Trends in international mathematics and science study (TIMSS) assessment for grade 4 mathematics (2007)
Source:R/timss07.R
timss07.RdThis is data from the United States sample of the 2007 TIMSS assessment for grade 4 mathematics. This data contains responses to 25 items from 698 respondents and has been used previously by Lee et al. (2011) and Park et al. (2014, 2018) to estimate diagnostic classification models. The data set was uploaded to the Item Response Warehouse (Domingue et al., 2025) and is reformatted here.
Format
timss07_data is a tibble containing TIMSS
response data with 698 rows and 26 variables.
id: Respondent identifier.M031085-M041258B: Dichotomous item responses to the 25 TIMSS items.
timss07_skill_qmatrix is a tibble that
identifies which skills are measured by each TIMSS 2007 item. The
timss07_skill_qmatrix is made up of 25 rows and 16 variables.
item: Item identifier, corresponds to item response columns intimss07_data.Attribute columns: 15 columns, one for each attribute. Attributes are named as
{domain}_{topic}_{skill}. For examplen_wn_representis the skill "Representing, comparing, and ordering whole numbers as well as demonstrating knowledge of place value," which falls under the "Whole Numbers" topic (wn) and "Number" domain (n). See Details for a complete list of skills. Each column is a dichotomous indicator for whether or not the skill is measured by each item. A value of1indicates the skill is measured by the item and a value of0indicates the skill is not measured by the item.
timss07_topic_qmatrix is a tibble that
identifies which topics are measured by each TIMSS 2007 item. This form of
the Q-matrix was used by Park et al. (2014, 2018), who combined the "Number
Sentences with Whole Numbers" and "Patterns and Relationships" topics in the
"Number" domain into a single attributes (n_nspr), as well as the "Reading
and Interpreting" and "Organizing and Representing" topics in the "Data &
Display" domain (dd_rior).
Thus, timss07_topic_qmatrix is made up of 25 rows and 8 variables.
item: Item identifier, corresponds to item response columns intimss07_data.Attribute columns: 7 columns, one for each attribute. Attributes are named as
{domain}_{topic}. For examplegm_lmis the topic "Location and Movement," which falls under the "Geometric Shapes & Measurement" (gm) domain. Each column is a dichotomous indicator for whether or not the topic is measured by each item. A value of1indicates the topic is measured by the item and a value of0indicates the topic is not measured by the item. See Details for complete list of topics.
timss07_domain_qmatrix is a tibble that
identifies which domains are measured by each TIMSS 2007 item.
The timss07_domain_qmatrix is made up of 25 rows and 3 variables.
item: Item identifier, corresponds to item response columns intimss07_data.Attribute columns: 3 columns, one for each attribute. Attributes are named as
{domain}. For exampleddis the domain "Data & Display." Each column is a dichotomous indicator for whether or not the domain is measured by each item. A value of1indicates the domain is measured by the item and a value of0indicates the domain is not measured by the item. See Details for a complete list of domains.
Details
The skills for the 2007 TIMSS are organized into domains and topics.
Attribute names in Q-matrices are named by combining the hierarchical
elements. For example, timss07_skill_qmatrix attributes names are
{domain}_{topic}_{skill}, whereas attributes in timss07_topic_qmatrix are
named {domain}_{topic}.
| Domain | Topic | Skill |
Number (n) | Whole Numbers (wn) | Representing, comparing, and ordering whole numbers as well as
demonstrating knowledge of place value (represent) |
Number (n) | Whole Numbers (wn) | Recognize multiples, computing with whole numbers using the four
operations, and estimating computations (compute) |
Number (n) | Whole Numbers (wn) | Solve problems, including those set in real life contexts (solve) |
Number (n) | Whole Numbers (wn) | Solve problems involving proportions (proportions) |
Number (n) | Fractions and Decimals (fd) | Recognize, represent, and understand fractions and decimals as parts of a
whole and their equivalents (parts) |
Number (n) | Fractions and Decimals (fd) | Solve problems involving simple fractions and decimals including their
addition and subtraction (solve) |
Number (n) | Number Sentences with Whole Numbers (ns) | Find the missing number or operation and model simple situations involving
unknowns in number sentence or expressions (model) |
Number (n) | Patterns and Relationships (pr) | Describe relationships in patterns and their extensions; generate pairs of
whole numbers by a given rule and identify a rule for every relationship
given pairs of whole numbers (describe) |
Geometric Shapes & Measurement (gm) | Lines and Angles (la) | Measure, estimate, and understand properties of lines and angles and be
able to draw them (properties) |
Geometric Shapes & Measurement (gm) | Two- and Three-dimensional Shapes (tt) | Classify, compare, and recognize geometric figures and shapes and their
relationships and elementary properties (figures) |
Geometric Shapes & Measurement (gm) | Two- and Three-dimensional Shapes (tt) | Calculate and estimate perimeters, area, and volume (calculate) |
Geometric Shapes & Measurement (gm) | Location and Movement (lm) | Locate points in an informal coordinate to recognize and draw figures and
their movement (locate) |
Data & Display (dd) | Reading and Interpreting (ri) | Read data from tables, pictographs, bar graphs, and pie charts (read) |
Data & Display (dd) | Reading and Interpreting (ri) | Comparing and understanding how to use information from data
(information) |
Data & Display (dd) | Organizing and Representing (or) | Understanding different representations and organizing data using tables,
pictographs, and bar graphs (data) |
For more details, see Table 2 of Lee et al. (2011).
References
Domingue, B., Braginsky, M., Caffrey-Maffei, L., Gilbert, J. B., Kanopka, K., Kapoor, R., Lee, H., Liu, Y., Nadela, S., Pan, G., Zhang, L., Zhang, S., & Frank, M. C. (2025). An introduction to the Item Response Warehouse (IRW): A resource for enhancing data usage in psychometrics. Behavior Research Methods, 57, Article 276. doi:10.3758/s13428-025-02796-y
Lee, Y.-S., Park, Y. S., & Taylan, D. (2011). A cognitive diagnostic modeling of attribute mastery in Massachusetts, Minnesota, and the U.S. national sample using the TIMSS 2007. International Journal of Testing, 11(2), 144-177. doi:10.1080/15305058.2010.534571
Park, Y. S., & Lee, Y.-S. (2014). An extension of the DINA model using covariates: Examining factors affecting response probability and latent classification. Applied Psychological Measurement, 38(5), 376-390. doi:10.1177/0146621614523830
Park, Y. S., Xing, K., & Lee, Y.-S. (2018). Explanatory cognitive diagnostic models: Incorporating latent and observed predictors. Applied Psychological Measurement, 42(5), 376-392. doi:10.1177/0146621617738012