(solutions[[k]]$scores, solutions[[6]]$scores)^2
  centre <- as.vector(r2 %*% final_pos / rowSums(r2))
  data.frame(level = k, id = seq_len(k), x = spread(centre), y = -k, label = solutions[[k]]$label)
}))

edges <- do.call(rbind, lapply(levels_k[-6], function(k) {
  r  <- cor(solutions[[k]]$scores, solutions[[k + 1]]$scores)
  ij <- which(abs(r) >= 0.30, arr.ind = TRUE)
  from <- nodes[nodes$level == k, ][ij[, 1], ]
  to   <- nodes[nodes$level == k + 1, ][ij[, 2], ]
  data.frame(x = from$x, y = from$y, xend = to$x, yend = to$y, r = r[ij],
             new_H = k == 5 & to$label == "H")
}))

ggplot() +
  geom_segment(data = edges, aes(x = x, y = y, xend = xend, yend = yend,
                                 linewidth = abs(r), colour = new_H)) +
  geom_label(data = edges, aes(x = (x + xend) / 2, y = (y + yend) / 2, label = sprintf("%.2f", r)),
             size = 2.6, label.size = 0, fill = "white") +
  geom_label(data = nodes, aes(x = x, y = y, label = label),
             size = 3.6, fontface = "bold", fill = "grey95") +
  scale_linewidth(range = c(0.4, 2.5), guide = "none") +
  scale_colour_manual(values = c(`FALSE` = "grey55", `TRUE` = "#d6604d"), guide = "none") +
  scale_y_continuous(breaks = -levels_k, labels = paste(levels_k, ifelse(levels_k == 1, "factor", "factors"))) +
  scale_x_continuous(expand = expansion(add = 0.6)) +
  theme_minimal(base_size = 10) +
  theme(axis.title = element_blank(), axis.text.x = element_blank(), panel.grid = element_blank()) +
  ggtitle("Bass-ackwards hierarchy of the IPIP-HEXACO facets",
          subtitle = "H = Honesty-Humility, E = Emotionality, X = Extraversion, A = Agreeableness, C = Conscientiousness, O = Openness\nRed: the step from five to six factors, where Honesty-Humility separates from Agreeableness")

Reading from the top: the single factor is defined mostly by Extraversion and Openness facets; two factors separate the interpersonal facets of Honesty-Humility and Agreeableness from Extraversion and Openness; Emotionality, Conscientiousness and Openness then split off one by one. Up to five factors, Honesty-Humility and Agreeableness travel together. Only at six does that factor divide, into a part that is almost the same as before (Agreeableness) and a new factor, Honesty-Humility.

Item-Level Check

The facet analyses average 10 items at a time. A six-factor analysis of all 240 items shows how many items follow their own domain individually.

efa_items <- fa(df, nfactors = 6, rotate = "oblimin", fm = "ml")
Li <- unclass(efa_items$loadings)
colnames(Li) <- sapply(seq_len(ncol(Li)), function(j) names(which.max(tapply(Li[, j], key$domain, mean))))
own <- colnames(Li)[apply(abs(Li), 1, which.max)] == key$domain
knitr::kable(data.frame(domain = domains,
                        items = as.vector(table(factor(key$domain, levels = domains))),
                        own = as.vector(tapply(own, factor(key$domain, levels = domains), sum))),
             row.names = FALSE, col.names = c("Domain", "Items", "Largest loading on own domain"))

Domain	Items	Largest loading on own domain
Honesty-Humility	40	28
Emotionality	40	31
Extraversion	40	36
Agreeableness	40	31
Conscientiousness	40	38
Openness	40	37

cat(sprintf("Total: %d of %d items\n", sum(own), length(own)))

Total: 201 of 240 items

misfit <- data.frame(item = key$item, facet = key$facet, largest = colnames(Li)[apply(abs(Li), 1, which.max)],
                     text = key$text)[!own, ]
knitr::kable(head(misfit[order(misfit$facet), ], 15), row.names = FALSE,
             col.names = c("Item", "Facet", "Largest loading on", "Wording"),
             caption = "First 15 items whose largest loading is on another domain")

First 15 items whose largest loading is on another domain

Item	Facet	Largest loading on	Wording
OAesA9	Aesthetic Appreciation	Extraversion	Do not like concerts.
OAesA10	Aesthetic Appreciation	Emotionality	Do not enjoy watching dance performances.
EDepe6	Dependence	Extraversion	Show my sadness.
EDepe9	Dependence	Extraversion	Can’t do without the company of others.
HFair4	Fairness	Emotionality	Would feel very badly for a long time if I were to steal from someone.
HFair5	Fairness	Emotionality	Try to follow the rules.
EFear5	Fearfulness	Openness	Would never go riding down a stretch of rapids in a canoe.
EFear6	Fearfulness	Openness	Like to do frightening things.
EFear7	Fearfulness	Openness	Face danger confidently.
EFear8	Fearfulness	Openness	Love dangerous situations.
EFear9	Fearfulness	Openness	Would be good at rescuing people from a burning building.
EFear10	Fearfulness	Openness	Am willing to take risks.
AFlex4	Flexibility	Emotionality	React strongly to criticism.
AFlex5	Flexibility	Emotionality	Get upset if others change the way that I have arranged things.
AFlex9	Flexibility	Honesty-Humility	Am hard to satisfy.

The misplaced items cluster in a few places, and most describe content that sits between two domains. The fearlessness items (Love dangerous situations, Am willing to take risks) load with Openness, the adventurous side of Openness, which is the risk-taking content of the seventh factor above. Some Flexibility items about being upset by criticism or change load with Emotionality, and some Dependence items about needing other people load with Extraversion. These are the items to revise if the inventory were shortened or improved.

Summary

Evidence	Result
Scoring key	All 240 items correlate positively with their facet (r = 0.19-0.85)
Reliability	Facet alpha 0.74-0.93, close to the published 0.69-0.88; domain alpha 0.88-0.95
Number of factors	6 eigenvalues above 1; BIC falls from 28293 (5 factors) to 14505 (6 factors)
Six-factor structure	24 of 24 facets load highest on their own domain
Five-factor structure	Honesty-Humility merges with Agreeableness into one broad factor
Hierarchy	Honesty-Humility is the last factor to emerge, splitting from Agreeableness
Item level	201 of 240 items load highest on their own domain

References

Ashton, M. C., & Lee, K. (2007). Empirical, theoretical, and practical advantages of the HEXACO model of personality structure. Personality and Social Psychology Review, 11(2), 150-166.

Ashton, M. C., Lee, K., & Goldberg, L. R. (2007). The IPIP-HEXACO scales: An alternative, public-domain measure of the personality constructs in the HEXACO model. Personality and Individual Differences, 42(8), 1515-1526.

Goldberg, L. R. (2006). Doing it all bass-ackwards: The development of hierarchical factor structures from the top down. Journal of Research in Personality, 40(4), 347-358.

Johnson, J. A. (2005). Ascertaining the validity of individual protocols from Web-based personality inventories. Journal of Research in Personality, 39(1), 103-129.

Lee, K., & Ashton, M. C. (2004). Psychometric properties of the HEXACO Personality Inventory. Multivariate Behavioral Research, 39(2), 329-358.

Data: Open-Source Psychometrics Project, openpsychometrics.org/_rawdata. Items and key: International Personality Item Pool, ipip.ori.org.