What an Individual Fit Panel Shows
An individual fit panel places observed concentrations and model predictions against time for one subject. Repeating the same display across subjects makes it possible to inspect how the observed and predicted profiles compare without pooling all records into one crowded plot. The purpose here is to construct a clear, consistent display, not to diagnose or explain particular residual patterns.
The central design choice is what prediction to show. Population predictions represent the model prediction without conditioning on a subject's individual random-effect estimates. Individual predictions use subject-specific estimates, while conditional predictions are based on the model's conditional estimates given the subject's data. These are different quantities; a panel must identify which one it displays. Do not label a curve simply “prediction” if the type is not clear.
A useful plotting record includes, at minimum, a subject identifier, time with units, observed concentration with units, and the selected prediction with its prediction type. The observed value and prediction must refer to the same subject, time, and analysis context. If the model output is stored separately from the observations, first align records using the appropriate identifiers and time information; row order alone is not a reliable match.
Set the Scales Before Comparing Panels
A shared horizontal scale means that the panels use the same displayed time range and the same mapping from time to horizontal position. A shared vertical scale means that they use the same concentration range and mapping from concentration to vertical position. Shared scales make cross-subject comparisons easier because a given location on an axis has the same meaning in each panel. Independent panel scales can make within-subject variation easier to see, but the same visual distance may then represent different time or concentration differences in different panels.
For a linear vertical scale with lower limit \(L\) and upper limit \(U\), the relative vertical position of a concentration \(C\) is determined by:
Thus, the fraction of panel height occupied by a concentration difference depends on the range width \(U-L\). A common range width makes equal concentration differences occupy equal fractions of panel height; ranges with different widths generally do not. A common range is still useful for direct comparisons of concentration levels and magnitudes. The endpoints themselves do not determine the fraction: for example, ranges 0–10 and 5–15 have the same width, so an equal concentration difference occupies the same fraction of each panel's height.
Choose scales deliberately. If the goal is to compare concentration levels across subjects, shared concentration limits are usually important. If the goal is to inspect each subject's profile in detail, a per-panel vertical range may reveal small changes but should be clearly indicated and should not be mistaken for a common scale. For time, use consistent units and a shared range when subjects' timing or coverage is being compared. Do not silently truncate observations or predictions to make a panel look cleaner.
Worked Example: Matching Observations to Subject Predictions
Suppose a hypothetical data set has two subjects, A and B, with concentrations measured in milligrams per liter (mg/L) at times measured in hours (h). The selected prediction is the individual prediction, also in mg/L. A small portion of the plotting data is:
| Subject | Time (h) | Observed (mg/L) | Individual prediction (mg/L) |
|---|---|---|---|
| A | 1 | 8.2 | 7.8 |
| A | 4 | 4.1 | 4.5 |
| B | 1 | 6.3 | 6.8 |
| B | 4 | 2.9 | 3.2 |
For subject A, plot points at \((1,8.2)\) and \((4,4.1)\) and place the corresponding prediction values at times 1 and 4. For subject B, make a separate panel with points \((1,6.3)\) and \((4,2.9)\), and predictions at those same times. Use the subject identifier as the facet label, time in h on the horizontal axis, and concentration in mg/L on the vertical axis. Since both subjects have observations from 1 to 4 h, a shared horizontal range of 1–4 h displays the same time positions in both panels.
If the two prediction values per subject are joined, the resulting segment shows a straight-line connection between the supplied prediction records; it does not establish that the underlying model prediction is linear between them. A smoother-looking prediction curve requires predictions evaluated on a suitably defined time grid, not an unjustified interpolation of sparse records.
Constructing and Checking the Panel Data
Before plotting, make the data relationship explicit. Each observed record should be paired with the intended prediction for that subject and time. If there are replicate observations at the same time, they remain distinct observed records; do not collapse them or duplicate a prediction by accident. If predictions are supplied on a grid that differs from observation times, show that distinction clearly—for example, draw a continuous prediction curve from grid records and show observations as points. The curve and points still need to use the same time and concentration units.
A concise construction workflow is:
Specify population, conditional, or individual prediction, and verify that the selected column contains that quantity.
Match predictions to the correct subject and time, retaining the intended observation records and noting any unmatched values.
Use a common time unit and concentration unit, select shared or independent scales for a stated comparison purpose, and label each axis.
Assign one panel per subject, use clear subject labels, and distinguish observed points from predictions with stable visual encodings.
Check panel counts, labels, axis limits, units, prediction type, and plotted records against the plotting data.
These steps can be encoded in a reusable plotting configuration. Store the subject field, time field and unit, observed concentration field and unit, prediction field and type, and scale policy as explicit settings or metadata. This reduces the chance that two reports use different columns or axis conventions while appearing to show the same diagnostic. The saved plot or its caption should state the prediction type and any non-obvious scale choice.
Worked Example: Comparing Vertical Positions Under Two Scale Choices
Consider hypothetical subject panels using concentration in mg/L. Subject A has values from 0 to 10 mg/L, and subject B has values from 5 to 15 mg/L. In each panel, compare a concentration of 8 mg/L with 6 mg/L. The difference is \(8-6=2\) mg/L in either case. The range width in each panel is \(10\) mg/L, so the relative vertical separation is:
Each 2 mg/L difference occupies 20% of panel height, even though the range endpoints differ. Now suppose one panel uses 0–10 mg/L and another uses 0–20 mg/L. The same 2 mg/L difference occupies:
The difference occupies 20% of the first panel and 10% of the second because the range widths differ. For direct cross-subject comparison, a shared vertical range avoids this change in visual scaling and also puts equal concentration levels at equal heights. If separate ranges are chosen to reveal within-subject detail, readers should be told that the scales vary.
Legibility, Diagnostics, and Alternatives
Panel layout affects whether the plot can be read. Each panel needs a visible subject identifier, and the facets should follow a stable order, such as a defined subject ordering rather than incidental row order. Choose a layout that leaves enough room for axis labels, tick labels, and observations. When the number of subjects is too large for a single readable display, a plot may require a different output strategy; do not compensate by making text or panels so small that labels and data are indistinguishable.
Use a consistent visual distinction, such as points for observed concentrations and a line for predictions, and include a legend or direct labels that define the encodings. If predictions are displayed as points at observation times rather than a grid-based line, explain that choice. Keep axis labels explicit, for example “Time (h)” and “Concentration (mg/L).” A title or caption should identify the prediction type. Do not combine predictions with different units or types in one undifferentiated curve.
A useful quality check compares the rendered plot with its source data. Confirm that the number of subject panels is as expected; each panel label corresponds to one subject; plotted time and concentration values fall within the declared axis limits; and the displayed records agree with the selected prediction column. Unexpectedly empty panels, duplicate points, missing prediction segments, and inconsistent units are construction warnings, not cosmetic details. A log concentration axis can be useful for positive concentrations spanning a wide range, but it changes the vertical mapping and cannot display zero or negative values on the ordinary logarithmic scale. State the transformation and apply it consistently.
Individual fit panels are not the only way to display these data. A single overlaid plot can be more compact and may reveal the overall spread, but many subjects can overlap and make subject-level matching difficult. A population-level observed-versus-predicted plot summarizes records across subjects rather than showing each subject's time course. A table can provide exact values but makes the time-profile comparison less immediate. These displays answer different questions; a faceted panel is appropriate when the reader needs to see observed and predicted profiles subject by subject.
Worked Example: Catching a Unit and Prediction-Type Mismatch
A hypothetical plotting routine uses observation times recorded in hours and observed concentrations recorded in mg/L. It overlays a prediction column that is labeled “population prediction” but whose source metadata describes individual predictions. The output is also labeled “Individual prediction,” and the prediction time column is in minutes. One row has an observed value at 2 h and a prediction value at 120 min.
The times can be aligned only after conversion: \(120\text{ min}\div 60\text{ min/h}=2\text{ h}\). That arithmetic shows the prediction time corresponds to the observation time, but the plot should not silently mix minutes and hours. Convert the prediction times to hours, then verify the units and subject-time key. Next resolve the prediction-type discrepancy from the model output metadata: the plot label and selected field must name the same type. If the source is individual prediction, correct the label; if population prediction was intended, select that output instead. Only after both checks should the subject panels be rendered.
This example illustrates why matching numeric values alone is insufficient. The time conversion resolves one alignment issue, but it does not resolve the prediction-type error. Labels and data provenance must agree with the quantity actually plotted.
Common Mistakes and Limitations
- Relying on row order to match predictions. Rows can be sorted or filtered differently. Match using the appropriate subject and time identifiers, and verify the resulting pairs.
- Using “prediction” without naming its type. Population, conditional, and individual predictions are not interchangeable. Identify the selected quantity in the legend, caption, or axis context.
- Changing scales without making that choice visible. Independent panel scales can support within-subject inspection, but identical visual distances may represent different concentration differences. Use shared scales for direct comparisons of levels and magnitudes, or state that the ranges vary.
- Joining sparse prediction records as if they were a fitted curve. A line segment only connects the plotted values. Evaluate predictions on a suitable grid when a smooth profile is needed.
- Assuming a panel explains a model discrepancy. The display shows observations and a chosen prediction; it does not by itself establish why they differ or whether a model is adequate.
Faceting also has practical limits: many subjects can produce a large report, sparse records may leave profiles visually incomplete, and a chosen scale can hide small changes or compress large ones. A panel is a diagnostic view, not a substitute for checking model-output definitions, data alignment, and units. Its interpretation depends on those choices being correct and transparent.
Check Your Understanding
Answer each question, then compare with the solutions below.
- What fields and metadata are needed to define an individual fit panel unambiguously?
- Two panels have linear vertical ranges 0–12 mg/L and 4–16 mg/L. What fraction of panel height does a 3 mg/L concentration difference occupy in each?
- Observations are recorded at 3 h, while a prediction record is at 180 min. What conversion is needed before plotting them on one time axis?
- Why is it misleading to connect two sparse prediction records and describe the segment as the model's smooth concentration-time curve?
- When is a shared vertical scale preferable to independent panel scales?
Solutions. (1) Include a subject identifier, time and its unit, observed concentration and its unit, the selected prediction and its type, and a rule for aligning observation and prediction records. (2) Both ranges have width \(12\) mg/L. The fraction is \(3/12=0.25\), or 25%, in each panel. The endpoints differ, but the widths are equal. (3) Convert \(180\text{ min}\div60\text{ min/h}=3\text{ h}\), then plot both on an axis in hours. (4) A straight segment only connects the two supplied values; it does not show how the model behaves between them. A curve should use predictions evaluated on an appropriate time grid. (5) A shared vertical scale is preferable when comparing concentration levels or magnitudes across subjects, because the same concentration maps to the same vertical position in every panel.