Examination for the Certificate of Proficiency in English (ECPE) Item Responses
items_ecpe
An object of class matrix
(inherits from array
) with 2922 rows and 28 columns.
The subjects answered the following assessment items:
item01
item02
item03
item04
item05
item06
item07
item08
item09
item11
item12
item13
item14
item15
item16
item17
item18
item19
item20
item21
item22
item23
item24
item25
item26
item27
item28
Data originated from:
Templin, J., & Bradshaw, L. (2014). Hierarchical diagnostic classification models: A family of models for estimating and testing attribute hierarchies. Psychometrika, 79(2), 317–339. doi:10.1007/s11336-013-9362-0
Templin, J., & Hoffman, L. (2013). Obtaining diagnostic classification model estimates using mplus. Educational Measurement: Issues and Practice, 32(2), 37–50. doi:10.1111/emip.12010
Data used in:
Culpepper, S. A., & Chen, Y. (2019). Development and application of an exploratory reduced reparameterized unified model. Journal of Educational and Behavioral Statistics, 44(1), 3–24. doi:10.3102/1076998618791306
Fraction Subtraction and Addition Assessment Item Responses
items_fractions
An object of class matrix
(inherits from array
) with 536 rows and 20 columns.
The subjects answered the following assessment items:
Item01
: $\frac{5}{3}-\frac{3}{4}$
Item02
: $\frac{3}{4}-\frac{3}{8}$
Item03
: $\frac{5}{6}-\frac{1}{9}$
Item04
: $3\frac{1}{2}-2\frac{3}{2}$
Item05
: $4\frac{3}{5}-3\frac{4}{10}$
Item06
: $\frac{6}{7}-\frac{4}{7}$
Item07
: $3-2\frac{1}{5}$
Item08
: $\frac{2}{3}-\frac{2}{3}$
Item09
: $3\frac{7}{8}-2$
Item10
: $4\frac{4}{12}-2\frac{7}{12}$
Item11
: $4\frac{1}{3}-2\frac{4}{3}$
Item12
: $\frac{11}{8}-\frac{1}{8}$
Item13
: $3\frac{3}{8}-2\frac{5}{6}$
Item14
: $3\frac{4}{5}-3\frac{2}{5}$
Item15
: $2-\frac{1}{3}$
Item16
: $4\frac{5}{7}-1\frac{4}{7}$
Item17
: $7\frac{3}{5}-2\frac{4}{5}$
Item18
: $4\frac{1}{10}-2\frac{8}{10}$
Item19
: $4-1\frac{4}{3}$
Item20
: $4\frac{1}{3}-1\frac{5}{3}$
Data originated from:
Tatsuoka, C. (2002). Data analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 51(3), 337–350. doi:10.1111/1467-9876.00272
Tatsuoka, K. K. (1984), Analysis of errors in fraction addition and subtraction problems (Final Report for Grant No. NIE-G-81-0002). Urbana: University of Illinois, Computer-Based Education Research Laboratory (CERL).
Data used in:
Chen, Y., Liu, Y., Culpepper, S. A., & Chen, Y. (2021). Inferring the number of attributes for the exploratory DINA model. Psychometrika, 86(1), 30–64. doi:10.1007/s11336-021-09750-9
Chen, Y., Culpepper, S. A., & Liang, F. (2020). A sparse latent class model for cognitive diagnosis. Psychometrika, 1–33. doi:10.1007/s11336-019-09693-2
Culpepper, S. A. (2019). Estimating the cognitive diagnosis $Q$
matrix
with expert knowledge: Application to the fraction-subtraction dataset.
Psychometrika, 84(2), 333–357.
doi:10.1007/s11336-018-9643-8
Culpepper, S. A., & Chen, Y. (2019). Development and application of an exploratory reduced reparameterized unified model. Journal of Educational and Behavioral Statistics, 44(1), 3–24. doi:10.3102/1076998618791306
Chen, Y., Culpepper, S. A., Chen, Y., & Douglas, J. (2018). Bayesian estimation of the dina q matrix. Psychometrika, 83(1), 89–108. doi:10.1007/s11336-017-9579-4
Experimental Matrix Reasoning Test Item Responses
items_matrix_reasoning
An object of class matrix
(inherits from array
) with 400 rows and 25 columns.
Items included:
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15
Q16
Q17
Q18
Q19
Q20
Q21
Q22
Q23
Q24
Q25
The subjects answered a set of assessment items seeking to determine their matrix reasoning abilities. Subjects that answered with a value between 0 to 7 were marked as incorrect. Subjects who answered a question with 10 selected the correct answer and, thus, were marked as correct.
From the OpenPsychometrics' code book that accompanied the data, they noted:
The possible answers were presented in two rows of four with a random order for each participant.
The collection of this data was of mediocre quality.
Data originated from:
OpenPsychometrics. (2012). Experimental matrix reasoning iq test. https://openpsychometrics.org/_rawdata/IQ1.zip
Data used in:
Chen, Y., Culpepper, S. A., & Liang, F. (2020). A sparse latent class model for cognitive diagnosis. Psychometrika, 1–33. doi:10.1007/s11336-019-09693-2
Narcissistic Personality Inventory Item Responses
items_narcissistic_personality_inventory
An object of class matrix
(inherits from array
) with 11243 rows and 40 columns.
Items with their desired option response bolded:
Q1
Option 1: I have a natural talent for influencing people
Option 2: I am not good at influencing people.
Q2
Option 1: Modesty doesn't become me
Option 2: I am essentially a modest person.
Q3
Option 1: I would do almost anything on a dare
Option 2: I tend to be a fairly cautious person.
Q4
Option 1: When people compliment me I sometimes get embarrassed
Option 2: I know that I am good because everybody keeps telling me so.
Q5
Option 1: The thought of ruling the world frightens the hell out of me
Option 2: If I ruled the world it would be a better place.
Q6
Option 1: I can usually talk my way out of anything
Option 2: I try to accept the consequences of my behavior.
Q7
Option 1: I prefer to blend in with the crowd
Option 2: I like to be the center of attention.
Q8
Option 1: I will be a success
Option 2: I am not too concerned about success.
Q9
Option 1: I am no better or worse than most people
Option 2: I think I am a special person.
Q10
Option 1: I am not sure if I would make a good leader
Option 2: I see myself as a good leader.
Q11
Option 1: I am assertive
Option 2: I wish I were more assertive.
Q12
Option 1: I like to have authority over other people
Option 2: I don't mind following orders.
Q13
Option 1: I find it easy to manipulate people
Option 2: I don't like it when I find myself manipulating people.
Q14
Option 1: I insist upon getting the respect that is due me
Option 2: I usually get the respect that I deserve.
Q15
Option 1: I don't particularly like to show off my body
Option 2: I like to show off my body.
Q16
Option 1: I can read people like a book
Option 2: People are sometimes hard to understand.
Q17
Option 1: If I feel competent I am willing to take responsibility for making decisions
Option 2: I like to take responsibility for making decisions.
Q18
Option 1: I just want to be reasonably happy
Option 2: I want to amount to something in the eyes of the world.
Q19
Option 1: My body is nothing special
Option 2: I like to look at my body.
Q20
Option 1: I try not to be a show off
Option 2: I will usually show off if I get the chance.
Q21
Option 1: I always know what I am doing
Option 2: Sometimes I am not sure of what I am doing.
Q22
Option 1: I sometimes depend on people to get things done
Option 2: I rarely depend on anyone else to get things done.
Q23
Option 1: Sometimes I tell good stories
Option 2: Everybody likes to hear my stories.
Q24
Option 1: I expect a great deal from other people
Option 2: I like to do things for other people.
Q25
Option 1: I will never be satisfied until I get all that I deserve
Option 2: I take my satisfactions as they come.
Q26
Option 1: Compliments embarrass me
Option 2: I like to be complimented.
Q27
Option 1: I have a strong will to power
Option 2: Power for its own sake doesn't interest me.
Q28
Option 1: I don't care about new fads and fashions
Option 2: I like to start new fads and fashions.
Q29
Option 1: I like to look at myself in the mirror
Option 2: I am not particularly interested in looking at myself in the mirror.
Q30
Option 1: I really like to be the center of attention
Option 2: It makes me uncomfortable to be the center of attention.
Q31
Option 1: I can live my life in any way I want to
Option 2: People can't always live their lives in terms of what they want.
Q32
Option 1: Being an authority doesn't mean that much to me
Option 2: People always seem to recognize my authority.
Q33
Option 1: I would prefer to be a leader
Option 2: It makes little difference to me whether I am a leader or not.
Q34
Option 1: I am going to be a great person
Option 2: I hope I am going to be successful.
Q35
Option 1: People sometimes believe what I tell them
Option 2: I can make anybody believe anything I want them to.
Q36
Option 1: I am a born leader
Option 2: Leadership is a quality that takes a long time to develop.
Q37
Option 1: I wish somebody would someday write my biography
Option 2: I don't like people to pry into my life for any reason.
Q38
Option 1: I get upset when people don't notice how I look when I go out in public
Option 2: I don't mind blending into the crowd when I go out in public.
Q39
Option 1: I am more capable than other people
Option 2: There is a lot that I can learn from other people.
Q40
Option 1: I am much like everybody else
Option 2: I am an extraordinary person.
We have applied list-wise deletion during pre-processing to remove any observations with missing values from the data set.
The subjects answered a set of assessment items seeking to determine the level of anxiety. Answers given in bold represent the desired response. If a subject matched this response, they were given a 1 inside of the item matrix, otherwise they received a zero.
Assessment Design:
Raskin, R., & Terry, H. (1988). A principal-components analysis of the narcissistic personality inventory and further evidence of its construct validity. Journal of Personality and Social Psychology, 54(5), 890. doi:10.1037/0022-3514.54.5.890
Data originated from:
OpenPsychometrics. 2013. Narcissistic Personality Inventory. https://openpsychometrics.org/_rawdata/NPI.zip.
Data used in:
TBA
Subset of Early Childhood Longitudinal Study, Kindergarten (ECLS-K)'s Approaches to Learning Item Responses
items_ordered_eclsk_atl
An object of class matrix
(inherits from array
) with 13354 rows and 12 columns.
Items were split between being answered by Parents and Teachers.
Parents:
P4SRS10
: Keep working at something until he/she is finished?
P4SRS13
: Show interest in a variety of things?
P4SRS15
: Concentrate on a task and ignore distractions?
P4SRS18
: Help with chores?
P4SRS22
: Eager to learn new things?
P4SRS24
: Creative in work or in play?
Teachers:
T4SRS11
: Keeps belongings organized.
T4SRS14
: Shows eagerness to learn new things.
T4SRS15
: Works independently.
T4SRS21
: Easily adapts to changes in routine.
T4SRS23
: Persists in completing tasks.
T4SRS24
: Pays attention well.
The Early Childhood Longitudinal Study, Kindergarten (ECLS-K) has been subset down both the number of observations and variables. In particular, only observations without any missing values from a set of reduced variables – given above – are included. If additional data is required, please visit the data download page found in the reference section.
Parents and teachers each answered a set of survey items involving a likert scale that ranged from "1 = never" to "4 = very often" regarding the subject. Within the teacher responses, they also had the option of marking "-7 = no opportunity to observe" option, which was treated as a missing observation. To align with C++, we perform a index shift backward of 1 and, thus, make the scale "0=never" to "3=very often".
Data originated from:
NCES. (2010). Early childhood longitudinal study, kindergarten class of 1998-99 (ecls-k) kindergarten through fifth grade approaches to learning and self-description questionnaire (sdq) items and public-use data files. https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2010070
Data used in:
Culpepper, S. (2019). An exploratory diagnostic model for ordinal responses with binary attributes: Identifiability and estimation. Psychometrika, 84(4), 921–940. doi:10.1007/s11336-019-09683-4
Elementary Probability Theory Assessment Item Responses
items_probability_part_one
An object of class matrix
(inherits from array
) with 504 rows and 12 columns.
Questions wording and answers are from the pks
package documentation.
Items with their desired responses bolded:
p101
: A box contains 30 marbles in the following colors:
8 red, 10 black, 12 yellow. What is the probability that a randomly
drawn marble is yellow? (0.40)
p102
: A bag contains 5-cent, 10-cent, and 20-cent coins.
The probability of drawing a 5-cent coin is 0.35, that of drawing a
10-cent coin is 0.25, and that of drawing a 20-cent coin is 0.40. What
is the probability that the coin randomly drawn is not a 5-cent
coin? (0.65)
p103
: A bag contains 5-cent, 10-cent, and 20-cent coins.
The probability of drawing a 5-cent coin is 0.20, that of drawing a
10-cent coin is 0.45, and that of drawing a 20-cent coin is 0.35. What
is the probability that the coin randomly drawn is a 5-cent coin or
a 20-cent coin? (0.55)
p104
: In a school, 40\
the pupils are right-handed. Suppose that gender and handedness are
independent. What is the probability of randomly selecting a
right-handed boy? (0.32)
p105
: Given a standard deck containing 32 different cards,
what is the probability of not drawing a heart? (0.75)
p106
: A box contains 20 marbles in the following colors:
4 white, 14 green, 2 red. What is the probability that a randomly
drawn marble is not white? (0.80)
p107
: A box contains 10 marbles in the following colors:
2 yellow, 5 blue, 3 red. What is the probability that a randomly
drawn marble is yellow or blue? (0.70)
p108
: What is the probability of obtaining an even number
by throwing a dice? (0.50)
p109
: Given a standard deck containing 32 different cards,
what is the probability of drawing a 4 in a black suit?
(Responses that round to 0.06 were considered correct.)
p110
: A box contains marbles that are red or yellow, small
or large. The probability of drawing a red marble is 0.70 (lab: 0.30),
the probability of drawing a small marble is 0.40. Suppose that the
color of the marbles is independent of their size. What is the
probability of randomly drawing a small marble that is not red? (0.12, lab: 0.28)
p111
: In a garage there are 50 cars. 20 are black and 10 are
diesel powered. Suppose that the color of the cars is independent of
the kind of fuel. What is the probability that a randomly selected car
is not black and it is diesel powered? (0.12)
p112
: A box contains 20 marbles. 10 marbles are red, 6 are
yellow and 4 are black. 12 marbles are small and 8 are large. Suppose
that the color of the marbles is independent of their size. What is the
probability of randomly drawing a small marble that is yellow or
red? (0.48)
Data originated from:
Heller, J., & Wickelmaier, F. (2013). Minimum discrepancy estimation in probabilistic knowledge structures. Electronic Notes in Discrete Mathematics, 42, 49–56. doi:10.1016/j.endm.2013.05.145
Data used in:
Chen, Yinghan, Liu, Y., Culpepper, S. A., & Chen, Y. (2021). Inferring the number of attributes for the exploratory DINA model. Psychometrika, 86(1), 30–64. doi:10.1007/s11336-021-09750-9
Revised PSVT:R Item Responses
items_revised_psvtr
An object of class matrix
(inherits from array
) with 516 rows and 30 columns.
Data set contains the subject's responses to Revised PSVT:R items. Correct answers are denoted by 1 and incorrect answers are denoted by 0.
Item01
: Subject's Response to Item 1.
Item02
: Subject's Response to Item 2.
Item03
: Subject's Response to Item 3.
Item04
: Subject's Response to Item 4.
Item05
: Subject's Response to Item 5.
Item06
: Subject's Response to Item 6.
Item07
: Subject's Response to Item 7.
Item08
: Subject's Response to Item 8.
Item09
: Subject's Response to Item 9.
Item10
: Subject's Response to Item 10.
Item11
: Subject's Response to Item 11.
Item12
: Subject's Response to Item 12.
Item13
: Subject's Response to Item 13.
Item14
: Subject's Response to Item 14.
Item15
: Subject's Response to Item 15.
Item16
: Subject's Response to Item 16.
Item17
: Subject's Response to Item 17.
Item18
: Subject's Response to Item 18.
Item19
: Subject's Response to Item 19.
Item20
: Subject's Response to Item 20.
Item21
: Subject's Response to Item 21.
Item22
: Subject's Response to Item 22.
Item23
: Subject's Response to Item 23.
Item24
: Subject's Response to Item 24.
Item25
: Subject's Response to Item 25.
Item26
: Subject's Response to Item 26.
Item27
: Subject's Response to Item 27.
Item28
: Subject's Response to Item 28.
Item29
: Subject's Response to Item 29.
Item30
: Subject's Response to Item 30.
Assessment Design:
Yoon, S. Y. (2011). Psychometric properties of the revised purdue spatial visualization tests: Visualization of rotations (the revised psvt: R). Purdue University.
Data originated from:
Culpepper, S. A., & Balamuta, J. J. (2017). A Hierarchical Model for Accuracy and Choice on Standardized Tests. Psychometrika, 82(3), 820–845. doi:10.1007/s11336-015-9484-7
Data used in:
Culpepper, S. A. (2015). Bayesian estimation of the dina model with gibbs sampling. Journal of Educational and Behavioral Statistics, 40(5), 454–476. doi:10.3102/1076998615595403
Culpepper, S. A., & Balamuta, J. J. (2017). A Hierarchical Model for Accuracy and Choice on Standardized Tests. Psychometrika, 82(3), 820–845. doi:10.1007/s11336-015-9484-7
Last Series of the Standard Progressive Matrices (SPM-LS) Item Responses
items_spm_ls
An object of class matrix
(inherits from array
) with 499 rows and 12 columns.
Items with the correct answer response based off of Table 9 of the Robitzsch (2020) pre-print paper.
SPM1: 7
SPM2: 6
SPM3: 8
SPM4: 2
SPM5: 1
SPM6: 5
SPM7: 1
SPM8: 6
SPM9: 3
SPM10: 2
SPM11: 4
SPM12: 5
The subjects answered a set of assessment items seeking to determine the level of matrix reasoning. Answers given in bold represent the desired response. If a subject matched this response, they were given a 1 inside of the item matrix, otherwise they received a zero.
Assessment Design:
Raven, J. C. (1941). Standardization of progressive matrices, 1938. British Journal of Medical Psychology, 19(1), 137–150. doi:10.1111/j.2044-8341.1941.tb00316.x
Data originated from:
Myszkowski, N., & Storme, M. (2018). A snapshot of g? Binary and polytomous item-response theory investigations of the last series of the standard progressive matrices (spm-ls). Intelligence, 68, 109–116. doi:10.1016/j.intell.2018.03.010
Robitzsch, A. (2020). Regularized latent class analysis for polytomous item responses: An application to spm-ls data. Preprint. doi:10.20944/preprints202007.0269.v1
Data used in:
TBA
Taylor Manifest Anxiety Scale Item Responses
items_taylor_manifest_anxiety_scale
An object of class matrix
(inherits from array
) with 4468 rows and 50 columns.
Questions alongside of their correct answer is based off of Table 1 of the Taylor (1953) paper.
Items with their desired response bolded:
Q1
: I do not tire quickly. (False)
Q2
: I am troubled by attacks of nausea. (True)
Q3
: I believe I am no more nervous than most others. (False)
Q4
: I have very few headaches. (False)
Q5
: I work under a great deal of tension. (True)
Q6
: I cannot keep my mind on one thing. (True)
Q7
: I worry over money and business. (True)
Q8
: I frequently notice my hand shakes when I try to do something. (True)
Q9
: I blush no more often than others. (False)
Q10
: I have diarrhea once a month or more. (True)
Q11
: I worry quite a bit over possible misfortunes. (True)
Q12
: I practically never blush. (False)
Q13
: I am often afraid that I am going to blush. (True)
Q14
: I have nightmares every few nights. (True)
Q15
: My hands and feet are usually warm. (False)
Q16
: I sweat very easily even on cool days. (True)
Q17
: Sometimes when embarrassed, I break out in a sweat. (True)
Q18
: I hardly ever notice my heart pounding and I am seldom short of breath. (False)
Q19
: I feel hungry almost all the time. (True)
Q20
: I am very seldom troubled by constipation. (False)
Q21
: I have a great deal of stomach trouble. (True)
Q22
: I have had periods in which I lost sleep over worry. (True)
Q23
: My sleep is fitful and disturbed. (True)
Q24
: I dream frequently about things that are best kept to myself. (True)
Q25
: I am easily embarrassed. (True)
Q26
: I am more sensitive than most other people. (True)
Q27
: I frequently find myself worrying about something. (True)
Q28
: I wish I could be as happy as others seem to be. (True)
Q29
: I am usually calm and not easily upset. (False)
Q30
: I cry easily. (True)
Q31
: I feel anxiety about something or someone almost all the time. (True)
Q32
: I am happy most of the time. (False)
Q33
: It makes me nervous to have to wait. (True)
Q34
: I have periods of such great restlessness that I cannot sit long I a chair. (True)
Q35
: Sometimes I become so excited that I find it hard to get to sleep. (True)
Q36
: I have sometimes felt that difficulties were piling up so high that I could not overcome them. (True)
Q37
: I must admit that I have at times been worried beyond reason over something that really did not matter. (True)
Q38
: I have very few fears compared to my friends. (False)
Q39
: I have been afraid of things or people that I know could not hurt me. (True)
Q40
: I certainly feel useless at times. (True)
Q41
: I find it hard to keep my mind on a task or job. (True)
Q42
: I am usually self-conscious. (True)
Q43
: I am inclined to take things hard. (True)
Q44
: I am a high-strung person. (True)
Q45
: Life is a trial for me much of the time. (True)
Q46
: At times I think I am no good at all. (True)
Q47
: I am certainly lacking in self-confidence. (True)
Q48
: I sometimes feel that I am about to go to pieces. (True)
Q49
: I shrink from facing crisis of difficulty. (True)
Q50
: I am entirely self-confident. (False)
We have applied list-wise deletion during pre-processing to remove any observations with missing values from the data set.
The subjects answered a set of assessment items seeking to determine the level of anxiety. Answers given in bold represent the desired response. If a subject matched this response, they were given a 1 inside of the item matrix, otherwise they received a zero.
Assessment Design:
Taylor, J. A. (1953). A personality scale of manifest anxiety. The Journal of Abnormal and Social Psychology, 48(2), 285–290. doi:10.1037/h0056264.
Data originated from:
OpenPsychometrics. 2012. Taylor Manifest Anxiety Scale. https://openpsychometrics.org/_rawdata/TMA.zip.
Data used in:
TBA
Examination for the Certificate of Proficiency in English (ECPE) Expert-Derived Q matrix
qmatrix_ecpe
An object of class q_matrix
(inherits from matrix
) with 28 rows and 3 columns.
Each entry in the matrix is either 1
, if the item uses the skill, or 0
, if
the item does not use the skill. The skills identified by this matrix
are:
skill1
: Morphosyntactic rules
skill2
: Cohesive rules
skill3
: Lexical rules
The subjects answered the following assessment items:
item01
item02
item03
item04
item05
item06
item07
item08
item09
item11
item12
item13
item14
item15
item16
item17
item18
item19
item20
item21
item22
item23
item24
item25
item26
item27
item28
Data originated from:
Templin, J., & Bradshaw, L. (2014). Hierarchical diagnostic classification models: A family of models for estimating and testing attribute hierarchies. Psychometrika, 79(2), 317–339. doi:10.1007/s11336-013-9362-0
Templin, J., & Hoffman, L. (2013). Obtaining diagnostic classification model estimates using mplus. Educational Measurement: Issues and Practice, 32(2), 37–50. doi:10.1111/emip.12010
Data used in:
Culpepper, S. A., & Chen, Y. (2019). Development and application of an exploratory reduced reparameterized unified model. Journal of Educational and Behavioral Statistics, 44(1), 3–24. doi:10.3102/1076998618791306
Fraction Subtraction and Addition Assessment Expert-Derived Q Matrix
qmatrix_fractions
An object of class matrix
(inherits from array
) with 20 rows and 8 columns.
Each entry in the matrix is either 1
, if the Item uses the Trait, or 0
, if
the Item does not use the Trait. The traits identified by this matrix
are:
Trait1
: Convert a whole number to a fraction,
Trait2
: Separate a whole number from fraction,
Trait3
: Simplify before subtraction,
Trait4
: Find a common denominator,
Trait5
: Borrow from the whole number part,
Trait6
: Column borrow to subtract the second numerator from the first,
Trait7
: Subtract numerators,
Trait8
: Reduce answers to simplest form.
The subjects answered the following assessment items:
Item01
: $\frac{5}{3}-\frac{3}{4}$
Item02
: $\frac{3}{4}-\frac{3}{8}$
Item03
: $\frac{5}{6}-\frac{1}{9}$
Item04
: $3\frac{1}{2}-2\frac{3}{2}$
Item05
: $4\frac{3}{5}-3\frac{4}{10}$
Item06
: $\frac{6}{7}-\frac{4}{7}$
Item07
: $3-2\frac{1}{5}$
Item08
: $\frac{2}{3}-\frac{2}{3}$
Item09
: $3\frac{7}{8}-2$
Item10
: $4\frac{4}{12}-2\frac{7}{12}$
Item11
: $4\frac{1}{3}-2\frac{4}{3}$
Item12
: $\frac{11}{8}-\frac{1}{8}$
Item13
: $3\frac{3}{8}-2\frac{5}{6}$
Item14
: $3\frac{4}{5}-3\frac{2}{5}$
Item15
: $2-\frac{1}{3}$
Item16
: $4\frac{5}{7}-1\frac{4}{7}$
Item17
: $7\frac{3}{5}-2\frac{4}{5}$
Item18
: $4\frac{1}{10}-2\frac{8}{10}$
Item19
: $4-1\frac{4}{3}$
Item20
: $4\frac{1}{3}-1\frac{5}{3}$
Data originated from:
Tatsuoka, C. (2002). Data analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 51(3), 337–350. doi:10.1111/1467-9876.00272
Tatsuoka, K. K. (1984), Analysis of errors in fraction addition and subtraction problems (Final Report for Grant No. NIE-G-81-0002). Urbana: University of Illinois, Computer-Based Education Research Laboratory (CERL).
Data used in:
Chen, Y., Liu, Y., Culpepper, S. A., & Chen, Y. (2021). Inferring the number of attributes for the exploratory DINA model. Psychometrika, 86(1), 30–64. doi:10.1007/s11336-021-09750-9
Chen, Y., Culpepper, S. A., & Liang, F. (2020). A sparse latent class model for cognitive diagnosis. Psychometrika, 1–33. doi:10.1007/s11336-019-09693-2
Culpepper, S. A. (2019). Estimating the cognitive diagnosis $Q$
matrix
with expert knowledge: Application to the fraction-subtraction dataset.
Psychometrika, 84(2), 333–357.
doi:10.1007/s11336-018-9643-8
Culpepper, S. A., & Chen, Y. (2019). Development and application of an exploratory reduced reparameterized unified model. Journal of Educational and Behavioral Statistics, 44(1), 3–24. doi:10.3102/1076998618791306
Chen, Y., Culpepper, S. A., Chen, Y., & Douglas, J. (2018). Bayesian estimation of the dina q matrix. Psychometrika, 83(1), 89–108. doi:10.1007/s11336-017-9579-4
Pre-generated identified Q matrices used in simulation studies to verify recovery.
A matrix
with varying numbers of traits (K
) and items (J
).
Specifically:
qmatrix_oracle_k2_j12
: 12 items and 2 traits.
qmatrix_oracle_k3_j20
: 20 items and 3 traits.
qmatrix_oracle_k4_j20
: 20 items and 4 traits.
qmatrix_oracle_k5_j30
: 30 items and 5 traits.
Each entry in the matrix is either 1
, if the item uses the skill, or 0
, if
the item does not use the skill.
Elementary Probability Theory Assessment Expert-Derived Q Matrix
qmatrix_probability_part_one
An object of class matrix
(inherits from array
) with 12 rows and 4 columns.
Each entry in the matrix is either 1
, if the item uses the trait, or 0
, if
the item does not use the trait. The traits identified by this matrix
are:
cp
: the probability of the complement of an event
id
: two independent events
pb
: probability of an event
un
: union of two disjoint events
For a detailed overview of items, please see items_probability_part_one
.
Note, the expert supplied Q-matrix is not strictly identified. Though, the expert matrix is generically identified.
Data originated from:
Heller, J., & Wickelmaier, F. (2013). Minimum discrepancy estimation in probabilistic knowledge structures. Electronic Notes in Discrete Mathematics, 42, 49–56. doi:10.1016/j.endm.2013.05.145
Data used in:
Chen, Yinghan, Liu, Y., Culpepper, S. A., & Chen, Y. (2021). Inferring the number of attributes for the exploratory DINA model. Psychometrika, 86(1), 30–64. doi:10.1007/s11336-021-09750-9
Pre-generated strategy matrices used in simulation studies to verify recovery.
An array
with varying numbers of items (J
), traits (K
), and strategies (S
).
Specifically:
strategy_oracle_k3_j20_s2
: 20 items, 3 traits, and 2 strategies.
strategy_oracle_k3_j30_s2
: 30 items, 3 traits, and 2 strategies.
strategy_oracle_k3_j40_s2
: 40 items, 3 traits, and 2 strategies.
strategy_oracle_k3_j50_s2
: 50 items, 3 traits, and 2 strategies.
strategy_oracle_k4_j20_s2
: 20 items, 4 traits, and 2 strategies.
strategy_oracle_k4_j30_s2
: 30 items, 4 traits, and 2 strategies.
strategy_oracle_k4_j40_s2
: 40 items, 4 traits, and 2 strategies.
strategy_oracle_k4_j50_s2
: 50 items, 4 traits, and 2 strategies.
Each entry in a strategy is denoted by either 1
, if the item uses the skill
under strategy s
, or 0
, if the item does not use the skill under strategy
s
.
Note: Each matrix in the strategy was generated independently under the criterion for a strictly identifiable Q matrix.