From an Account of the Outcome to Candidate Predictors
A data set may contain dozens of columns, but a defensible regression specification does not begin by treating every column as a possible term. It begins with a question about how the outcome might arise. Subject-matter knowledge can suggest processes that precede, shape, or help explain the outcome; those processes, in turn, point to variables worth considering.
The goal is not to declare in advance that every suggested variable belongs in the final model. A candidate predictor is a variable with a reasoned connection to the outcome for the stated purpose of the analysis. It earns consideration, not automatic inclusion. Variables can be recorded because they are convenient, required administratively, or useful for identification without having a substantive reason to explain or predict the outcome.
A useful chain of reasoning is: outcome → plausible process → potentially informative variable. For example, if the outcome is whether a patient is readmitted soon after discharge, a substantive account might mention illness severity, the ability to obtain follow-up care, and the support available after discharge. Those processes suggest possible variables to investigate. A hospital's internal record number, by contrast, may be present in the file but has no general substantive connection to a patient's readmission.
The account should be specific enough to explain the proposed link. “This variable might matter” is not yet a rationale. Ask what process it represents in the setting, how that process could be related to the outcome, and whether the variable is measured at an appropriate time for the purpose. The prediction-time information set matters for prediction: a value not available when a forecast is made cannot serve as an available predictor for that forecast. For explanatory work, distinguish a variable's proposed role from mere association; regression alone does not establish a causal effect.
A Practical Way to Generate the List
Start by stating the outcome and the intended use of the model. Then describe the substantive process in ordinary language before inspecting which recorded columns happen to correlate with the outcome. Translate relevant parts of that account into candidate variables, using names and units that make their meaning clear. Finally, write one sentence for each candidate explaining why it is on the list.
Specify what is being explained or predicted, for whom, and, for prediction, when the prediction is made.
Use knowledge of the setting to identify circumstances or mechanisms that could be related to the outcome. Keep the account tied to this population and context.
Ask what observable information could represent or indicate each relevant part of the account. Record a reason for every proposed variable.
Ask whether the variable is appropriate for the model's purpose and available at the relevant time. Do not confuse being present in a data file with being substantively justified.
Candidate generation identifies terms for consideration; it does not decide the final specification or guarantee that the data can estimate every proposed term well.
Worked Example: Readmission After Hospital Discharge
Hypothetical setting. A health system wants to understand which patient and care circumstances are associated with an unplanned readmission within 30 days of discharge. Its file includes readmission status, age, a severity score recorded during the admission, whether a follow-up appointment was arranged before discharge, a patient record number, and the name of the billing office. The objective is explanatory, not a forecast made at a specified future time.
First, describe plausible processes. A patient's underlying illness burden may be related to the need for further care. Planning a follow-up appointment may be related to continuity of care after discharge. Those accounts support considering the severity score and the appointment indicator as candidates. Age can also be considered if subject-matter knowledge suggests that age-related differences in health or care needs could be relevant in this setting. These are reasons to examine the variables, not evidence that any particular coefficient will be nonzero.
Next, reject the idea that every column is a candidate just because it is recorded. The patient record number identifies a file; changing its numerical value would not describe a change in the patient's condition or care. The billing office name may be administratively useful, but this account provides no reason to treat it as a predictor. The resulting provisional candidate list is age, severity score, and follow-up appointment arranged.
A schematic expression for the proposed mean structure, if these variables are represented numerically or with suitable indicators, is:
Here \(Y_i\) denotes the readmission outcome for patient \(i\), and the \(X\)'s stand for the three candidate variables. This expression records a possible starting specification; it does not imply that the appointment indicator causes fewer readmissions. Other explanations, including differences among patients who do and do not receive appointments, may matter. The key result of this exercise is the rationale for each candidate and the exclusion of columns with no stated substantive connection.
Work Through the Process, Not the Spreadsheet
A strong subject-matter account does more than name a broad topic. It identifies steps or conditions that could plausibly connect to the outcome, then asks what data could speak to those steps. This makes the candidate list explainable to another analyst and helps reveal when a proposed variable is present only because it was easy to collect.
Worked Example: Crop Yield on Experimental Plots
Hypothetical setting. An agricultural team is studying grain yield, measured in kilograms per plot, for 60 experimental plots during one growing season. The data file also contains rainfall during the growing season, soil nutrient measurements collected before planting, the fieldworker's initials, and a plot label used to locate each plot.
The team’s substantive account is that crop growth may depend on water availability and nutrients in the soil. Rainfall and pre-planting nutrient measurements therefore have direct process-based rationales as candidates. A plausible schematic model could be written as
where \(Y_i\) is yield in kilograms for plot \(i\), \(R_i\) is the recorded rainfall measure, and \(N_i\) is a soil nutrient measure. The data description does not provide actual values, so there is no numerical coefficient to calculate; the expression simply names the outcome and the justified candidates. The units should be specified for rainfall and nutrients in any actual analysis.
The fieldworker's initials and plot label are recorded, but neither has a stated connection to crop growth in this account. The label is useful for locating a plot, not by itself a reason for a general predictor. The initials might prompt a question about differences in measurement procedures if there were evidence of such differences, but the mere presence of the initials does not establish that process. With the information given, the defensible list is rainfall and soil nutrients, not every column in the file.
Check the Rationale for Each Candidate
A compact candidate ledger helps keep the reasoning visible. For each proposed variable, state the process it relates to and why that process is relevant to the outcome. Also note whether the variable is recorded at a time appropriate to the model's purpose. This is not a ranking of variables by apparent strength of association; it is a record of why each variable deserves consideration in the first place.
| Question | What a defensible answer supplies |
|---|---|
| What process is relevant? | A specific part of the account that could plausibly relate to the outcome. |
| Why this variable? | A clear connection between the recorded variable and that process. |
| Is the timing appropriate? | A reason the variable is suitable for the explanatory question or available at the prediction time. |
| Why not another column? | A reason to distinguish substantive relevance from administrative presence or convenience. |
Worked Example: Assessment Scores in a Tutoring Program
Hypothetical setting. A school district wants to explain variation in students' end-of-term mathematics scores. Its file includes each student's prior mathematics score, attendance during the term, hours of tutoring attended, a student identification number, and the date the final score was entered into the district system.
A plausible account is that prior preparation may be related to later performance, attendance may affect opportunities to learn, and tutoring participation may be related to additional instruction. These considerations support treating prior score, attendance, and tutoring hours as candidates for an explanatory analysis. They do not establish that tutoring improves scores: participation may also be related to students' needs or other circumstances.
The student identification number is necessary for matching records but has no stated educational process connecting its digits to achievement. The entry date may be useful for data management, but there is no reason in this account to treat it as a predictor of mathematical understanding. A candidate list based on the stated account therefore includes the three educational variables, while leaving the identifier and entry date out unless further subject-matter information supplies a defensible rationale.
The distinction is not “useful column” versus “useless column.” An identifier can be essential for organizing a data set, and an entry date can help track data quality. The narrower question here is whether a column has a plausible role as a predictor for the specified model.
Why This Discipline Matters
A data-driven list built from every available column can produce a model that is difficult to interpret and poorly matched to its purpose. Administrative details may have no stable relationship to the outcome, while important processes may be absent from the data altogether. Starting from an account of the outcome makes the limitations visible: a proposed process may be conceptually relevant but not measured in the available data, or a recorded variable may describe only a small part of that process.
This approach also makes the analysis easier to explain. A reader can see why a term was considered without being asked to infer the reasoning from a table of coefficients. Candidate generation is a substantive step, separate from later decisions about exact model form, which variables can be retained, or how competing specifications should be assessed.
- Mistake: “The data set has a column for hospital, so hospital should be included.” Correction: State a plausible process connecting hospital to the outcome and explain why it matters for the model's purpose. The column's presence alone is not that rationale.
- Mistake: “This variable is a candidate, so its coefficient must have a meaningful or causal interpretation.” Correction: Candidate status means there is a reason to consider the variable. Interpretation depends on the specified model, the data, and the assumptions supporting the intended claim.
- Mistake: “If a variable was not recorded, the process it relates to is irrelevant.” Correction: A process may matter even when the data do not measure it. Note the gap rather than treating absence from the file as evidence of irrelevance.
Check Your Understanding
Use a process-based rationale for each answer.
- A clinic file contains patients' follow-up attendance, appointment reminders sent, and record numbers. Give one plausible rationale for considering reminders and explain why the record number is not a candidate merely because it is recorded.
- For a study of household energy use, describe one process that could motivate a candidate predictor and name a variable that might provide information about it.
- Why does a plausible connection to an outcome make a variable a candidate rather than guaranteeing its inclusion in a final model?
- A forecasting system must predict tomorrow's demand using information available today. Explain why a variable recorded only after tomorrow's demand is observed is not suitable for that prediction.
- A variable is absent from a data set, but subject-matter knowledge suggests its process may matter. What should an analyst conclude, and what should the analyst avoid concluding?