Topic
Spaghetti plot
About: Spaghetti plot is a research topic. Over the lifetime, 8 publications have been published within this topic receiving 127 citations. The topic is also known as: Spaghetti plot & spaghetti chart.
Papers
TL;DR: A procedure for visualization and exploration that is particularly useful for categorical outcomes and missingness is proposed, and so-called heatmaps provide an alternative, or at least complementary, graphical-data-exploration technique.
Abstract: Longitudinal data are key to causal inference in epidemiologic studies. As the number of subjects, frequency of measurements, and period of active data collection grow, so does the size of the data set. As the dataset grows, so do the burden and complexity of graphically exploring and summarizing the data without obscuring salient features.
The gold standard for graphically displaying longitudinal data is the classic spaghetti plot, which plots a subject's values for the repeated outcome measure (vertical axis) versus time (horizontal axis) and connects the dots chronologically, using lines of uniform color and intensity for each subject. However, the classic spaghetti plot presents obstacles to the display of longitudinal data. Although useful for fewer subjects, trends and patterns are obscured with the larger numbers of subjects typical of modern epidemiologic studies. For example, trajectories commonly overlap in a classical spaghetti plot, as both subjects and the magnitude of the outcome measure are displayed on the vertical axis. With large datasets, the figure often succumbs to "over-plotting," in which the multiple intersecting lines have no discernible patterns. One solution has been to plot a subset of the data based on medians or deciles, but this approach fails to utilize the whole dataset.1 Furthermore, repeated-measures data containing different enrollment times, missing data, or loss to follow-up (censoring) typically are difficult to display in the classic spaghetti plot.
Exploratory plots generally are used to reveal various structures in the data: trends (how most people respond over time), outliers (whether some subjects differ from most), clusters (groups of patients responding the same, maybe due to a covariate such as treatment assignment), as well as data-quality checks of reasonable values and sensible collection patterns of multi-center repeated-measures data. Classic spaghetti plots suffering from over-plotting reduce the chances of seeing such patterns.
Spaghetti plots can be improved. Color saturation, a method of handling over-plotting, has been implemented in parallel coordinate plots, of which the spaghetti plot is a special case.2–4 In many situations a classic spaghetti plot or the more-modern parallel-coordinates plot can visualize data sufficiently. However, two common data features limit the usefulness of parallel coordinate / spaghetti plots: categorical outcomes and missing outcome values (see eFigure 16 in eAppendix; https://links.lww.com). We propose a procedure for visualization and exploration that is particularly useful for categorical outcomes and missingness.
So-called heatmaps5 provide an alternative, or at least complementary, graphical-data-exploration technique. Heatmaps enjoy frequent use in the genomics literature and other areas with high-throughput data.6–8 However, in more standard longitudinal studies, they are less popular, as evidenced by the recommendation of spaghetti plots of the raw data1,9,10 or summarized data11 in popular texts of longitudinal data analysis.
A lasagna plot is a heatmap well-suited for longitudinal data. In spaghetti plots, each subject's trajectory over time is like a noodle, that can cross other trajectories (Figure 1). In lasagna plots, each subject's trajectory over time is a horizontal layer, with the simultaneous plotting of trajectories resulting in a stacking of layers, as in lasagna.
Figure 1
Lasagna plots as derived from spaghetti plots involve making noodles into layers. From left to right, (A) a spaghetti plot with three noodles where trajectories overlap. (B) Extracting each noodle representing repeated measures on a subject, (C) a layer ...
The proposed lasagna plot uses color or shading to depict the magnitude of the outcome measurement and fixes the vertical dimension per subject. The lasagna plot takes advantage of color to provide a third dimension and display additional information, rather than relying upon the vertical dimension to display overlapping magnitudes of change. All information about the value of the outcome is through color (intensity), making color choice important.
Haphazard color selection can produce varying appearance in different media, induce optical illusions and after-image effects, confuse those with colorblindness, and produce misleading interpretations of data characteristics via relative aspects of color.12–15 One good principle for color selection is to have equally spaced hues with constant chroma and luminance across hues in a perceptually uniform colorspace, such as hue-chromaluminance (HCL) (as opposed to red-green-blue [RGB] or hue-saturation-value [HSV]).13 For unordered categorical outcomes, such as group membership, fixed chroma and luminance for hues equally spaced within a hue-chroma-luminance colorspace provide a flexible framework for the generation of qualitative palettes. To visualize ordered outcomes, consider the sequential-palette approach of allowing at least one and possibly all three colorspace dimensions (hue, chroma, luminance) to vary according to some function of interest based upon the ordering of the categories. If the outcomes to be visualized are ordered and have an inherent neutral value from which they diverge, say 0 for correlations, then two sequential palettes of different hues can be combined into a diverging palette to achieve color gradient symmetry about the neutral value.15 Practical and immediately accessible color selection resources include http://cran.r-project.org/web/packages/colorspace/vign as well as http://colorbrewer.org.16,17 The colors of most of the lasagna plots in this commentary were selected from the R packages colorspace or RColorBrewer.16,18
To reduce after-image effects and to afford viewers less eye strain, it is recommended to avoid fully saturated colors.16 Missing values should not be assigned a color by default but instead should be portrayed by the background color. If the background color is one of full saturation (e.g., white), then change to an off-white or directly assign missingness a color, preferably one sharing attributes of the palette in use (e.g. tantamount luminance). Epidemiologic longitudinal data sometimes have truly continuous outcomes, resulting in many unique values; this may cause some coloring procedures to categorize automatically how values are binned and assigned color. To have fullest control, it may be best to define meaningful categories of truly continuous data for visualization, such as deciles to be visualized with a palette of 10 colors and an off-white background for missing values.
There are several advantages of the lasagna plot: (1) group-, cohort-, and subject-level data are preserved regardless of the number of subjects or time points; (2) dynamic sorting of data can be used to ascertain group-level behavior over time; (3) intermittent missing data can be easily handled and clearly displayed; and (4) the distribution of onset and ending times can be easily displayed.
121 citations
TL;DR: In this article, the authors present results from a computational study of predictability in fully-developed baroclinically unstable laboratory flows and devise an ensemble prediction scheme using the breeding method to study the predictability of the annulus in the perfect model scenario.
Abstract: . We present results from a computational study of predictability in fully-developed baroclinically unstable laboratory flows. This behaviour is studied in the Met Office/Oxford Rotating Annulus Laboratory Simulation – a model of the classic rotating annulus laboratory experiment with differentially heated cylindrical sidewalls, which is firmly established as an insightful laboratory analogue for certain kinds of atmospheric dynamical behaviour. This work is the first study of "predictability of the first kind" in the annulus experiment. We devise an ensemble prediction scheme using the breeding method to study the predictability of the annulus in the perfect model scenario. This scenario allows one simulation to be defined as the true state, against which all forecasts are measured. We present results from forecasts over a range of quasi-periodic and chaotic annulus flow regimes. A number of statistical and meteorological techniques are used to compare the predictability of these flows: bred vector growth rate and dimension, error variance, "spaghetti plots", probability forecasts, Brier score, and the Kolmogorov-Smirnov test. These techniques gauge both the predictability of the flow and the performance of the ensemble relative to a forecast using a climatological distribution. It is found that in the perfect model scenario, the two quasi-periodic regimes examined may be indefinitely predictable. The two chaotic regimes (structural vacillation and period doubled amplitude vacillation) show a loss of predictability on a timescale of hundreds to thousands of seconds (65–280 annulus rotation periods, or 1–3 Lyapunov times).
14 citations
1 Jan 2016
TL;DR: A novel speculative variant of the Metropolis algorithm is used to increase the similarity of paths and achieve higher coherence, which decreases the computation time significantly and improves memory access by optimizing the data layout to better utilize coalesced access.
Abstract: We propose a novel approach that enables a comparative visual exploration of the transport variability in ensembles
of 2D flow fields. To reveal when and where divergences in transport occur, we first present a new approach to
analyze the time-varying pairwise dissimilarities of ensemble trajectories, by using Gaussian Mixture Models
(GMMs) to identify the distribution modes and the Mahalanobis distance to refine the dissimilarity measures.
This enables drawing enhanced spaghetti plots, by using the color of the contour of each trajectory to encode the
temporal evolution of the member, and the opacity for its representativeness relative to the ensemble behavior. To
also allow a global view of the transport variability across selected sub-domains, we introduce a new graphical
abstraction based on the visualization of miniaturized versions of the enhanced spaghetti plots in a small-multiples
layout. To achieve this, we propose a new kind of downscaling that preserves the relevant trends in the transport
behavior. We have designed a user interface comprising multiple linked views to visualize simultaneously global
and local transport variations, as well as how similar the transport behavior of the ensemble members is.
13 citations
TL;DR: In this article, critical time requirements for operational use of the deterministic model track forecasts are summarized for the U.S. and other selected non-U.S tropical cyclone warning centers.
Abstract: Tropical cyclone track forecasts have been improved, and forecast intervals have been extended to five days, owing to improved global and regional numerical model guidance. Critical time requirements that must be met for operational use of the deterministic model track forecasts are summarized for the U.S. and other selected non-U.S. tropical cyclone warning centers. One of the most accurate deterministic model forecasts from the European Center for Medium-range Weather Forecasts arrives too late to be used with other models at the + 6 h warning time, and thus is at least 12 h old before it can be operationally used. The time-critical nature of the tropical cyclone warning system is a major obstacle to operational use of single-model, or proposed multi-model, ensemble prediction system (EPS) mean and spread information, which is 12 h (or 18 h) delayed. This EPS mean and spread must also be superior to the mean and spread of the consensus of deterministic models that are available six hours earlier. These requirements must be met before the EPS tropical cyclone tracks will be operationally useful in specifying the uncertainty in the official track forecasts, which is the next challenge in tropical cyclone track warnings.
5 citations
TL;DR: The conclusion made so far is that ensemble weather predictions beyond forecast day 3 should be used with care as the randomness in dispersion patterns may be of less use for decision making.
Abstract: Ensemble weather forecasts have been used to demonstrate their applicability on regional dispersion models. The conclusion made so far is that ensemble weather predictions beyond forecast day 3 should be used with care as the randomness in dispersion patterns may be of less use for decision making. The lagged forecast approach, or the poor-man ensemble technique, enables use of high resolution forecasts. The drawback is the shorter forecast ranges possible and that lagged forecasts mainly demonstrated the consistency between forecasts.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 2 |
| 2019 | 1 |
| 2016 | 1 |
| 2010 | 2 |
| 2008 | 1 |
| 2007 | 1 |