HED conditions and design matrices

This tutorial discusses how information from neuroimaging experiments should be stored and annotated so that the underlying experimental design and experimental conditions for a dataset can be automatically extracted, summarized, and used in analysis. The mechanisms for doing this use HED (Hierarchical Event Descriptors) in conjunction with a BIDS (Brain Imaging Data Structure) representation of the dataset.

The tutorial assumes that you have a basic understanding of HED and how HED annotations are used in BIDS. Please review Annotating a BIDS dataset, the BIDS annotation quickstart, and the HED annotation quickstart tutorials as needed.

The Neuorimaging experimental design section at the end of this tutorial provides a basic introduction to the ideas of factor vectors and experimental design if you are unfamiliar with these topics.

This tutorial introduces tools and strategies for encoding information about the experimental design as part of a dataset metadata without excessive effort on the part of the researcher. The discussion mainly focuses on categorical variables.

HED annotations for conditions

As mentioned above, HED (Hierarchical Event Descriptors) provide several mechanisms for easily annotating the experimental conditions represented by a BIDS dataset so that the information can be automatically extracted, summarized, and used by tools.

HED has three ways of annotating experimental conditions: condition variables without definitions, condition variables with definitions but no levels, and condition variables with levels. All three mechanisms use the Condition-variable tag as part of the annotation. The three mechanisms can be used in any combination to document the experimental design for a dataset.

Direct condition variables

The simplest way to encode experimental conditions is to use named Condition-variable tags for each condition value. The following is a sample excerpt from a simplified event file for an experiment to distinguish brain responses for houses and faces.

Example 1. Excerpt from a sample event file from a simplified house-face experiment.

onset

duration

event_type

stim_file

2.010

0.1

show_house

ranch1.png

3.210

0.1

show_house

colonial68.png

4.630

0.1

show_face

female43.png

6.012

0.1

show_house

castle2.png

7.440

0.1

show_face

male81.png

As explained in BIDS annotation quickstart, the most commonly used strategy for annotating events in a BIDS dataset is to create a single JSON file located in the dataset root containing the annotations for the columns. The following shows a minimal example:

Example 2: Minimal JSON sidecar with HED annotations for Example 1.

{
   "event_type": {
      "HED": {
         "show_house": "Sensory-presentation, Visual-presentation, Experimental-stimulus, (Image, Building/House), Condition-variable/House-cond",
         "show_face": "Sensory-presentation, Visual-presentation, Experimental-stimulus, (Image, Face), Condition-variable/Face-cond"
      }
   },
   "stim_file": {
      "HED": "(Image, Pathname/#)"
   }
}

Each row in an events.tsv file represents a time marker in the corresponding data recording. At analysis time, HED tools look up each events.tsv column value in the JSON file and concatenate the corresponding HED annotation into a single string representing the annotation for that row. Annotations without #’s are used directly, while annotations with # have the corresponding column values substituted when the annotation is assembled.

Example 3 shows the Hed annotation for the first row in the events.tsv file of Example 1.

Example 3: HED annotation for first event in Example 1 using JSON sidecar of Example 2.

Sensory-presentation, Visual-presentation, Experimental-stimulus,
(Image, Building/House), Condition-variable/House-cond,
(Image, Pathname/ranch1.png)”

Notice that Building/House is a partial path rather than a single tag. This is because House is currently not part of the base HED vocabulary. However, users are allowed to extend tags at most nodes in the HED schema, but they must use a path that includes a least one ancestor in the HED schema.

HED tools have the capability of automatically detecting Condition-variable tags in annotated HED datasets to create factor vectors and summaries automatically. Example 4 shows the event file after HED tools have appended one-hot factor vectors for the two condition variables Condition-variable/House-cond and Condition-variable/Face-cond. The 1’s and 0’s house_cond and face-cond columns indicate presence or absence of the corresponding condition variables.

Example 4. Event file from Example 2 after one-hot factor vector extraction.

onset

duration

event_type

stim_file

house-cond

face-cond

2.010

0.1

show_house

ranch1.png

1

0

3.210

0.1

show_house

colonial68.png

1

0

4.630

0.1

show_face

female43.png

0

1

6.012

0.1

show_house

castle2.png

1

0

7.440

0.1

show_face

male81.png

0

1

Example 5 shows a JSON summary that HED tools can extract from a single events file once a dataset has been annotated using HED. This very simple example only had two condition variables and only used direct references to these condition variables. Dataset-wide summaries can also be extracted.

Example 5: The HED tools summary of condition variables for Example 4.

{
   "house-cond": {
      "name": "house-cond",
      "variable_type": "condition-variable",
      "levels": 0,
      "direct_references": 3,
      "total_events": 5,
      "number_type_events": 3,
      "number_multiple_events": 0,
      "multiple_event_maximum": 1,
      "level_counts": {}
   },
   "face-cond": {
      "name": "face-cond",
      "variable_type": "condition-variable",
      "levels": 0,
      "direct_references": 2,
      "total_events": 5,
      "number_type_events": 2,
      "number_multiple_events": 0,
      "multiple_event_maximum": 1,
      "level_counts": {}
   }
}

The summary shows that of the total of 5 events in the file: 3 events were under the house condition and 2 events were under the face condition. There were no events in multiple categories of the same condition variables (which would not be possible since these condition variables were referenced directly rather than using assigned levels). All names are translated to lower case as HED is case-insensitive with respect to analysis, and the summary and factorization tools convert to lower case before processing.

These HED summaries can be created for other tags besides Condition-variable, hence the variable_type is given in the summary of Example 5. Other commonly created summaries are for Task and Control-variable.

In this example, the two conditions: house-cond and face-cond are treated is though they are unrelated. These direct condition variables are very easy to annotate— just make up a name and stick the tags anywhere you want to create factor variables or summaries. However, a more common situation is for a condition variable to have multiple levels, which direct use condition variables does not support.

Another disadvantage of direct condition variables is that there is no information about what the conditions represent beyond the arbitrarily chosen condition names.

A third disadvantage is that direct condition variables can not be used to anchor events with temporal extent.

The next section introduces defined condition variables, which address both of these disadvantages.

Defined condition variables

Example 6: A revised JSON sidecar using defined conditions for Example 1.

{
   "event_type": {
      "HED": {
         "show_house": "Sensory-presentation, Visual-presentation, Experimental-stimulus, (Image, Building/House), Def/House-cond",
         "show_face": "Sensory-presentation, Visual-presentation, Experimental-stimulus, (Image, Face), Def/Face-cond"
      }
   },
   "stim_file": {
      "HED": "(Image, Pathname/#)"
   },
   "my_definitions": {
      "HED": {
          "house_cond_def": "(Definition/House-cond, (Condition-variable/Presentation-type, (Image, Building/House)))",
          "face_cond_def": "(Definition/Face-cond, (Condition-variable/Presentation-type, (Image, Face)))"
}

Example 6 defines a condition variable called Presentation-type with two levels: House-cond and Face-cond. The definitions of House-cond and Face-cond both include the same Presentation-type Condition-variable so tools recognize these as levels of the same variable and automatically extract the 2-factor experimental design.

Notice that the (Image, Building/House) tags are included both in the definition of the House-cond level of the Presentation-type condition variable and in the tags for the event_type column value show_house. Similarly, the (Image, Face) tags appear in both the definition of the Face-cond level of the Presentation-type condition variable and in the tags for the event_type column value show_face. We have included these tags in both places because generally the condition variable definitions are removed prior to searching for HED tags. The tags in the definitions define the meaning of the conditions.

Example 7: The summary extracted when the JSON sidecar of Example 6 is used.

{
   "presentation-type": {
      "name": "presentation-type",
      "variable_type": "condition-variable",
      "levels": 2,
      "direct_references": 0,
      "total_events": 5,
      "number_type_events": 5,
      "number_multiple_events": 0,
      "multiple_event_maximum": 1,
      "level_counts": {
         "house-cond": 3,
         "face-cond": 2
      }
  }
}

Column vs row conditions

In this section, we look at a more complicated example based on the Wakeman-Henson face-processing dataset. This dataset, which is available on OpenNeuro under accession number ds003654, was used in as a case study on HED annotation described in the Capturing the nature of events paper. The experiment is based on a 3 x 3 x 2 experimental design: face type x repetition status x key choice.

The experimental stimulus in each trial was the visual presentation of one of 3 possible types of images: a well-known face, an unfamiliar face, and a scrambled face image. The type of face was randomized across trials.

The repetition status condition variable also had one of three possible values and indicated whether the stimulus image had not been seen before (first show), was just seen in the previous trial (immediate repeat), or had been last seen several trials ago (delayed repeat). The repetition status was randomized across trials.

The final condition variable in the experimental design was the key assignment. In the right symmetry condition, participants pressed the right mouse button to indicate that the presented face had above average symmetry, while in the left symmetry condition, participants pressed the left mouse button to indicate that the presented face had above average symmetry. The key assignment was held constant for each recording, but the key choice was counter-balanced across participants.

Example 8 shows an excerpt from the event file of sub-002 run-1. (You may find it useful to look at the full event file sub-002_task-FacePerception_run-1_events.tsv and the dataset’s JSON sidecar with full HED annotations: task-facePerception_events.json

Example 8: An excerpt from the Wakeman-Henson face-processing dataset.

onset

duration

event_type

face_type

rep_status

trial

rep_lag

value

stim_file

0.004

n/a

setup_right_sym

n/a

n/a

n/a

n/a

3

n/a

24.2098

n/a

show_face_initial

unfamiliar_face

first_show

1

n/a

13

u032.bmp

25.0353

n/a

show_circle

n/a

n/a

1

n/a

0

circle.bmp

25.158

n/a

left_press

n/a

n/a

1

n/a

256

n/a

26.7353

n/a

show_cross

n/a

n/a

2

n/a

1

cross.bmp

27.2498

n/a

show_face

unfamiliar_face

immediate_repeat

2

1

14

u032.bmp

27.8971

n/a

left_press

n/a

n/a

2

n/a

256

n/a

28.0998

n/a

show_circle

n/a

n/a

2

n/a

0

circle.bmp

29.7998

n/a

show_cross

n/a

n/a

3

n/a

1

cross.bmp

30.3571

n/a

show_face

unfamiliar_face

first_show

3

n/a

13

u088.bmp

Example 8 illustrates two different ways of using defined conditions for encoding: inserting an event with temporal extent or using column encoding.

The key assignment condition is marked by inserting an event with event_type equal to setup_right_sym at the beginning of the file. As we shall see below, this event is annotated with having temporal extent, as defined by HED Onset and Offset tags, so the condition is in effect until the event’s extent ends.

In the column strategy, an event file column represents the condition variable, and the values in that column represent the levels. With this encoding, the condition variable is only applicable at a particular level when that level name appears in the column. An n/a value in that column indicates the condition does not apply to that event.

Example 9 shows the portion of the task-facePerception_events.json that encodes information about the setup_right_sym event found as the first event in the event file excerpt of Example 8. This excerpt only contains the relevent definition and the relevant annotation.

Example 9: Excerpt of the JSON sidecar relevant to the setup_right_sym event.

{
   "event_type": {
      "HED": {
         "setup_right_sym": "Experiment-structure, (Def/Right-sym-cond, Onset), (Def/Initialize-recording, Onset)"
      }
   },
   "hed_def_conds": {
      "HED": {
        "right_sym_cond_def": "(Definition/Right-sym-cond, (Condition-variable/Key-assignment, ((Index-finger, (Right-side-of, Experiment-participant)), (Behavioral-evidence, Symmetrical)), ((Index-finger, (Left-side-of, Experiment-participant)), (Behavioral-evidence, Asymmetrical)), Description/Right index finger key press indicates a face with above average symmetry.))"
      }
   }
}

Only the event_type column is relevant for assembling the annotations for the first row of Example 8, since the other annotated columns have n/a values. The assembled HED annotation for the first row of Example 8 is shown in Example 10.

Example 10: The HED annotation of the first row of Example 8.

Experiment-structure, (Def/Right-sym-cond, Onset), (Def/Initialize-recording, Onset)”

HED represents events of temporal extent using HED definitions with the Onset and Offset tags grouped with a user-defined term. The (Def/Right-sym-cond, Onset) specifies that an event defined by Right-sym-cond begins at the time-marker represented by this row in the event file. This event continues until the end of the file or until an event marker with (Def/Right-sym-cond, Offset) occurs. In this case, no Offset marker for Right-sym-cond appears in the file, so the event represented by Right-sym-cond occurs over the entire recording.

The user-defined term is prefixed with Def/ and indicates what the event of temporal extent represents. If the definition includes a Condition-variable, then the event represents the occurrence of that experimental condition. The user-defined terms are usually defined in the events.json file located at the top-level of the BIDS dataset.

Example 11 shows a more readable form for the definition of Right-sym-cond.

Example 11: The contents of the definition for Right-sym-cond.

(  
   Definition/Right-sym-cond, (  
      Condition-variable/Key-assignment,   
      ((Index-finger, (Right-side-of, Experiment-participant)), (Behavioral-evidence, Symmetrical)),  
      ((Index-finger, (Left-side-of, Experiment-participant)), (Behavioral-evidence, Asymmetrical)),  
      Description/Right index finger key press indicates a face with above average symmetry.  
   )  
)

The primary use of the definitions for condition variables is to encode the experimental design in an actionable format. Thus, as a general practice, Defs representing condition variables are removed prior to searching for other tags to avoid repeats. Notice that both Right-side-of and Left-side-of appear in the definition. Thus, if these Defs were included, every event would have both left and right tags.

Once a dataset includes the appropriate annotations, HED tools can automatically extract the experimental design. Example 12 shows the result of extraction of categorical factor vectors for the event file of Example 8.

Example 12: HED tools categorical form extraction of the design matrix for Example 8.

onset

key-assignment

face-type

repetition-type

0.004

right-sym-cond

n/a

n/a

24.2098

right-sym-cond

unfamiliar-face-cond

first-show-cond

25.0353

right-sym-cond

n/a

n/a

25.158

right-sym-cond

n/a

n/a

26.7353

right-sym-cond

n/a

n/a

27.2498

right-sym-cond

unfamiliar-face-cond

immediate-repeat-cond

27.8971

right-sym-cond

n/a

n/a

28.0998

right-sym-cond

n/a

n/a

29.7998

right-sym-cond

n/a

n/a

30.3571

right-sym-cond

unfamiliar-face-cond

first-show-cond

In the categorical representation, HED uses the condition variable name as the column name. The level values appear in the columns for event markers at which the condition variable at that level applies. Notice that right-sym-cond appears in every row because it was used in an event that extended to the end of the file. On the other hand, the other condition variables were encoded using columns and only appear when present in the column.

Note that if an event has multiple levels of the same condition, categorical and ordinal encoding cannot be used. Only one-hot encoding supports multiple levels in the same event.

Example 13 below shows the condition variable summary that HED produces for the full sub-002_task-FacePerception_run-1_events.tsv and JSON sidecar task-facePerception_events.json.

Example 13: The condition variable summary extracted from the full event file.

{
   "key-assignment": {
      "name": "key-assignment",
      "variable_type": "condition-variable",
      "levels": 1,
      "direct_references": 0,
      "total_events": 552,
      "number_type_events": 552,
      "number_multiple_events": 0,
      "multiple_event_maximum": 1,
      "level_counts": {
         "right-sym-cond": 552
      }
   },
   "face-type": {
      "name": "face-type",
      "variable_type": "condition-variable",
      "levels": 3,
      "direct_references": 0,
      "total_events": 552,
      "number_type_events": 146,
      "number_multiple_events": 0,
      "multiple_event_maximum": 1,
      "level_counts": {
         "unfamiliar-face-cond": 47,
         "famous-face-cond": 49,
         "scrambled-face-cond": 50
      }
   },
   "repetition-type": {
      "name": "repetition-type",
      "variable_type": "condition-variable",
      "levels": 3,
      "direct_references": 0,
      "total_events": 552,
      "number_type_events": 146,
      "number_multiple_events": 0,
      "multiple_event_maximum": 1,
      "level_counts": {
         "first-show-cond": 75,
         "immediate-repeat-cond": 36,
         "delayed-repeat-cond": 35
      }
    }
}

The file has 552 events. Since the key-assignment condition variable with level right-sym-cond applies to every event in this file, the number_type_events is also 552. On the other hand, the face-type condition variable is only applicable in 146 events.

All the condition variables have number_multiple_events equal to 0, so any of the three possible encodings: categorical, ordinal, or one-hot can be used.

Review of experimental design concepts

Traditional neuroimaging experiments are carefully designed to control and document the external conditions under which the experiment is conducted. Often a few items such as the task or the properties of a stimulus are systematically varied as the stimulus is presented and participant responses are recorded.

For example, in an experiment to test for differences in brain responses to pictures of houses versus pictures of faces, the researcher would label time points in the recording corresponding to presentations of the respective pictures so that differences in brain responses between the two types of pictures could be observed. An fMRI analysis might determine which brain regions showed a significant response differential between the two types of responses. An EEG/MEG analysis might also focus on the differences in time courses between the responses to the two types of images.

Thus, the starting point for many analyses is the association of labels corresponding to different experimental conditions with time points in the data recording. In BIDS, this association is stored an events.tsv file paired with the data recording, but this information may also be stored as part of the recording itself, depending on the technology and the format of the recording.

Design matrices and factor variables

The type of information included for the experimental conditions and how this information is stored depends very much on the experiment. Most analysis tools require a vector (sometimes called a factor vector) of elements associated with the event markers for each type of experimental condition.

For linear modeling and other types of regression, these factor vectors are assembled into design matrix to use as input for the analysis. Design matrices can also include other types of columns depending on the modeling strategy.

Types of condition encoding

Consider the simple example introduced above of an experiment which varies the stimuli between pictures of houses and faces to measure differences in response. The following example shows three possible types of encodings (categorical, ordinal, and one-hot) that might be sued for this association. The table shows an excerpt from a putative events file, with the onset column (required by BIDS) containing the time of the event marker relative to the start of the associated data recording. The duration column (also required by BIDS) contains the duration of the image presentation in seconds.

Example 14: Illustration of categorical and one-hot encoding of categorical variables.

onset

duration

categorical

ordinal

one_hot.house

one_hot.face

2.010

0.1

house

1

1

0

3.210

0.1

house

1

1

0

4.630

0.1

face

2

0

1

6.012

0.1

house

1

1

0

7.440

0.1

face

2

0

1

The categorical encoding assigns laboratory-specific names to the different types of stimuli. In theory, this categorical column consisting of the strings house and face could be used as a factor vector or as part of a design matrix for regression. However, many analysis tools require that these names be assigned numerical values.

The ordinal encoding assigns an arbitrary sequence of numbers corresponding to the unique values. If there are only 2 values, the values -1 and 1 are often used. Ordinal encodings impose an order based on the values chosen, which may have undesirable affects on the results of analyses such as regression if the ordering/relative sizes do not reflect the properties of the encoded experimental conditions.

In Example 14, the experimental conditions houses and faces do not have an ordering/size relationship reflected by the encoding (house=1, face=2). In addition, neither categorical nor ordinal encoding can represent items falling into multiple categories of the same condition at the same time. For these reasons, many statistical tools require one-hot encoding.

In one-hot encoding, each possible value of the condition is represented by its own column with 1’s representing the presence of that condition value and experimental conditions and 0’s otherwise. One-hot encodes all values without bias and allows for a given event to be a member of multiple categories. This representation is required for many machine-learning models. A disadvantage is that it can generate a large number of columns if there are many unique categorical values. It can also cause a problem if not all files contain the same values, as then different files may have different columns.